Conversions 1-1 Conversions are important for administering medications. Nurses need to be familiar with three types of measurement systems: the metric system, the household system (for example, cups and tablespoons), and the apothecary system (used by pharmacists and quickly being replaced with the metric system). Some measurements, like the pound and gallon, appear in two systems and don't need converting. However, if a nurse gets an order for medication that's in fluid ounces, and the medication bottle is in cubic centimeters, a conversion must be made.
1. 18 + (–25) = –7 ANSWER ? ? 4 1 2. – – = 2 3 2 3 Lesson 1.1, For use with pages 2-9 ANSWER
ANSWER 23º F Lesson 1.1, For use with pages 2-9 3.What is the difference between a daily low temperature of –5º F and a daily high temperature of 18º F?
5 Graph the real numbers – and 3 on a number line. 4 5 Note that –= – 1.25. Use a calculator to approximate 3 to the nearest tenth: 4 3 1.7 (The symbol means is approximately equal to.) 5 So, graph – between –2 and –1, and graph 3 between 1 and 2, as shown on the number line below. 4 EXAMPLE 1 Graph real numbers on a number line SOLUTION
ANSWER The correct answer is D. EXAMPLE 2 Standardized Test Practice SOLUTION From lowest to highest, the elevations are – 408, –156, –86, –40, –28, and –16.
7 1. Graph the numbers – 0.2, , –1, 2 , and –4 on a number line. 10 2 –4 –1 – 0.2 – 2 – 1 – 4 – 3 0 1 2 3 4 7 10 for Examples 1 and 2 GUIDED PRACTICE SOLUTION
2. Which list shows the numbers in increasing order? – 0.5, 1.5, – 2, – 0.75, 7 – 0.5, – 2, – 0.75, 1.5, 7 – 2, – 0.75, – 0.5, 1.5, 7 7 , 1.5, – 0.5 , – 0.75, – 2 ANSWER The correct answer is C. for Examples 1 and 2 GUIDED PRACTICE
1 7 + 4 = 4 + 7 13 = 1 13 EXAMPLE 3 Identify properties of real numbers Identify the property that the statement illustrates. SOLUTION Commutative property of addition SOLUTION Inverse property of multiplication
a + (2 – a) = a + [2 + (– a)] EXAMPLE 4 Use properties and definitions of operations Use properties and definitions of operations to show that a + (2 – a) = 2. Justify each step. SOLUTION Definition of subtraction = a + [(– a) + 2] Commutative property of addition = [a + (– a)] + 2 Associative property of addition = 0 + 2 Inverse property of addition Identity property of addition = 2
(2 3) 9 = 2 (3 9) 15 + 0 = 15 for Examples 3 and 4 GUIDED PRACTICE Identify the property that the statement illustrates. SOLUTION Associative property of multiplication. SOLUTION Identityproperty of addition.
4(5 + 25) = 4(5) + 4(25) 1 500 = 500 for Examples 3 and 4 GUIDED PRACTICE Identify the property that the statement illustrates. SOLUTION Distributive property. SOLUTION Identityproperty of multiplication.
3x + (6 + 4x) = 7x + 6 3x + (6 + 4x) = 3x + (4x + 6) for Examples 3 and 4 GUIDED PRACTICE Use properties and definitions of operations to show that the statement is true. Justify each step. SOLUTION Comm. prop. of addition = (3x + 4x) + 6 Assoc. prop. of addition Combine like terms. = 7x + 6
You work 4 hours and earn $36. What is your earning rate? You travel for 2.5 hours at 50 miles per hour. How far do you go? 36dollars 4hours 50miles (2.5hours) 1hour EXAMPLE 5 Use unit analysis with operations SOLUTION = 9dollars per hour SOLUTION = 125 miles
5280feet 1hour 1minute 45miles You drive 45 miles per hour. What is your speed in feet per second? 1mile 60seconds 60minutes 1hour EXAMPLE 5 Use unit analysis with operations SOLUTION = 66 feet per second
Driving Distance Convert the distance from Montpelier to Montreal to kilometers. Convert the distance from Montreal to Quebec City to miles. EXAMPLE 6 Use unit analysis with conversions The distance from Montpelier, Vermont, to Montreal, Canada, is about 132 miles. The distance from Montreal to Quebec City is about 253 kilometers.
1.61kilometers 213 kilometers 132miles 1mile 1mile 253kilometers 157 miles 1.61kilometers EXAMPLE 6 Use unit analysis with conversions SOLUTION
You work 6 hours and earn $69. What is your earning rate? How long does it take to travel 180 miles at 40 milesper hour? 69dollars 6hours 180miles 1hour 40 miles for Examples 5 and 6 GUIDED PRACTICE Solve the problem. Use unit analysis to check your work. SOLUTION = 11.5dollars per hour SOLUTION = 4.5 hour
You drive 60 kilometers per hour. What is your speed in miles per hour? 1mile 60km 1.61km 1hour for Examples 5 and 6 GUIDED PRACTICE Solve the problem. Use unit analysis to check your work. SOLUTION = about 37 mph
150yardstofeet 3 feet 150 yard 1 yard for Examples 5 and 6 GUIDED PRACTICE Perform the indicated conversion. SOLUTION = 450 ft
4 gallons to pints 8 pints 4 gallon 1 gallon for Examples 5 and 6 GUIDED PRACTICE Perform the indicated conversion. SOLUTION = 32 pints
16 years to seconds 60 seconds 1 minute 16 years 60 minutes 24 hours 1 hour 365 days 1 day 1 year for Examples 5 and 6 GUIDED PRACTICE Perform the indicated conversion. SOLUTION = 504,576,000 sec
