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Equivalent Forms of Rational Numbers

1 2. 1 8. 3 4. 7 8. , , ,. 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. 4-2. 3,225 1,000. 3.225 1. 3.225 =.

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Equivalent Forms of Rational Numbers

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  1. 1 2 1 8 3 4 7 8 , , , 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. 4-2

  2. 3,225 1,000 3.225 1 3.225 = Write as a fraction with the denominator 1. Since there are 3 digits to the right of the decimal, multiply the numerator and denominator by 103 or 1,000. = 3,225 ÷ 25 1,000 ÷ 25 = = Simplify using the GCF, 25. 9 40 129 40 Write as a mixed number. = 3 COURSE 3 LESSON 4-2 Equivalent Forms of Rational Numbers Write 3.225 as a mixed number. 4-2

  3. 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. Step 3 Subtract to eliminate the repeating part, 0.23. 100n = 23.23 100n = 23.232323 . . . Use the Subtraction Property of Equality. – n = – 0.232323 . . . 99n = 23.000000 Simplify. 99n = 23 COURSE 3 LESSON 4-2 Equivalent Forms of Rational Numbers Write the repeating decimal 0.23 as a fraction in simplest form. 4-2

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

  5. 2 3 3 4 – 2 25 99 7 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 12 18 30 42 5 7 2 9 2 5 4-2

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