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How to Convert Fractions to Decimals Without A Calculator Ks2

Reviewed by Calculator Editorial Team

Converting fractions to decimals is a fundamental math skill that helps with more advanced calculations. This guide explains how to do it without a calculator, with clear steps, examples, and a built-in converter for quick reference.

Introduction

Fractions and decimals are two ways to represent parts of a whole. Converting between them is essential for understanding measurements, money, and many other real-world quantities. For Key Stage 2 (KS2) students, learning this skill builds a strong foundation for future math learning.

There are two main methods for converting fractions to decimals: long division and equivalent fractions. This guide focuses on the long division method, which is more commonly used for KS2 students.

Step-by-Step Method

To convert a fraction to a decimal using long division:

  1. Write the fraction with the numerator (top number) divided by the denominator (bottom number).
  2. Divide the numerator by the denominator.
  3. If there's a remainder, add a decimal point and zeros to the numerator.
  4. Continue dividing until you either get a zero remainder or the decimal repeats.
  5. Write down the decimal result.

Formula

To convert a fraction a/b to a decimal:

a ÷ b = decimal result

Important Notes

  • Terminating decimals end after a few digits (e.g., 1/2 = 0.5).
  • Repeating decimals have digits that repeat indefinitely (e.g., 1/3 ≈ 0.333...).
  • Always check your work by converting back to the original fraction.

Worked Examples

Example 1: Simple Fraction

Convert 3/4 to a decimal.

  1. 3 ÷ 4 = 0 with a remainder of 3.
  2. Add decimal point and zeros: 3.00 ÷ 4.
  3. 30 ÷ 4 = 7 with a remainder of 2.
  4. Bring down another 0: 20 ÷ 4 = 5.
  5. Final result: 0.75

Check: 0.75 × 4 = 3, which matches the numerator.

Example 2: Repeating Decimal

Convert 1/3 to a decimal.

  1. 1 ÷ 3 = 0 with a remainder of 1.
  2. Add decimal point and zeros: 1.00 ÷ 3.
  3. 10 ÷ 3 = 3 with a remainder of 1.
  4. Bring down another 0: 10 ÷ 3 = 3 with a remainder of 1.
  5. This pattern repeats indefinitely, so the decimal is 0.333...

Check: 0.333... × 3 ≈ 1, which matches the numerator.

Comparison of Fraction to Decimal Conversions
Fraction Decimal Type
1/2 0.5 Terminating
1/3 0.333... Repeating
3/8 0.375 Terminating
5/7 0.714285... Repeating

Tips for Success

  • Practice with simple fractions first before moving to more complex ones.
  • Use paper and pencil to keep track of your work during long division.
  • Remember that some fractions convert to repeating decimals, which is normal.
  • Check your work by converting the decimal back to a fraction to verify accuracy.
  • Use the built-in calculator below for quick reference when practicing.

FAQ

Why do some fractions convert to repeating decimals?

Fractions with denominators that have prime factors other than 2 or 5 (like 3, 7, 11, etc.) will typically convert to repeating decimals. This happens because the division doesn't terminate cleanly.

How do I know when to stop dividing?

Stop when you either get a zero remainder or when the decimal starts to repeat. For KS2 students, it's usually sufficient to stop after 4-5 decimal places for most fractions.

Can I convert mixed numbers to decimals this way?

Yes, first convert the mixed number to an improper fraction, then use the long division method. For example, 1 1/2 becomes 3/2, which converts to 1.5.