Math: Units of Measurement 115

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1 Math: Units of Measurement 115 Welcome to the Tooling University. This course is designed to be used in conjunction with the online version of this class. The online version can be found at We offer high quality web -based e -learning that focuses on today's industrial manufacturing training needs. We deliver superior training content over the Internet using text, photos, video, audio, and illustrations. Our courses contain "roll -up -your -sleeves" content that offers real -world solutions on subjects such as Metal Cutting, Workholding, Materials, and CNC with much more to follow. Today's businesses face the challenge of maintaining a trained workforce. Companies must locate apprenticeship programs, cover travel and lodging expenses, and disrupt operations to cover training needs. Our web -based training offers low -cost, all -access courses and services to maximize your training initiatives. Class Outline

2 Class Outline Objectives The Importance of Measurement Common Base Units of Measurement The English System The Metric System The English System: Length English Units of Length: Sample Problem English Units of Length: Sample Problem #2 The Metric System: Length Converting Metric Units of Length Converting Length from English to Metric Converting Length from Metric to English Area Volume Mass and Weight Mass and Weight: Sample Problem Derived Units Summary Lesson: 1/18 Objectives l Explain the importance of measurement. l List common base units of measurement. l Identify common units in the English system. l Identify common units in the Metric system. l List common units of length for the English system. l Convert length measurements within the English system. l List common units of length for the Metric system. l Convert length measurements within the Metric system. l Explain how to convert length measurements from English to Metric. l Convert a length measurement from Metric to English. l Describe the characteristics of area. l Describe the characteristics of volume. l Describe the characteristics of mass and weight. l Convert an English weight measurement to a Metric mass measurement. l Describe derived units. Figure 1. Most shops are equipped with reference charts.

3 Lesson: 1/18 Objectives l Explain the importance of measurement. l List common base units of measurement. l Identify common units in the English system. l Identify common units in the Metric system. l List common units of length for the English system. l Convert length measurements within the English system. l List common units of length for the Metric system. l Convert length measurements within the Metric system. l Explain how to convert length measurements from English to Metric. l Convert a length measurement from Metric to English. l Describe the characteristics of area. l Describe the characteristics of volume. l Describe the characteristics of mass and weight. l Convert an English weight measurement to a Metric mass measurement. l Describe derived units. Figure 1. Most shops are equipped with reference charts. Figure 2. Speed is an example of using a measurement. Lesson: 2/18 The Importance of Measurement Every day, you deal with units of measurement. Whether it is observing the speed limit while driving or checking the time on your watch, as shown in Figures 1 and 2, nearly everything you deal with at work or at home is measured in some way. In the shop, precise measurement is crucial for producing accurate parts. More importantly, part measurements are often expressed in different units. This means you must be familiar with the two most common systems of measurement, especially if your shop works with international customers. When working with measurements, you are often required to convert from one unit of measurement to another. This is because if you are working with more than one measurement, you must always work with like units. Working with like units allows you to easily compare measurements and accurately calculate dimensions. This class will discuss common units of measurement that you encounter in manufacturing. You will also learn how to convert from one unit of measurement to another.

4 Lesson: 2/18 The Importance of Measurement Every day, you deal with units of measurement. Whether it is observing the speed limit while driving or checking the time on your watch, as shown in Figures 1 and 2, nearly everything you deal with at work or at home is measured in some way. In the shop, precise measurement is crucial for producing accurate parts. More importantly, part measurements are often expressed in different units. This means you must be familiar with the two most common systems of measurement, especially if your shop works with international customers. When working with measurements, you are often required to convert from one unit of measurement to another. This is because if you are working with more than one measurement, you must always work with like units. Working with like units allows you to easily compare measurements and accurately calculate dimensions. This class will discuss common units of measurement that you encounter in manufacturing. You will also learn how to convert from one unit of measurement to another. Figure 1. A speedometer on a car measures speed. Figure 2. A watch measures time. Lesson: 3/18 Common Base Units of Measurement When working with measurements, you must first be familiar with the most basic units of measurement, or base units. The following are common base units used in manufacturing: Length measures how long something is and is the distance between two points. For example, your height is an example of a length measurement. Figure 1 shows an example of measuring the length of a screw. l Area measures the space contained within an enclosed, flat shape. If you need to find how much paint will cover a wall, you would measure the wall's area. l Volume measures the amount of space contained within a three-dimensional shape. For example, a fish tank that holds 30 gallons is a volume measurement. l Figure 1. Length measures the distance from one point to another.

5 Lesson: 3/18 Common Base Units of Measurement When working with measurements, you must first be familiar with the most basic units of measurement, or base units. The following are common base units used in manufacturing: l l l l l Length measures how long something is and is the distance between two points. For example, your height is an example of a length measurement. Figure 1 shows an example of measuring the length of a screw. Area measures the space contained within an enclosed, flat shape. If you need to find how much paint will cover a wall, you would measure the wall's area. Volume measures the amount of space contained within a three-dimensional shape. For example, a fish tank that holds 30 gallons is a volume measurement. Mass and weight measure the amount of material inside something, which tells you the heaviness of an object. Most grocery items like produce and meats are sold by their weight or mass. Temperature is a measurement of the hotness or coldness of a substance. One of the most common temperature measurements taken is of the outside air to determine the weather. Figure 2 shows an example of a thermometer, which measures temperature. Figure 1. Length measures the distance from one point to another. You most likely encounter a wide range of measurement units in the shop beyond this list. However, these base units provide the foundation for all measurements. Figure 2. Thermometers measure temperature. Lesson: 4/18 The English System The system used for measurements in the United States and England is the English system. Common units of measurement in the English system include inches, feet, pounds, and gallons. Figure 1 shows a scale that measures weight in pounds and ounces. Figure 2 shows a barrel of coolant that is measured by the gallon. If you use the English system, think about how much you rely on its units every day. You think of distances in terms of miles or feet and temperatures in terms of degrees Fahrenheit. However, most of the world uses another system of measurement known as the Metric system. Because the English system is only used in England and the United States, this can cause a problem with other countries. People spend time and money on converting units from one system to another. Naturally, it would be much easier for all nations to have the same system of measurement, but making this change is quite difficult. For those of you in the United States, imagine how strange it would seem to say that it is a sweltering hot, 35 day, or to talk about your body weight in kilograms, not pounds. As you can see, a change in a system of measurement requires individuals to "re-program" their ideas of measurements, since they are so closely tied to their daily lives. Figure 1. This scale measures weight in pounds and ounces.

6 Lesson: 4/18 The English System The system used for measurements in the United States and England is the English system. Common units of measurement in the English system include inches, feet, pounds, and gallons. Figure 1 shows a scale that measures weight in pounds and ounces. Figure 2 shows a barrel of coolant that is measured by the gallon. If you use the English system, think about how much you rely on its units every day. You think of distances in terms of miles or feet and temperatures in terms of degrees Fahrenheit. However, most of the world uses another system of measurement known as the Metric system. Because the English system is only used in England and the United States, this can cause a problem with other countries. People spend time and money on converting units from one system to another. Naturally, it would be much easier for all nations to have the same system of measurement, but making this change is quite difficult. For those of you in the United States, imagine how strange it would seem to say that it is a sweltering hot, 35 day, or to talk about your body weight in kilograms, not pounds. As you can see, a change in a system of measurement requires individuals to "re-program" their ideas of measurements, since they are so closely tied to their daily lives. Figure 1. This scale measures weight in pounds and ounces. Figure 2. The volume of this barrel of coolant is measured in gallons. Lesson: 5/18 The Metric System The Metric system, or International System of Units (SI) was invented by the French in the late 1700s to obtain measurement consistency from city to city. The Metric system has since been adopted by nearly every other part of the world. Even the United States has committed to changing over to the Metric system. However, the U.S. still uses the English system in most applications, except for the sciences. Common units of measurement in the Metric system include millimeters, centimeters, meters, and liters. The Metric system is based on numbers in powers of ten. It is easy to recognize to what power of ten a number is because Metric measurements use a prefix combined with a base unit. The prefix indicates the power of ten, and the base unit indicates the type of measurement. Figure 1 shows common prefixes and their meanings. Figure 2 shows common base units. For example, with Copyright 2015 Tooling U, LLC. All Rights"hundredth," Reserved. centimeter, the prefix "centi" indicates and the base unit "meter" indicates a length measurement. Figure 1. Common prefixes used in the Metric system.

7 Lesson: 5/18 The Metric System The Metric system, or International System of Units (SI) was invented by the French in the late 1700s to obtain measurement consistency from city to city. The Metric system has since been adopted by nearly every other part of the world. Even the United States has committed to changing over to the Metric system. However, the U.S. still uses the English system in most applications, except for the sciences. Common units of measurement in the Metric system include millimeters, centimeters, meters, and liters. The Metric system is based on numbers in powers of ten. It is easy to recognize to what power of ten a number is because Metric measurements use a prefix combined with a base unit. The prefix indicates the power of ten, and the base unit indicates the type of measurement. Figure 1 shows common prefixes and their meanings. Figure 2 shows common base units. For example, with centimeter, the prefix "centi" indicates "hundredth," and the base unit "meter" indicates a length measurement. Figure 1. Common prefixes used in the Metric system. Figure 2. Common base units used in the Metric system. Lesson: 6/18 The English System: Length The smallest unit of length measurement in the English system is the inch. The inch is abbreviated as "in." and is one of the most common length measurements used in manufacturing. As Figure 1 shows, there are 12 inches in 1 foot (ft.), 3 feet in 1 yard (yd.), and 1,760 yards in 1 mile (mi). When working with dimensions in math calculations, you must work with all of the same units. Consider the sample problem in Figure 2. If you had a piece of bar stock labeled A that is 48 in. long and another labeled B that is 2 ft., which is larger? If you convert these measurements to like units, you can easily determine which piece of bar stock is larger. You know that there are 12 inches in a foot. Convert the dimension for bar stock A to ft. by dividing 48 by 12 (48 / 12 = 4). You find that there are 4 ft. in 48 inches. Bar stock A is larger than bar stock B. Figure 1. English system length conversions. Most shops use quick reference charts to convert from one unit of measurement within the English system to another. Some charts tell you which numbers to use to solve for the missing value. Other charts list numerical values in one column with their equivalent conversion in the next column. These charts quickly tell you the correct conversion. However, it also helps to know how to convert units quickly without using charts. Figure 2. To solve this problem, you need to convert from inches to feet.

8 Lesson: 6/18 The English System: Length The smallest unit of length measurement in the English system is the inch. The inch is abbreviated as "in." and is one of the most common length measurements used in manufacturing. As Figure 1 shows, there are 12 inches in 1 foot (ft.), 3 feet in 1 yard (yd.), and 1,760 yards in 1 mile (mi). When working with dimensions in math calculations, you must work with all of the same units. Consider the sample problem in Figure 2. If you had a piece of bar stock labeled A that is 48 in. long and another labeled B that is 2 ft., which is larger? If you convert these measurements to like units, you can easily determine which piece of bar stock is larger. You know that there are 12 inches in a foot. Convert the dimension for bar stock A to ft. by dividing 48 by 12 (48 / 12 = 4). You find that there are 4 ft. in 48 inches. Bar stock A is larger than bar stock B. Figure 1. English system length conversions. Most shops use quick reference charts to convert from one unit of measurement within the English system to another. Some charts tell you which numbers to use to solve for the missing value. Other charts list numerical values in one column with their equivalent conversion in the next column. These charts quickly tell you the correct conversion. However, it also helps to know how to convert units quickly without using charts. Figure 2. To solve this problem, you need to convert from inches to feet. Lesson: 7/18 English Units of Length: Sample Problem Imagine you are traveling in your car and you need to find the nearest gas station. You know that station A is 26,400 ft. away, and station B is 4.5 mi. away. Which gas station is closer? Figure 1 shows the solution to this problem. First, you must convert the feet dimension for station A to miles so that you can compare like units. You know that there are 5,280 ft. in 1 mile. This means that you must divide the amount of feet you have by 5,280. The easiest way to do this is to use a calculator. Enter the number 26,400, the division symbol ( ), 5,280, and then the equal sign (=) to find that there are 5.0 mi. in 26,400 feet. Since gas station A is 5.0 mi. away, and gas station B is 4.5 mi. away, station B is closer and should be your next destination. Figure 1. To solve this problem, you need to convert from feet to miles.

9 Lesson: 7/18 English Units of Length: Sample Problem Imagine you are traveling in your car and you need to find the nearest gas station. You know that station A is 26,400 ft. away, and station B is 4.5 mi. away. Which gas station is closer? Figure 1 shows the solution to this problem. First, you must convert the feet dimension for station A to miles so that you can compare like units. You know that there are 5,280 ft. in 1 mile. This means that you must divide the amount of feet you have by 5,280. The easiest way to do this is to use a calculator. Enter the number 26,400, the division symbol ( ), 5,280, and then the equal sign (=) to find that there are 5.0 mi. in 26,400 feet. Since gas station A is 5.0 mi. away, and gas station B is 4.5 mi. away, station B is closer and should be your next destination. Figure 1. To solve this problem, you need to convert from feet to miles. Lesson: 8/18 English Units of Length: Sample Problem #2 Imagine you have to machine a batch of parts that are each 10 in. long, and you have 6 pieces of bar stock that are each 12 ft. long, as shown in Figure 1. How many total parts are you able to machine? Figure 2 shows the solution to this problem. To solve this problem, you must first have all like units. You know that there are 12 in. in a foot. To determine how many inches are contained in each piece of bar stock, you must multiply the length of the bar stock by 12 (12 x 12 = 144). Each piece of bar stock is 144 in. long. If each part you must machine is 10 in. long, and you know how many inches of material are contained in each piece of bar stock, you can now determine how many parts a piece of bar stock will yield. To do this, you must divide the total inches of bar stock by the number of inches per part (144 / 10 = 14.4). Notice that when you divide you have an answer of This means that each piece of bar stock yields 14 parts. The extra 0.4 indicates material that is left over. To determine how many total parts you are able to machine, you must multiply the number of bar stock you have by the number of parts that a piece of bar stock yields (6 x 14 = 84). You can machine a total of 84 parts. Figure 1. If you have 6 pieces of 12 ft. bar stock, how many 10 in. parts can you machine?

10 Lesson: 8/18 English Units of Length: Sample Problem #2 Imagine you have to machine a batch of parts that are each 10 in. long, and you have 6 pieces of bar stock that are each 12 ft. long, as shown in Figure 1. How many total parts are you able to machine? Figure 2 shows the solution to this problem. To solve this problem, you must first have all like units. You know that there are 12 in. in a foot. To determine how many inches are contained in each piece of bar stock, you must multiply the length of the bar stock by 12 (12 x 12 = 144). Each piece of bar stock is 144 in. long. If each part you must machine is 10 in. long, and you know how many inches of material are contained in each piece of bar stock, you can now determine how many parts a piece of bar stock will yield. To do this, you must divide the total inches of bar stock by the number of inches per part (144 / 10 = 14.4). Notice that when you divide you have an answer of This means that each piece of bar stock yields 14 parts. The extra 0.4 indicates material that is left over. To determine how many total parts you are able to machine, you must multiply the number of bar stock you have by the number of parts that a piece of bar stock yields (6 x 14 = 84). You can machine a total of 84 parts. Figure 1. If you have 6 pieces of 12 ft. bar stock, how many 10 in. parts can you machine? Figure 2. You must convert from feet to inches to determine how many parts you can machine. Lesson: 9/18 The Metric System: Length In the Metric system, the smallest unit of length used in the shop is the millimeter (mm). As Figure 1 shows, there are 10 millimeters in a centimeter (cm), 100 centimeters in a meter (m), and 1,000 meters in a kilometer (km). These are the most commonly used units of length in the Metric system. Just like with units from the English system, you must work with like units in the Metric system when comparing values or solving for missing values. There are many ways to convert units within the Metric system. Shops are usually equipped with quick reference charts to make the conversions

11 Lesson: 9/18 The Metric System: Length In the Metric system, the smallest unit of length used in the shop is the millimeter (mm). As Figure 1 shows, there are 10 millimeters in a centimeter (cm), 100 centimeters in a meter (m), and 1,000 meters in a kilometer (km). These are the most commonly used units of length in the Metric system. Just like with units from the English system, you must work with like units in the Metric system when comparing values or solving for missing values. There are many ways to convert units within the Metric system. Shops are usually equipped with quick reference charts to make the conversions for you. Another way to convert units is either to multiply or divide. You multiply to convert to a smaller sized unit and divide to convert to a larger sized unit. For example, if you are machining a part with a length of mm, what are its dimensions in centimeters? You know that there are 10 mm in a centimeter. To find out how many centimeters equal mm, you must divide to convert to the larger size unit. You may use a calculator to divide (28.44 / 10 = 2.844). You find that mm is the same as centimeters. Figure 1. These are common units of length in the Metric system. Lesson: 10/18 Converting Metric Units of Length There is a much easier way to convert units within the Metric system. Because the Metric system is based on powers of ten, you can convert any unit of measurement by simply moving the decimal point. You can do this as long as you know the equivalent number of units contained in the other unit. Converting to a larger unit requires moving the decimal point to the left, as Figure 1 shows. For example, you know that there are 10 mm in 1 centimeter. To convert millimeters to centimeters, move the decimal point over one place to the left. Because you know that there are 100 cm in 1 m, move the decimal point over two places to the left to convert from centimeters to meters. To convert meters to kilometers, move the decimal point to the left three places because there are 1000 m in 1 kilometer. To convert to a smaller unit, move the decimal to the right instead, as Figure 2 shows. If you are converting kilometers to meters, you would move the decimal point to the right three places, since there are 1000 m in 1 kilometer. To convert meters to centimeters, move the decimal point over two places to the right since there are 100 cm in 1 meter. And lastly, to convert centimeters to millimeters, move the decimal point one place to the right. Most shop conversions are between centimeters and millimeters. If you have just measured a part to find that it is 6.75 cm long, and you need to know the dimension in millimeters, move the decimal to the right one place to show that the part is 67.5 mm long. Lesson: 11/18 Figure 1. Converting to larger units requires you to move the decimal to the left. Figure 2. Converting to smaller units requires you to move the decimal to the right.

12 Lesson: 10/18 Converting Metric Units of Length There is a much easier way to convert units within the Metric system. Because the Metric system is based on powers of ten, you can convert any unit of measurement by simply moving the decimal point. You can do this as long as you know the equivalent number of units contained in the other unit. Converting to a larger unit requires moving the decimal point to the left, as Figure 1 shows. For example, you know that there are 10 mm in 1 centimeter. To convert millimeters to centimeters, move the decimal point over one place to the left. Because you know that there are 100 cm in 1 m, move the decimal point over two places to the left to convert from centimeters to meters. To convert meters to kilometers, move the decimal point to the left three places because there are 1000 m in 1 kilometer. To convert to a smaller unit, move the decimal to the right instead, as Figure 2 shows. If you are converting kilometers to meters, you would move the decimal point to the right three places, since there are 1000 m in 1 kilometer. To convert meters to centimeters, move the decimal point over two places to the right since there are 100 cm in 1 meter. And lastly, to convert centimeters to millimeters, move the decimal point one place to the right. Most shop conversions are between centimeters and millimeters. If you have just measured a part to find that it is 6.75 cm long, and you need to know the dimension in millimeters, move the decimal to the right one place to show that the part is 67.5 mm long. Figure 1. Converting to larger units requires you to move the decimal to the left. Figure 2. Converting to smaller units requires you to move the decimal to the right. Lesson: 11/18 Converting Length from English to Metric If more than one country is involved in either the design or manufacturing of a part, chances are that either the designer or the shop personnel will have to convert the measurements on the part. There is no simple way to remember the equivalents for converting units from Metric to English. But every shop should have some basic tools for unit conversions. Most shops are equipped with reference charts, like the one in Figure 1, to remind shop personnel how to convert units. Many charts list pages of numerical values with Metric and English equivalents. You may also use a digital caliper, which will automatically display values for both units of measurement. Even some machines allow you to enter the values in one unit of measurement and automatically calculate the conversion. However, if you must convert between units manually, you can use the following values for length conversions, as shown in Figure 2: 1 in. contains 2.54 cm or 25.4 millimeters. One foot contains meters. Figure 1. Most shops are equipped with reference charts, which make converting much easier. Figure 2. When charts are not available, you must know the manual conversions.

13 Lesson: 11/18 Converting Length from English to Metric If more than one country is involved in either the design or manufacturing of a part, chances are that either the designer or the shop personnel will have to convert the measurements on the part. There is no simple way to remember the equivalents for converting units from Metric to English. But every shop should have some basic tools for unit conversions. Most shops are equipped with reference charts, like the one in Figure 1, to remind shop personnel how to convert units. Many charts list pages of numerical values with Metric and English equivalents. You may also use a digital caliper, which will automatically display values for both units of measurement. Even some machines allow you to enter the values in one unit of measurement and automatically calculate the conversion. However, if you must convert between units manually, you can use the following values for length conversions, as shown in Figure 2: 1 in. contains 2.54 cm or 25.4 millimeters. One foot contains meters. Figure 1. Most shops are equipped with reference charts, which make converting much easier. Figure 2. When charts are not available, you must know the manual conversions. Lesson: 12/18 Converting Length from Metric to English Imagine that a German engineer designs a part for a customer in England. The diameter of the part is 35 mm, and it is 234 mm long, as Figure 1 shows. For the English customer to manufacture the part, the dimensions must be converted from Metric to English. What are the dimensions of this part in inches? One of the easiest ways to convert these units is to look up the values on a shop chart or a digital caliper. However, if you do not have these resources, you must do the conversion manually, as shown in Figure 2. You know that there are 25.4 mm in 1 inch. To find the diameter of the part in inches, you must divide to find out how many inches are contained within 35 mm (35 / 25.4 = 1.378). You find out that the part is in. in diameter. Likewise, to find out the length of the part in inches, you must divide to find out how many inches are in 234 total mm (234 / 25.4 = 9.213). The English company will manufacture a part with a in. diameter and in. length. Figure 1. This part's dimensions are in Metric units.

14 Lesson: 12/18 Converting Length from Metric to English Imagine that a German engineer designs a part for a customer in England. The diameter of the part is 35 mm, and it is 234 mm long, as Figure 1 shows. For the English customer to manufacture the part, the dimensions must be converted from Metric to English. What are the dimensions of this part in inches? One of the easiest ways to convert these units is to look up the values on a shop chart or a digital caliper. However, if you do not have these resources, you must do the conversion manually, as shown in Figure 2. You know that there are 25.4 mm in 1 inch. To find the diameter of the part in inches, you must divide to find out how many inches are contained within 35 mm (35 / 25.4 = 1.378). You find out that the part is in. in diameter. Figure 1. This part's dimensions are in Metric units. Likewise, to find out the length of the part in inches, you must divide to find out how many inches are in 234 total mm (234 / 25.4 = 9.213). The English company will manufacture a part with a in. diameter and in. length. Figure 2. To convert from Metric to English units, you must know the conversion from millimeters to inches. Lesson: 13/18 Area Area is a measurement of the amount of space contained within an enclosed, flat surface. For example, if you need to purchase carpeting for a room, you would measure the area of the floor. Area is expressed in terms of square inches (in 2), square feet (ft 2), or square yards (yd 2). These units tell you how many square-shaped units of the same size fit within a specific space. In the United States, carpeting is sold by the square yard. The best way to understand area is with a basic square or rectangle. To find the area, multiply the length and width, as shown in Figure 1. For example, if you need to make a part that is square in shape with a length of 15 in. and a width of 25 in., what is the surface area of the part? Because the part is square in shape, you can multiply 15 by 25 to determine that the area of the part's top surface is 375 square inches. Figure 1. The area of a square is its length multiplied by its width.

15 Lesson: 13/18 Area Area is a measurement of the amount of space contained within an enclosed, flat surface. For example, if you need to purchase carpeting for a room, you would measure the area of the floor. Area is expressed in terms of square inches (in 2), square feet (ft 2), or square yards (yd 2). These units tell you how many square-shaped units of the same size fit within a specific space. In the United States, carpeting is sold by the square yard. The best way to understand area is with a basic square or rectangle. To find the area, multiply the length and width, as shown in Figure 1. For example, if you need to make a part that is square in shape with a length of 15 in. and a width of 25 in., what is the surface area of the part? Because the part is square in shape, you can multiply 15 by 25 to determine that the area of the part's top surface is 375 square inches. Figure 1. The area of a square is its length multiplied by its width. Lesson: 14/18 Volume Volume is a measurement of the amount of space contained within a three-dimensional shape. You may also see volume referred to as capacity. In the Metric system, volume is expressed in liters. As shown in Figure 1, there are 1,000 milliliters (ml) in 1 liter (L), and 1,000 liters in a kiloliter (kl). Note that you may also see liters expressed with a lowercase "l." In the English system, volume is expressed in terms of cups, pints, quarts, and gallons. As shown in Figure 2, there are 2 cups in 1 pint (pt.), 2 pints in 1 quart (qt.), and 4 quarts in 1 gallon (gal). Just like with length measurements, you must convert volume to like units. Again, there is no easy way to remember this conversion. One of the most common conversions to remember is that 1 gallon is equal to liters. Figure 1. Metric volume conversions. For example, if you were running a German-manufactured CNC lathe in the U.S. that used 27 L of coolant, how would you re-fill the coolant if you only had a 1 gal. bucket for measuring? As Figure 3 shows, to convert the liter measurement to gallons, you must divide to find out how many gallons are contained within the liter measurement (27 / = 7.133). You find that you must fill the CNC lathe with slightly more than 7 gal. of coolant. Figure 2. English volume conversions. Figure 3. If you use a machine from an international manufacturer, you will probably need to convert from Metric to English.

16 Lesson: 14/18 Volume Volume is a measurement of the amount of space contained within a three-dimensional shape. You may also see volume referred to as capacity. In the Metric system, volume is expressed in liters. As shown in Figure 1, there are 1,000 milliliters (ml) in 1 liter (L), and 1,000 liters in a kiloliter (kl). Note that you may also see liters expressed with a lowercase "l." In the English system, volume is expressed in terms of cups, pints, quarts, and gallons. As shown in Figure 2, there are 2 cups in 1 pint (pt.), 2 pints in 1 quart (qt.), and 4 quarts in 1 gallon (gal). Just like with length measurements, you must convert volume to like units. Again, there is no easy way to remember this conversion. One of the most common conversions to remember is that 1 gallon is equal to liters. Figure 1. Metric volume conversions. For example, if you were running a German-manufactured CNC lathe in the U.S. that used 27 L of coolant, how would you re-fill the coolant if you only had a 1 gal. bucket for measuring? As Figure 3 shows, to convert the liter measurement to gallons, you must divide to find out how many gallons are contained within the liter measurement (27 / = 7.133). You find that you must fill the CNC lathe with slightly more than 7 gal. of coolant. Figure 2. English volume conversions. Figure 3. If you use a machine from an international manufacturer, you will probably need to convert from Metric to English. Lesson: 15/18 Mass and Weight Mass is a measurement of the amount of material in an object. Mass is expressed in Metric units, in grams (g). As shown in Figure 1, there are 1000 milligrams (mg) in 1 g, and 1000 g in 1 kilogram (kg). Technically, weight is a measurement of the force of gravity on an object on the earth's surface and is expressed in English units. However, those who use the English system often think of weight as having the same meaning as mass. For the shop, mass and weight are interchangeable. Weight is expressed in ounces and pounds. As shown in Figure 2, there are 16 ounces (oz.) in 1 pound (lb.), and 2000 pounds in 1 ton (T). Of course, there is often a need to convert from unit to unit with weight and mass measurements. As with all conversions, it is easiest to check a reference chart to get the correct conversion. However, common conversions include: 1 oz. contains g, and 1 lb. contains kg, shown in Figure 3. Figure 1. Metric units of conversion for mass. Figure 2. English units of conversion for weight.

17 Lesson: 15/18 Mass and Weight Mass is a measurement of the amount of material in an object. Mass is expressed in Metric units, in grams (g). As shown in Figure 1, there are 1000 milligrams (mg) in 1 g, and 1000 g in 1 kilogram (kg). Technically, weight is a measurement of the force of gravity on an object on the earth's surface and is expressed in English units. However, those who use the English system often think of weight as having the same meaning as mass. For the shop, mass and weight are interchangeable. Weight is expressed in ounces and pounds. As shown in Figure 2, there are 16 ounces (oz.) in 1 pound (lb.), and 2000 pounds in 1 ton (T). Of course, there is often a need to convert from unit to unit with weight and mass measurements. As with all conversions, it is easiest to check a reference chart to get the correct conversion. However, common conversions include: 1 oz. contains g, and 1 lb. contains kg, shown in Figure 3. Figure 1. Metric units of conversion for mass. Figure 2. English units of conversion for weight. Figure 3. English weight to Metric mass conversions. Lesson: 16/18 Mass and Weight: Sample Problem An international shipping department provides a good example for mass and weight conversions. If a U.S. company needs to ship a 16 lb. 6 oz. box of product to Spain, the U.S. company must declare the shipment in kilograms. What is the mass of the box? Some shipping departments will round to the nearest pound. This is because pound and ounces do not work like a decimal system. In other words, a 16 lb. 6 oz. box is not the same as 16.6 lb. If your shop procedure is to round to the nearest pound, you would convert 17 lb. to kg instead of working with ounces. If your shop is equipped with a chart, like the one in Figure 1, you can simply reference the values. If you need to be more precise and find exact values, you must first convert the pounds to kilograms, and then convert the ounces to kilograms. Lastly, you must add both conversions to find the total mass of the box. Figure 2 shows the steps for solving this problem. You know that there is kg in 1 pound. To calculate how many kilograms are in 16 lb., you must multiply (16 x = ). You find that 16 lb. is equivalent to kilograms. Now, you must convert 6 oz. to Metric units. You know that there are g in an ounce. To calculate how many grams are in 6 oz., you must multiply (6 x = ). There are g in 6 oz., but you must convert this to kilograms. To convert grams to kilograms, move the decimal to the left three places since "kilo" indicates You find that there is kg in 6 ounces. Now add the equivalent for pounds and ounces to determine the total mass of the box in kg ( = ). There are a total of kg in a 16 lb. 6 oz. box. Figure 1. You can use reference charts to convert from pounds to kilograms.

18 Lesson: 16/18 Mass and Weight: Sample Problem An international shipping department provides a good example for mass and weight conversions. If a U.S. company needs to ship a 16 lb. 6 oz. box of product to Spain, the U.S. company must declare the shipment in kilograms. What is the mass of the box? Some shipping departments will round to the nearest pound. This is because pound and ounces do not work like a decimal system. In other words, a 16 lb. 6 oz. box is not the same as 16.6 lb. If your shop procedure is to round to the nearest pound, you would convert 17 lb. to kg instead of working with ounces. If your shop is equipped with a chart, like the one in Figure 1, you can simply reference the values. If you need to be more precise and find exact values, you must first convert the pounds to kilograms, and then convert the ounces to kilograms. Lastly, you must add both conversions to find the total mass of the box. Figure 2 shows the steps for solving this problem. You know that there is kg in 1 pound. To calculate how many kilograms are in 16 lb., you must multiply (16 x = ). You find that 16 lb. is equivalent to kilograms. Now, you must convert 6 oz. to Metric units. You know that there are g in an ounce. To calculate how many grams are in 6 oz., you must multiply (6 x = ). There are g in 6 oz., but you must convert this to kilograms. To convert grams to kilograms, move the decimal to the left three places since "kilo" indicates You find that there is kg in 6 ounces. Now add the equivalent for pounds and ounces to determine the total mass of the box in kg ( = ). There are a total of kg in a 16 lb. 6 oz. box. Figure 1. You can use reference charts to convert from pounds to kilograms. Figure 2. You must first convert from pounds to kilograms, and then convert from ounces to kilograms. Lesson: 17/18 Derived Units Base units such as length, volume, and mass are just the beginning when learning about units of measurement. Once you know the base units of measurement, there are hundreds of possible measurements derived by combining one or more of the base units. These types of measurements are called derived units. One of the most common derived units of measurement is speed, which is measured in miles per hour (mph) or kilometers per hour (kph). Figure 1 shows speed limit signs found in the United

19 Lesson: 17/18 Derived Units Base units such as length, volume, and mass are just the beginning when learning about units of measurement. Once you know the base units of measurement, there are hundreds of possible measurements derived by combining one or more of the base units. These types of measurements are called derived units. One of the most common derived units of measurement is speed, which is measured in miles per hour (mph) or kilometers per hour (kph). Figure 1 shows speed limit signs found in the United States that post the maximum mph you are to travel. Speed is calculated by dividing the distance traveled by the time elapsed, as shown in Figure 2. Of course, speed determines how fast a car goes, but it also measures the movement of machine components in the shop. Another example of a derived unit that combines base units is pressure. Pressure measures how much force is being applied onto an object. Even pressure is a complex measurement unit that combines time, area, and mass all in one unit. As you can see, when dealing with units of measurement, it is very easy to get caught up in formulas for deriving units because it is such a vast field of study. However, if you have a strong knowledge of the base units, you will learn to use derived units with ease. Figure 1. Mph is a derived unit that we use daily. Figure 2. This formula determines the speed of an object. Lesson: 18/18 Summary Every day you deal with units of measurement. Even time is a unit of measurement. The common base units of measurement are length, area, volume, mass, and temperature. The system of measurement used in England and the United States is the English system. However, the system used in the rest of the world is the Metric system. The Metric system is a decimal system that uses base units combined with prefixes. You must often convert between units, especially for businesses dealing internationally. The English system uses inches, feet, yards, and miles to measure length. You can convert units within the English system manually, but many shops use reference charts to make these conversions easier. The Metric system uses the meter as the base unit for measuring length. The most common Metric length measurements are the millimeter, centimeter, and kilometer. To convert between Metric length units manually, you need only to know the equivalent number of units, and move the decimal point accordingly. When converting between Metric and English length units, it is always easiest to use a reference chart. If you convert units manually, you must either multiply or divide, depending on the conversion. Area is a measurement of the amount of space contained within an enclosed, flat surface. Volume is a measurement of the amount of space contained within a three-dimensional shape. Mass is a measurement of the amount of material in an object, and weight is technically a measurement of the gravitational pull on an object. In the shop, mass and weight are interchangeable. Figure 1. Length measures the distance from one point to another. Figure 2. English to Metric length conversions.

20 Lesson: 18/18 Summary Every day you deal with units of measurement. Even time is a unit of measurement. The common base units of measurement are length, area, volume, mass, and temperature. The system of measurement used in England and the United States is the English system. However, the system used in the rest of the world is the Metric system. The Metric system is a decimal system that uses base units combined with prefixes. You must often convert between units, especially for businesses dealing internationally. The English system uses inches, feet, yards, and miles to measure length. You can convert units within the English system manually, but many shops use reference charts to make these conversions easier. The Metric system uses the meter as the base unit for measuring length. The most common Metric length measurements are the millimeter, centimeter, and kilometer. To convert between Metric length units manually, you need only to know the equivalent number of units, and move the decimal point accordingly. When converting between Metric and English length units, it is always easiest to use a reference chart. If you convert units manually, you must either multiply or divide, depending on the conversion. Area is a measurement of the amount of space contained within an enclosed, flat surface. Volume is a measurement of the amount of space contained within a three-dimensional shape. Mass is a measurement of the amount of material in an object, and weight is technically a measurement of the gravitational pull on an object. In the shop, mass and weight are interchangeable. Figure 1. Length measures the distance from one point to another. Figure 2. English to Metric length conversions. Figure 3. Area is length multiplied by width. Class Vocabulary Term Definition Area Base Unit CNC Lathe Derived Unit Diameter A measurement of the amount of space contained within a flat, enclosed shape. A unit of measurement that can be determined by taking one measurement without having to combine any other measurement. Length, mass, and temperature are examples of base units. A lathe that is controlled by a computer running programs driven by numerical data. A unit of measurement that is determined by combining one or more measurements. Miles per hour or kilometers per hour are examples of derived units. The distance from one end of the circle to the opposite end through the center. Digital Caliper A measuring instrument typically used in inspection that contains two pairs of jaws on one end and a long beam containing a marked scale of unit divisions. Digital calipers display measurements in both English andreserved. Metric units. Copyright 2015 Tooling U, LLC. All Rights English System A standard system of measurements based on the inch, pound, and Fahrenheit degrees. English measurements are primarily used in the United States and England.

21 Class Vocabulary Term Definition Area Base Unit CNC Lathe Derived Unit Diameter Digital Caliper English System International System Of Units Kilometers Per Hour Length Mass A measurement of the amount of space contained within a flat, enclosed shape. A unit of measurement that can be determined by taking one measurement without having to combine any other measurement. Length, mass, and temperature are examples of base units. A lathe that is controlled by a computer running programs driven by numerical data. A unit of measurement that is determined by combining one or more measurements. Miles per hour or kilometers per hour are examples of derived units. The distance from one end of the circle to the opposite end through the center. A measuring instrument typically used in inspection that contains two pairs of jaws on one end and a long beam containing a marked scale of unit divisions. Digital calipers display measurements in both English and Metric units. A standard system of measurements based on the inch, pound, and Fahrenheit degrees. English measurements are primarily used in the United States and England. Another name used for the Metric System. International System of Units is often abbreviated as SI. A derived unit that indicates speed, or how many kilometers an object travels in one hour. Kilometers per hour is calculated by dividing the distance traveled by the time elapsed. A measurement of distance from one point to another. A measurement of the heaviness of an object. Mass is usually expressed in Metric units. In the shop, weight and mass are used interchangeably. Measurement The act or process of measuring an object. We use units of measurement daily. Metric System A standard system of measurements based on the meter, kilogram, and Celsius degrees. The metric system is internationally recognized. Miles Per Hour A derived unit that indicates speed, or how many miles an object travels in one hour. Mph is calculated by dividing the distance traveled by the time elapsed. Prefix Pressure Rectangle Speed Square Temperature A word attached to the beginning of another word. Prefixes are attached to the beginning of a base unit of a Metric measurement to indicate the specific power of ten. The amount of force applied upon an object. Pressure is a derived unit that combines time, area, and mass. A shape with four angles and four sides forming 90 angles. The rate at which an object travels. Speed is calculated by dividing the distance traveled by the time elapsed. A shape with four equal angles and four equal sides. A measurement of the hotness or coldness of an object. Volume A measurement of the amount of space contained within a three-dimensional shape. Weight A measurement of the gravitational pull on an object on the earth's surface. Weight is expressed in English units. In the shop, weight and mass are used interchangeably.

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