# MATH FOR NURSING MEASUREMENTS. Written by: Joe Witkowski and Eileen Phillips

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1 MATH FOR NURSING MEASUREMENTS Written by: Joe Witkowski and Eileen Phillips

2 Section 1: Introduction Quantities have many units, which can be used to measure them. The following table gives common units associated with certain dimensions. Dimension Time Distance Speed Weight Volume Common units seconds, minutes, hours days, months, years inches, feet, yards centimeters, meters, kilometers miles per hour, feet per second meters per second ounces, pounds, micrograms, milligrams, grams, kilograms teaspoons, tablespoons, fluid ounces, milliliters, liters, cubic centimeters, cubic meters, cubic feet, cubic yards When using formulas it is often necessary to change units. For instance, if you had to find the distance traveled using the formula d = vt, and v = 30 miles per hour and t = 45 minutes, you would have to convert time to hours or velocity to miles per minute because the units are not the same. Section 2: Unit Conversions In order to convert units, treat the units just as if they were algebraic quantities. As algebraic quantities they can be multiplied and divided. For example, just focusing on units, ft ft in in ft in in All conversion facts that are written as equations, such as 1 ft = 12 in, can be written as a 1 ft 12 in conversion factor, or that is equivalent to 1. These conversion factors are then used 12 in 1 ft to divide out the unwanted units, leaving the desired units for the conversion. Since the conversion factors are equivalent to 1, when multiplied to a quantity, the value of the quantity does not change. Witkowski and Phillips Page 2

3 Example 1 : Convert 38 inches to feet. Round the answer to the nearest tenth of a foot. Recall that there were two conversion factors for converting feet to inches; 1 ft 12 in and. In order to decide which one to use, look at the units in 12 in 1 ft the quantity we were given to convert. Since we were given inches, we need to choose the conversion factor that has inches in the denominator so that the two units will divide out, leaving feet in the answer. 1 ft 38 in 38 in 38 in = 12 in 1 1 ft 12 in 38 1 ft = 3.2 ft 1 12 in ( units can be divided out; in Therefore, 38 inches = 3.2 feet. 1.) Example 2 : Convert 60 feet per second to yards per second. Note that 60 feet per second is the same as 60 ft ft or 60. 1sec sec Recall that 1 yard = 3 feet, which gives us two conversion factors, and 3 ft 1 yd 1 yd 3 ft. Since we are asked to convert the feet to yards, we will need the feet to divide out and thus we need to choose factor. 1 yd as the conversion 3 ft 60 ft 1 sec 1 yd 3 ft = 60 ft 1 sec 1yd 3 ft ( units can be divided out; ft ft 1.) = 60 1 yd 60 yd 20 yd = = = 20 yd 3sec 3sec 1 sec sec Witkowski and Phillips Page 3

4 Activity 1 a) If you were going to convert 96 pounds to kilograms, would you multiply by 1 kg 2.2 lbs or? Explain. 2.2 lbs 1 kg ml ml b) If you were going to convert 40 to, would you multiply by sec min 1min 60sec or 60sec? Explain. 1min Please use the following conversion chart as reference for the rest of the problems contained in this unit. These common conversion facts must be memorized. METRIC CONVERSIONS HOUSEHOLD & APOTHECARY EXACT VOLUME EQUIVALENTS Volume Weight Volume (Liquid) Weight (Dry) Liter (L) Kilogram (kg) Measuring cup Pounds (lb) 1 L = 1000 ml 1 kg = 2.2 lbs 1 cup = 8 oz 2.2 lbs = 1 kg 1 kg = 1000 g 1 cup = 240 ml 1 lb = g Milliliter (ml) 2 cups = 1 pint 1 lb = 16 oz 1 ml = L Milligrams (mg) 1 ml = 1000 mcl 1 mg = g Ounces (oz) 30 ml = 1 oz 1 mg = 1000 mcg 1 oz = 30 ml 5 ml = 1 tsp 1 oz = 2 Tbs 15 ml = 1 Tbs Microgram (mcg) 8 oz = 1 cup 1 mcg = mg 16 oz = 1 pint Microliter (mcl) 1 mcl = ml Gram (g) Tablespoons (Tbs) 1000 mcl = 1 ml 1 g = 1000 mg 1 Tbs = 3 tsp Length Centimeter (cm) 2.54 cm = 1 inch 1 g = 1 ml 1 Tbs = 15 ml 1 g = kg 2 Tbs = 1 oz g = 1 lb Teaspoon (tsp) 1 tsp = 5 ml 3 tsp = 1 Tbs Witkowski and Phillips Page 4

5 Example 4 : How many ml are in 6 teaspoons of cough medicine? One method would be to use the conversion factor 6 tsp 5 ml 6 5 ml 6 tsp 30 ml 1 1 tsp 1 1 tsp ( units can be divided out; 1.) tsp 5 ml. 1 tsp There are 30 ml in 6 teaspoons. A second method would be to set up a proportion. 1 tsp 5 ml 6 tsp x ml x 6(5) 30 There are 30 ml in 6 teaspoons. A third method would be to recognize that if 1 tsp = 5 ml, then 6 tsp would be 5 times as many or 30 ml. Example 5 : How many kilograms does a 150 pound person weigh? Round the number of kilograms to the nearest tenth. 1 kg One method would be to use the conversion factor. 2.2 lbs 150lbs 1 kg kg lbs kg = 68.2 kg lbs There are 68.2 kg in 150 lbs. A second method would be to set up a proportion. 2.2 lbs 150 lbs 2.2x x kg x kg 68.2 There are 68.2 kg in 150 lbs. Witkowski and Phillips Page 5

6 A third method would be to recognize that if 1 kg = 2.2 lbs, then 150 lbs must be divided by 2.2 lbs to determine the number of kilograms, Activity 2 Use the conversion table on page 4 and any of the methods shown to answer the questions below. If necessary, round the answer to the nearest tenth. a) How many ounces are in 8 pints? b) How many inches are in 76 centimeters? c) How many pounds are in 80 kilograms? d) How many tablespoons are in 120 milliliters? e) Convert 240 ml per hour to ml per minute. Witkowski and Phillips Page 6

7 Section 3: The Metric System The metric system is very similar to our decimal number system. It is an easy system to use because calculations are based on multiples of 10. Different units of length in the metric system are obtained by combining an appropriate prefix with the base unit, which is the meter. The prefixes, their symbols, and their meanings are given in the following table. Prefix Symbol Power of 10 Meaning mega M 10 6 one million times kilo k 10 3 one thousand times hecto h 10 2 one hundred times deka da 10 1 ten times deci d 10-1 one tenth of centi c 10-2 one hundredth of milli m 10-3 one thousandth of micro mc 10-6 one millionth of Activity 3 Complete the following table, which gives names for different units of length along with their relationship to the meter. Unit Symbol Relationship to Base Unit kilometer _ 1000 meters 100 meters _ dam _ meter m bas e unit _ dm 0.1 meter centimeter _ mm The prefixes can also be used for measurements involving mass and volume. The mass of an object is the quantity of material making up the object. The base unit for mass in the metric system is the gram (g). The volume is the amount of space an object or liquid occupies. The base unit for volume in the metric system is the liter (L). The prefixes work the same way with these base units as they did with the meter. Witkowski and Phillips Page 7

8 It is important to have some idea as to the size of some of these metric units. A meter is about 39 inches which is a little longer than a yard (36 inches). One centimeter is about the width of your little finger or the diameter of the head of a thumbtack. Nine football fields, including end zones, laid end to end are approximately 1 kilometer long. The thickness of a dime is about 1 millimeter. A common paper clip has a mass of about 1 gram. One grain of salt has a mass of about 1 mg. A quart of milk is a little less than a 1 liter. A teaspoon of cough medicine is about 5 ml. Activity 4 a) Which metric unit (km, m, cm, or mm) should be used to measure each item? i) Length of a pencil ii) Your height iii) Length of a car race iv) Diameter of a nickel b) Which metric unit (kg, g, or mg) should be used to measure each item? i) Mass of a pencil ii) Mass of a football player c) Which metric unit (L, ml) should be used to measure each item? i) Volume of a single serving of mouth wash ii) Volume of a jug of water Witkowski and Phillips Page 8

9 It is important to be able to change units so that you can input the correct units when working with formulas. We will now look at some examples that convert from one metric unit to another metric unit. To convert from metric to metric, you can use the same techniques discussed in section 2, but the metric system is based on multiples of ten so we are able to use our knowledge of decimals and simply move the decimal point to the left or right depending on which units are being converted. Memorizing the order of prefixes in the following table allows us to simply start at the unit given and move the decimal point to the converted unit. Whichever direction we move and however many spaces we move determines the direction and number of spaces we move the decimal point in the given number. * * * * * * * kilo(k) hecto(h) deka(da) base unit deci(d) centi(c) milli(m) (base units: meter, gram, liter) Example 6 : Change 125 mm to cm. We would go to the table above, start at mm and move one place to the left. So to change 125 mm to cm, move the decimal point one place to the left. 125 mm = 12.5 cm We could also use the conversion factor 1 cm. 10 mm 125 mm 1 cm 125cm 125 mm cm 1 10 mm 10 Example 7 : Change 2.34 km to cm. According to the table above, to go from km to cm you have to move 5 places to the right. So to change 2.34 km to cm, you have to move the decimal point 5 places to the right km = 234,000 cm. Witkowski and Phillips Page 9

10 Example 8 : Change 5.8 kg to mg. We can use the same table as we did for length, we just need to change the meter to the gram. The prefixes stay the same. To go from kg to mg, we need to move 6 places to the right. So to change 5.8 kg to mg, we have to move the decimal point 6 places to the right. 5.8 kg = 5,800,000 mg. We could also use the conversion factor method. Since we do not have a conversion fact in the chart on page 4 that takes us directly from kg to mg, we will need to multiply by two conversion factors to reach the desired units kg 1000 g 1000mg kg 5,800, 000 mg 1 1 kg 1 g Note: While the first method is much quicker, learning how to use conversion factors will be helpful when you need solve dosage problems later on in nursing. You can set up as many conversion factors as you need, all multiplied together, until you reach the desired units. Example 9 : Change 0.38 mg to mcg. Since the table on page 9 ends at mg, we will need to recall from the conversion chart on page 4 that 1 mg = 1000 mcg. From that we can either use the conversion factor or realize that if we extend the table, mcg would be three places to the right of mg. Using the conversion factor 1000mcg 1 mg, give us mg 1000 mcg mcg mg 380 mcg 1 1 mg 1 Extending the table, we would move the decimal point in 0.38 mg to the right 3 places, giving us 0.38 mg = 380 mcg Witkowski and Phillips Page 10

11 Example 10 : Change 135 ml to L. We can use the same table as we did for length, we just need to change the meter to the liter. The prefixes stay the same. To go from ml to L, we need to move 3 places to the left. So to change 135 ml to L, we have to move the decimal point 3 places to the left. 135 ml = L Activity 5 a) Change 2.3 km to m. b) Change 48 cm to km. c) Change 120 grams to kg. d) Change 0.72 mg to mcg. e) Change 320 ml to L. f) Change 6.5 L to ml. Witkowski and Phillips Page 11

12 Exercises for Measurements Do all the exercises on separate paper, showing all work neatly. If necessary, round answers to the nearest tenth. 1. Convert 8 Tbs to teaspoons. 2. Convert 170 lb to kilograms. 3. Convert 42 tsp to milliliters. 4. Convert 125 ml to ounces. 5. Convert 32 in to centimeters. 6. Convert 2 ml per minute to ml per hour. 7. A foreign car's gasoline tank holds 56 L. Convert this capacity to gallons. Use the following conversion facts: 1 L = quarts and 4 quarts = 1 gallon. 8. Suppose a swimmer on the swim team can swim 40 yards in 30 seconds. Convert this to miles per hour. Use the following conversion facts: 1 yd = 3 ft and 1 mile = 5280 ft. Fill in the blanks to find the number of miles per hour: 40 yd x 30 s ft yd mi x ft x s min x min hr = miles hour 9. Twenty grams of a medication are to be dissolved in L of water. Convert this to milligrams per deciliter. 10. Convert the following. a) 4.8 L to ml b) 7.25 km to m c) 350 ml to L d) 25 g to mcg e) 18 mm to cm f) mg to g Witkowski and Phillips Page 12

13 Math for Nursing Solutions To Activities MEASUREMENTS Activity 1: a) You would multiply 96 pounds by kilograms. 1 kg because the pounds would divide out, leaving 2.2 lbs b) You would multiply 40 ml by sec 60 sec because the seconds would divide out, leaving minutes. 1 min ********************************************************************************************************************** Activity 2 16 oz 1 in a) 8 pts 128 oz b) 76 cm in 1 pts 2.54 cm 2.2 lbs 1Tbs c) 80 kg 176lbs d) 120 ml 8 Tbs 1 kg 15 ml e) 240 ml 1 hr 4 ml 1 hr 60 min 1 min so 4 ml per minute *************************************************************************************************************** Activity 3 Unit Symbol Relationship to Base Unit kilometer km 1000 meters hectometer hm 100 meters dekameter dam 10 meters meter m base unit decimeter dm 0.1 meter centimeter cm 0.01 meter millimeter mm meter *************************************************************************************************************** Activity 4 a) i) mm or cm ii) cm or m iii) m or km iv) mm b) i) m ii) kg c) i) ml ii) L Witkowski and Phillips Page 13

14 Measurements Solutions continued Activity m 1 m 1 km a) 2.3 km 2300 m b) 48 cm km 1 km 100 cm 1000 m c) 120 g = 0.12 kg move the decimal point 3 places to the left d) 0.72 mg = 720 mcg move the decimal point 3 places to the right e) 320 ml = 0.32 L move the decimal point 3 places to the left f) 6.5 L = 6500 ml move the decimal point 3 places to the right Witkowski and Phillips Page 14

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