Equivalent Forms of Rational Numbers COURSE 3 LESSON 4-2 Equivalent 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. 1 2 , , , 8 3 4 7 4-2

Equivalent Forms of Rational Numbers COURSE 3 LESSON 4-2 Equivalent Forms of Rational Numbers Write 3.225 as a mixed number. 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. = 3,225 1,000 Simplify using the GCF, 25. = 3,225 ÷ 25 1,000 ÷ 25 129 40 Write as a mixed number. = 3 9 40 4-2

Equivalent Forms of Rational Numbers COURSE 3 LESSON 4-2 Equivalent Forms of Rational Numbers Write the repeating decimal 0.23 as a fraction in simplest form. 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

Equivalent Forms of Rational Numbers COURSE 3 LESSON 4-2 Equivalent Forms of Rational Numbers (continued) Step 4 Solve the new equation. Divide each side by 99. 99n 99 23 = Simplify. n = 23 99 The repeating decimal 0.23 equals . 23 99 Check Use a calculator to divide 23 by 99. 23 99 0.23232323 4-2

Equivalent Forms of Rational Numbers COURSE 3 LESSON 4-2 Equivalent 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 30 42 12 18 5 7 2 3 – 3 4 2 2 9 2 5 25 99 7 4-2