ALGEBRA READINESS Chapter 5 Section 1

5.1: Compare and Order Rational Numbers A rational number is a number that can be written as a/b where a and b are integers and b ≠ 0. Every rational number can also be written either as a terminating decimal or a repeating decimal.

Show that (a) 1.9 and (b) 8.25 are rational numbers. – Example 1 Identifying Rational Numbers Show that (a) 1.9 and (b) 8.25 are rational numbers. – = 1 10 9 Write as mixed number. a. 1.9 = 10 19 Write as improper fraction. Write as mixed number. = 8 4 1 – b. 8.25 = – -8 25 100 Write as improper fraction. = 4 33 – Both numbers are rational numbers because they are quotients of two integers.

Practice for Example 1 Show that the number is a rational number by writing it as a quotient of two integers. ANSWER 5 2 1. 0.4 ANSWER 20 23 2. 1.15 ANSWER 5 6 – 3. 1.2 – ANSWER 5 13 – 4. 2.6 –

Graph 3.9 and on a number line. Then tell which is greater. Example 2 Graphing and Comparing Rational Numbers 7 Graph 3.9 and on a number line. Then tell which is greater. – – 2 The number 3.9 is nine-tenths to the left of 3 on the number line. The number is equal to 3.5, which is five-tenths to the left of 3 on the number line. 2 7 – On the number line, is to the right of 3.9. So, 2 7 – 3.9. >

Graph the numbers on a number line. Then tell which number is greater. Practice for Example 2 Graph the numbers on a number line. Then tell which number is greater. 5. and 0.3 5 2 – ANSWER 5 2 6. and 4.2 8 11 – ANSWER 8 11 – 7. 7.1 and – 4 29 ANSWER 7.1 –

Order the rational numbers 2.2, -1.7, , , 0, least to greatest. Example 3 Ordering Rational Numbers Order the rational numbers 2.2, -1.7, , , 0, least to greatest. 5 2 3 1 – and from Begin by graphing the numbers on a number line. From least to greatest, the numbers are 1.7, , 0, , and 2.2. – 3 1 5 2

Order the rational numbers from least to greatest. Practice for Example 3 Order the rational numbers from least to greatest. 8. 2, 1.5, 3, 0.5 – ANSWER 3, 0.5, 1.5, 2 – 9. 0, 0.3, 0.6, 0.1 – ANSWER 0.6, 0.3, 0.1, 0 –

Order the rational numbers from least to greatest. Practice for Example 3 Order the rational numbers from least to greatest. 10. 3.2, 1, 2.5, – 2 1 ANSWER 3.2, , 1, 2.5 – 2 1 , 11. – 5 1 3 2 –1 ANSWER –1 – 3 2 1 , 5

The table shows the change in temperature every hour Example 4 Comparing Data Values The table shows the change in temperature every hour during a winter snowstorm. Hour 1 2 3 4 5 6 Change in Temperature (°F) – 0.8 1.2 – 1.6 – 2.9 0.5 – 1.3 a. Which hour shows the greatest increase in temperature? b. Which hour shows the greatest absolute decrease in temperature?

Example 4 Comparing Data Values SOLUTION a. Hour 2 shows the greatest increase in temperature, because 1.2 is the greatest positive number. b. The negative number that has the greatest absolute value is 2.9, so hour 4 shows the greatest absolute decrease in temperature. – 11

Practice for Example 4 12. In Example 4, does hour 2 or hour 5 show the greater increase in temperature? ANSWER Hour 2 In Example 4, does hour 3 or hour 6 show the greater absolute decrease in temperature? 13. ANSWER Hour 3