ALGEBRA READINESSChapter 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.

Example 1

Show that (a) 1.9 and (b) 8.25 are rational numbers.

Identifying Rational Numbers

a. 1.9 = 110

9Write as mixed number.

=10

19Write as improper fraction.

b. 8.25 =–Write as mixed number.= 8

4

1–

Write as improper fraction.=4

33–

–

Both numbers are rational numbers because they are quotients of two integers.

-8 25

100

Show that the number is a rational number by writing it as a quotient of two integers.

ANSWER5

21. 0.4

2. 1.15 ANSWER20

23

3. 1.2– ANSWER5

6–

4. 2.6– ANSWER5

13–

Practice for Example 1

Example 2 Graphing and Comparing Rational Numbers

Graph 3.9 and on a number line. Then tell whichis greater.

2

7––

On the number line, is to the right of 3.9. So, 2

7– –

2

7– 3.9.> –

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–

– –

–

–

Graph the numbers on a number line. Then tell which number is greater.

ANSWER5

25. and 0.3

5

2–

6. and 4.28

11– – ANSWER

8

11–

7. 7.1 and–4

29– ANSWER 7.1–

Practice for Example 2

Example 3 Ordering Rational Numbers

From least to greatest, the numbers are 1.7, , 0, ,

and 2.2.

–3

1–

5

2

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.

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– – –

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,

5

2, –1

2

1

ANSWER –1 –3

2

2

1, ,

5

1,

5

2

Practice for Example 3

Example 4 Comparing Data Values

The table shows the change in temperature every hourduring a winter snowstorm.

1

Change in

Temperature (°F)

Hour

– 0.8

2

1.2

3

– 1.6

4

– 2.9

5

0.5

6

– 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

a. Hour 2 shows the greatest increase in temperature, because 1.2 is the greatest positive number.

SOLUTION

b. The negative number that has the greatest absolute value is 2.9, so hour 4 shows the greatest absolute decrease in temperature.

–

In Example 4, does hour 2 or hour 5 show the greater increase in temperature?

12.

ANSWER Hour 2

In Example 4, does hour 3 or hour 6 show the greater absolute decrease in temperature?

13.

ANSWER Hour 3

Practice for Example 4