Measurement. Mr. Martin

Transcription

1 Measurement Mr. Martin

2 1. Distance (Length) How wide is the floppy disk? How wide is the black metal tab?

3 Measure Accurately Measuring Length of Book Zero mark at one edge of book. Read measurement at other edge. Here you can read to the nearest tenth of a cm.

4 Breaking News! King Hector died Monday drinking chocolate milk!

5 The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. King Hector died Monday drinking chocolate milk. Kilo hecto deca meter deci centi milli Kilometer (km) 1000m Hectometer (hm) 100m Decameter (dam) 10m Meter (m) 1m Decimeter (dm).1m Centimeter (cm).01m Millimeter (mm).001m Micrometer (um) m Nanometer (nm) m

6 You try and measure some distances. Width of table in cm? in meters? in decimeters? Length of table in cm? in meters? in decimeters? Width of Pre-Algebra math book in cm? in meters? Length of Pre-Algebra math book in cm? in meters? Depth of Pre-Algebra math book in cm? in mm? Dimensions (length and width) of floor of room in meters? Length of pencil? (You choose appropriate metric measure) Diameter of a coin? (You choose the coin and the appropriate metric measure)

7 Conversions (Why King Hector is important!) King Hector died Monday drinking chocolate milk! K H D M D C M

8 You Try! 5.75m = cm 5.8km = m 1,345cm = m = dam = dm 52cm = m = km 127mm = cm = m = dm 0.056km = m = cm

9 2. Area Definition Number of square units that fit into a two dimensional space. 7cm 5cm Area = 5cm x 7cm = 35 cm 2 = 35 square centimeters

10 Area Applications The square feet in a house. In metric, the square meters in a house. The square feet of carpet in the classroom. In metric, the square meters of carpet in the classroom. Calculate it! The area in square centimeters of the cover of the Pre-Algebra book. Calculate it!

11 Big Areas Large areas of land in the United States are frequently measured in acres. One square mile, which is called a section, has 640 acres. Therefore, one acre is 1/640 of a square mile. One mile = 5280 feet. One square mile is hence equal to 5280 feet x 5280 feet = square feet. One acre is 1/640 times = 43,560 square feet. Large areas of land in the metric system are measured in Hectares. 1 hectare is equal to 10,000 square meters (100 meters x 100 meters) 1 hectare is about 2.5 acres

12 3. Volume Definition volume the amount of three dimensional space an object occupies. Measured in cubic units such as cubic meters, cubic centimeters, etc. 1cm 1cm 1cm 1cm One Cubic Centimeter (cm 3 ) 1m 1m One Cubic Meter 1m

13 What s the volume? Calculate it! 4cm 5cm Answer? 140 cm 3 7cm Answer? 10m 280m 3 7m 4m

14 The cube is one decimeter by one decimeter by one decimeter What is the volume in cubic decimeters? 1 dm 3 What is the volume in cubic centimeters? Clue: What are the dimensions in cm? 10cm x 10cm x 10cm = 1,000 cm 3

15 Some Interesting Volume Names 1 cubic decimeter = 1,000 cubic centimeters = 1 Liter (L) 1 cubic centimeter (cm 3 ) is abbreviated in medicine frequently as cc. 1 cm 3 = 1 cc = 1 milliliter = 1 ml 1 ml of water at standard temperature and pressure has a Mass of 1 gram (gm) 1 L of water at standard temperature and pressure has a Mass of 1 kilogram (Kg) More on Mass later

16 Practice with Metric Volume Find the volume of the classroom in: Cubic meters Liters (Remember a liter is a cubic decimeter) Milliliters (Remember a ml is a cubic cm)

17 King Hector died Monday drinking chocolate milk! (Again!) King Hector is useful for converting metric units of volume also King Hector died Monday drinking chocolate milk! K H D M D C M

18 You Try! 57.5L = dl (deciliter)= ml 5.2mL = cc = cm 3 5.8m 3 = L 1,345mL = L = dl 52kL = L.05L = ml 1mL = L

19 Date: Name: Homework 1. Use a tape measure to measure the dimensions of your bedroom. Use 2.5m for the height of the room. (I don t want you climbing!) Ans. 2. What is the area of the floor in square meters? 3. What is the area of any one of your walls in square meters? 4. What is the volume of your room in cubic meters? In liters?

20 Common Places Where Volume is Used Diet Coke can holds 355 ml of Diet Coke Water bottle holds 500 ml or 0.5 L of water

21 In chemistry, we can measure volume with a flask, beaker or more accurately with a graduated cylinder Graduated cylinder beaker Erlenmeyer flask

22 Volume from Geometry Coke can has inner diameter of about 6.1cm and a height of about 12 cm It is roughly a cylinder Area = area base x height = Πr 2 h = 3.14x3.05cmx3.05cmx 12cm= 351 cm 3, which is close to what the Coke can says

23 Volume from Graduated Cylinder Or pour the liquid into a graduated cylinder

24 How do I find the volume of the rock?

25 Does this give you an idea? It reads 200 ml at the bottom of the meniscus. How does this help in finding the volume of the rock? Ideas?

26 What do I do with the rock? Put rock in water See how much water it displaces That equals the volume of the rock Here, the original volume of the water was 200mL The new volume is about 245mL The volume of the rock is 245mL 200mL = 45mL

27 4. Mass Mass- the measure of the amount of matter in an object Root prefix unit is gram (In SI the base unit is kilogram. A gram is 1/1000 of a kilogram.) King Hector died Monday drinking chocolate milk kilo hecto deca (gram) deci centi milli As a practical matter, people primarily use kilogram (1,000 grams), grams and milligrams (.001 gram or 1/1,000 of a gram) Informally, a kilogram is about 2.2 pounds, a paper clip has a mass of about 1 gram and a new penny has a mass of about 2.5 gram. Milligrams are very small and are frequently used to measure the mass of medicines.

28 Mass versus Weight In everyday language, people often use mass and weight interchangeably. They are different, however. Weight is the mass of an object multiplied by its acceleration due to gravity. Weight is a force. In the metric system it is measured in Newtons. In customary units it is measured in pounds. Your mass is same on earth as it is on the moon. Your weight on earth is different from your weight on the moon since there is less gravity on the moon. If I weigh 100 pounds on earth, I would weigh only 16.6 pounds on the moon. I would weigh pounds on Jupiter. (

29 How to Measure Mass Mass is measured with a balance like the simple balance or triple beam balance below Simple Balance Triple Beam Balance

30 Measuring Mass with Triple Beam Balance Set object on pan Move largest mass (middle) to point just before balance tips Move mass in back to point just before balance tips Move smallest mass (front) until line is exactly at zero

31 A Scale Measure Weight, Not Mass The spring scale here technically measures weight, not mass Weight is a force that is equal to the mass times the acceleration of gravity This scale will show different weights on earth and the moon. A balance will give the same measure of mass. The metric unit for weight is a Newton This spring scale actually reads in grams, however, a unit of mass. It is a reasonably accurate measure of mass on earth.

32 A Digital Scale A digital scale is fast and easy to use. While technically a scale that measures weight, this is set up to measure mass in grams also It would not give an accurate mass on the moon Here, the rock has a mass of 115 grams It is precise to the nearest gram

33 5. Density Density is mass divided by volume I.e., density is mass per unit volume A measure of density is grams/ml

34 Each is about the same volume. Golf Ball Table Tennis Ball Which one has the greater density?

35 Let s find the density of each. Volume of sphere = Table Tennis Ball Diameter of table tennis ball is: Find volume: Mass of table tennis ball is: (Use balance to measure) Density = Mass/Volume Make sure you have appropriate units in the result Golf Ball Diameter of golf ball is: Find volume: Mass of golf ball is: (Use balance to measure) Density = Mass/Volume Make sure you have appropriate units in the result

36 Measuring the Mass with Triple Beam Balance

37 Let s see the result Table Tennis Ball Diameter of table tennis ball is: 3.6 cm Find volume: Golf Ball Diameter of golf ball is: 4.0 cm Find volume: Mass of table tennis ball is: 2.6g Density = Mass/Volume 2.6g/24.43mL = 0.106g/ ml Mass of golf ball is: 46.0g Density = Mass/Volume 46.0g/33.51mL = 1.37 g/ml The golf ball is almost 13 times more dense. (1.37/.106 =12.9)

38 You Do It! Determine the density of the tennis ball and baseball.

39 Find the density of each. Volume of sphere = Tennis Ball Diameter of tennis ball is: Find volume: Mass of tennis ball is: (Use balance to measure) Density = Mass/Volume Make sure you have appropriate units in the result Baseball Diameter of baseball is: Find volume: Mass of baseball is: (Use balance to measure) Density = Mass/Volume Make sure you have appropriate units in the result

40 6. Temperature How hot or cold a substance is A measure of the average kinetic energy of an object Two common scales to measure Celsius and Fahrenheit Celsius is used in science and in countries using the metric system Celsius 100ºC 0ºC 212ºF 32ºF Fahrenheit Water Boils Water Freezes

41 Converting from Fahrenheit to Celsius and Celsius to Fahrenheit If you know the Celsius temperature, you can convert to Fahrenheit by plugging in the Celsius temperature in this formula. The same formula in decimal form. If you know the Fahrenheit temperature, you can convert to Celsius by plugging in the Fahrenheit temperature in this formula. It s good to know at least the top formula since they show up on standardized tests. If you know the top formula, you can also solve for C to get the bottom formula.

42 If you are familiar with the slope intercept form of a line, you can figure out the formulas.