Equivalent Forms of Rational NumbersEquivalent Forms of Rational Numbers

Write a fraction in lowest terms, with a single digit numerator, that is about the same as each decimal: 0.52, 0.13, 0.74, 0.88.

COURSE 3 LESSON 4-2COURSE 3 LESSON 4-2

12 , , ,

18

34

78

4-2

Write 3.225 as a mixed number.

Equivalent Forms of Rational NumbersEquivalent Forms of Rational NumbersCOURSE 3 LESSON 4-2COURSE 3 LESSON 4-2

3.225 = Write as a fraction with the denominator 1. 3.225

1

Since there are 3 digits to the right of the decimal, multiply the numerator and denominator by 103 or 1,000.

=3,2251,000

Simplify using the GCF, 25.=3,225 ÷ 251,000 ÷ 25 =

12940

Write as a mixed number.= 39

40

4-2

Write the repeating decimal 0.23 as a fraction in

simplest form.

Equivalent Forms of Rational NumbersEquivalent Forms of Rational NumbersCOURSE 3 LESSON 4-2COURSE 3 LESSON 4-2

Step 1 Let the variable n represent the given decimal.

n = 0.23

Step 2 Since 2 digits repeat, multiply each side by 102, or 100.

100n = 23.23

100n = 23.232323 . . .

– n = – 0.232323 . . .

99n = 23.000000

99n = 23

Use the Subtraction Property of Equality.

Simplify.

Step 3 Subtract to eliminate the repeating part, 0.23.

4-2

(continued)

Equivalent Forms of Rational NumbersEquivalent Forms of Rational NumbersCOURSE 3 LESSON 4-2COURSE 3 LESSON 4-2

Step 4 Solve the new equation.

Divide each side by 99.99n99

2399=

Simplify.n =2399

The repeating decimal 0.23 equals . 2399

Check Use a calculator to divide 23 by 99.

23 99 0.23232323

4-2

Equivalent Forms of Rational NumbersEquivalent Forms of Rational Numbers

Write each as a fraction in simplest form.

1. 2. – 3. 2.75

4. 0.2 5. 0.4 6. 7.25

57

29

COURSE 3 LESSON 4-2COURSE 3 LESSON 4-2

25

3042

1218

23

– 34

2

2599

7

4-2