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Decimal Conversions: Fractions, Decimals, and Bar Notation

Learn how to convert fractions to decimals and decimals to fractions, including terminating and repeating decimals. Practice converting and simplifying fractions and mixed numbers to decimals. Examples provided for easy understanding.

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Decimal Conversions: Fractions, Decimals, and Bar Notation

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  1. Math 7 Converting Fractions to Decimals & Decimals to Fractions

  2. Vocabulary • Terminating Decimal—A decimal whose digits end. • Repeating Decimal—A decimal whose digits repeats in groups of one or more. • Bar Notation—In repeating decimals, the line or bar placed over the digits that repeat. • 0.33333…= 0.3 • 0.121212…= 0.12 • 11.3858585…= 11.385

  3. Changing Fractions to Decimals • Divide the numerator by the denominator

  4. ¼ 5 ¾ 1/8 7 3/5 7/9 8 1/3 1/11 6 4/9 5/8 2/3 1 3/11 6 2/5 4 5/6 Write each fraction or mixed number as a decimal.

  5. There were 6 girls and 18 boys in Mrs. Johnson’s math class. Write the number of girls as a fraction of the number of boys. Then convert the fraction to a repeating decimal.

  6. In a neighborhood of 72 families, 18 families own one or more cats. Write the number of families who own one or more cats as a fraction. Then convert the fraction to a decimal.

  7. In Italy, about 74 of every 100 people use cellular telephones. Write the fraction of cellular phone users in Italy. Then write the fraction as a decimal.

  8. Converting Decimals to Fractions • Use the place value of the final digit as the denominator. • Be sure to simplify! • Example: .62 = 62 = 31 100 50 (I used 100 as the denominator because the final digit (2) is in the hundredths place.)

  9. 0.48 0.56 0.3 2.8 .72 4.6 Write each number as a fraction in simplest form.

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