Decimal-Fraction Conversion Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Decimal-Fraction Conversion.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Converting between fraction form and decimal form of a number: divide numerator by denominator for fraction-to-decimal, and use place value to go the other way.

Fractions and decimals are two ways to write the same number. \frac{3}{4} and 0.75 are the same amount—just different notation.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Fraction to decimal: divide numerator by denominator. Decimal to fraction: use place value and simplify.

Common stuck point: Repeating decimals: \frac{1}{3} = 0.333\ldots doesn't terminate, and students round prematurely.

Sense of Study hint: Try long division on paper: write the numerator inside the division bracket and the denominator outside, then divide step by step.

Worked Examples

Example 1

easy
Convert \frac{7}{8} to a decimal.

Solution

  1. 1
    Divide the numerator by the denominator: 7 \div 8.
  2. 2
    7.000 \div 8: 8 goes into 70 eight times (64), remainder 6. Bring down: 60. 8 into 60 is 7 (56), remainder 4. Bring down: 40. 8 into 40 is 5, remainder 0.
  3. 3
    Result: 7 \div 8 = 0.875.

Answer

0.875
To convert a fraction to a decimal, perform long division of the numerator by the denominator. When the remainder reaches zero, the decimal terminates. A fraction terminates when the denominator (in lowest terms) has only factors of 2 and/or 5.

Example 2

medium
Convert 0.36 to a fraction in simplest form.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Convert \frac{3}{5} to a decimal.

Example 2

hard
Convert 0.125 to a fraction, then determine whether \frac{1}{8} and 0.125 are equal by comparing their decimal equivalents.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

fractionsdecimals