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Fractions practice

Convert fractions and decimals

Convert fractions to decimals with explicit rounding and convert finite written decimals back to exact fractions.

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For a fraction, divide and round to the requested decimal places when necessary; an exact halfway case rounds away from zero. For a written finite decimal, use its place value to form an exact fraction and simplify. Keep approximate and exact equality distinct.

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Learning objective

What this activity builds

Distinguish an exact terminating decimal from a rounded approximation and preserve the exact value of a given finite decimal.

Worked example

Round 2/3 to three decimal places, then convert the written decimal 0.667 to an exact fraction.

2/3 ≈ 0.667; exactly, 0.667 = 667/1000.

The decimal for 2/3 repeats, so 0.667 is a rounded approximation. The finite number 0.667 means 667 thousandths; it is not exactly 2/3, even though it came from rounding that fraction.

Teaching notes

Make the practice count

  • Write an approximation sign whenever rounding changes the exact value.
  • Count decimal places before choosing a power-of-ten denominator.
  • Contrast a terminating case, such as 3/8 = 0.375, with a recurring case.

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Math SheetNameScoreTeacherDate/ 20Fractions and DecimalsConvert fractions to rounded decimals and finite decimals to exact fractions. Fraction-to-decimal answers use 3 places andround halfway values away from zero.1.Write as a decimal.23=2.Write as a decimal.18=3.Write as a decimal.23=4.Write as a decimal.25=5.Write as a decimal.25=6.Write as a decimal.310=7.Write as a decimal.18=8.Write as a decimal.23=9.Write as a decimal.34=10.Write as a decimal.58=11.Write as a fraction.0.667=12.Write as a fraction.0.253=13.Write as a fraction.0.111=14.Write as a fraction.0.924=math-sheet.comPage 1 / 2
Math SheetNameScoreTeacherDate/ 20Fractions and DecimalsConvert fractions to rounded decimals and finite decimals to exact fractions. Fraction-to-decimal answers use 3 places andround halfway values away from zero.15.Write as a fraction.0.508=16.Write as a fraction.0.465=17.Write as a fraction.0.364=18.Write as a fraction.0.363=19.Write as a fraction.0.279=20.Write as a fraction.0.541=math-sheet.comPage 2 / 2

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