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Fractions and decimals

Convert between fractions and decimals that end exactly.

Practice + answer key · 2 pages

Worksheet settings10 questions · 2 columns · A4
Original denominator range

Choose denominators between 2 and 100. Only terminating-decimal denominators in the selected range are eligible.

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mathsprig-1
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Fractions and decimalsFractions and decimals. Practice. Write 1/5 as an exact decimal. Write 0.1875 as a fraction in simplest form. Write 4/5 as an exact decimal. Write 0.875 as a fraction in simplest form. Write 3/10 as an exact decimal. Write 0.75 as a fraction in simplest form. Write 3/4 as an exact decimal. Write 0.375 as a fraction in simplest form. Write 7/16 as an exact decimal. Write 0.500 as a fraction in simplest form.Name __________________________Date _______________Fractions and decimalsConvert as requested. Write fraction answers in simplest form.Worked exampleWrite 3/8 as an exact decimal. → 0.375Multiply the denominator by 125 to reach 1000.1.Write 1/5 as an exact decimal.2.Write 0.1875 as a fraction insimplest form.3.Write 4/5 as an exact decimal.4.Write 0.875 as a fraction insimplest form.5.Write 3/10 as an exact decimal.6.Write 0.75 as a fraction insimplest form.7.Write 3/4 as an exact decimal.8.Write 0.375 as a fraction insimplest form.9.Write 7/16 as an exact decimal.10.Write 0.500 as a fraction insimplest form.MathSprig · mathsprig.site · support@mathsprig.sitePage 1 of 1mathsprig-1 · mathsprig-v1 · 311cb4be
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Practice + answer key · 2 pages

Decimals

What you’ll practice

Convert terminating proper fractions to decimals and finite decimals to simplest fractions.

Use tenths, hundredths or thousandths to connect a fraction to a decimal. When you go the other way, write the decimal as a fraction and simplify it.

How this skill works

A reduced denominator made only from factors 2 and 5 can be scaled to a power of ten. That power of ten determines how many decimal places are needed.

To convert a displayed decimal back to a fraction, use its digits over the matching power of ten, then reduce numerator and denominator together.

Worked example

Write 3/8 as an exact decimal.
  1. Multiply the denominator by 125 to reach 1000.
  2. Multiply the numerator by the same factor: 3 × 125 = 375.
  3. 3/8 = 375/1000 = 0.375.

Answer: 0.375

Teaching notes

  • Use the same multiplier for the numerator and denominator.
  • A finite decimal may need more than two places, as 1/8 = 0.125 shows.
Practice questions
  1. Write 1/5 as an exact decimal.
  2. Write 0.1875 as a fraction in simplest form.
  3. Write 4/5 as an exact decimal.
  4. Write 0.875 as a fraction in simplest form.
  5. Write 3/10 as an exact decimal.
  6. Write 0.75 as a fraction in simplest form.
  7. Write 3/4 as an exact decimal.
  8. Write 0.375 as a fraction in simplest form.
  9. Write 7/16 as an exact decimal.
  10. Write 0.500 as a fraction in simplest form.
Answers and steps
  1. 0.2
    1. Scale the denominator to 10: 1/5 = 2/10 = 0.2.
  2. 3/16
    1. The decimal has 4 displayed fractional places, so it is 1875/10000. Simplify to 3/16.
  3. 0.8
    1. Scale the denominator to 10: 4/5 = 8/10 = 0.8.
  4. 7/8
    1. The decimal has 3 displayed fractional places, so it is 875/1000. Simplify to 7/8.
  5. 0.3
    1. Scale the denominator to 10: 3/10 = 3/10 = 0.3.
  6. 3/4
    1. The decimal has 2 displayed fractional places, so it is 75/100. Simplify to 3/4.
  7. 0.75
    1. Scale the denominator to 100: 3/4 = 75/100 = 0.75.
  8. 3/8
    1. The decimal has 3 displayed fractional places, so it is 375/1000. Simplify to 3/8.
  9. 0.4375
    1. Scale the denominator to 10000: 7/16 = 4375/10000 = 0.4375.
  10. 1/2
    1. The decimal has 3 displayed fractional places, so it is 500/1000. Simplify to 1/2.