How to Convert Fractions to Decimals (With Examples)

Why Convert Fractions to Decimals?

Fractions and decimals are two ways of expressing the same value. Converting between them is essential for:

• Comparing numbers: Is 3/8 bigger than 0.4? Converting to decimals makes comparisons instant.
• Calculators and computers: Most technology works with decimals, not fractions.
• Real-world applications: Money, measurements, and statistics use decimals.
• Standardized tests: Many exam questions require you to convert between formats.

The good news? The process is simple — it's just division.

The Division Method

To convert any fraction to a decimal, divide the numerator by the denominator.

Formula: a/b = a ÷ b

Example 1: Convert 3/4 to a decimal

3 ÷ 4 = 0.75

Example 2: Convert 7/8 to a decimal

7 ÷ 8 = 0.875

Example 3: Convert 1/3 to a decimal

1 ÷ 3 = 0.333... (repeating)

Tip: If you don't have a calculator, use long division. Place a decimal point after the numerator and add zeros, then divide normally.

Long division walkthrough: 5/8

1. 5 ÷ 8 = 0 remainder 5
2. 50 ÷ 8 = 6 remainder 2
3. 20 ÷ 8 = 2 remainder 4
4. 40 ÷ 8 = 5 remainder 0

Result: 5/8 = 0.625

Common Fraction-to-Decimal Conversions

Memorizing these common conversions saves time on tests:

| Fraction | Decimal | |---|---| | 1/2 | 0.5 | | 1/3 | 0.333... | | 1/4 | 0.25 | | 1/5 | 0.2 | | 1/8 | 0.125 | | 1/10 | 0.1 | | 2/3 | 0.666... | | 3/4 | 0.75 | | 2/5 | 0.4 | | 3/5 | 0.6 | | 3/8 | 0.375 | | 5/8 | 0.625 | | 7/8 | 0.875 |

Pro tip: If the denominator is a power of 10 (10, 100, 1000), the conversion is instant. For example, 47/100 = 0.47.

Repeating Decimals

Some fractions produce decimals that never end — they repeat a pattern forever. These are called repeating decimals.

Examples:

• 1/3 = 0.333... (written as 0.3̄)
• 1/6 = 0.1666... (written as 0.16̄)
• 2/7 = 0.285714285714... (written as 0.2̄8̄5̄7̄1̄4̄)
• 1/9 = 0.111... (written as 0.1̄)

How to identify repeating decimals

A fraction produces a terminating decimal (one that ends) only if the denominator's prime factors are limited to 2 and 5. Otherwise, it will repeat.

• 1/4 = 0.25 ✅ terminates (4 = 2²)
• 1/8 = 0.125 ✅ terminates (8 = 2³)
• 1/3 = 0.333... ❌ repeats (3 is not 2 or 5)
• 1/6 = 0.1666... ❌ repeats (6 = 2 × 3)

Rounding repeating decimals

For practical purposes, round to the required number of decimal places:

• 1/3 ≈ 0.33 (rounded to 2 places)
• 2/3 ≈ 0.67 (rounded to 2 places)

Mixed Numbers to Decimals

A mixed number like 3 1/4 has a whole number part and a fraction part.

Method: Convert the fraction part to a decimal and add it to the whole number.

• 3 1/4 = 3 + 0.25 = 3.25
• 5 3/8 = 5 + 0.375 = 5.375
• 2 1/3 = 2 + 0.333... = 2.333...

Alternatively, convert the mixed number to an improper fraction first, then divide:

• 3 1/4 = 13/4 = 13 ÷ 4 = 3.25

Both methods give the same result.

Practice Problems

Convert these fractions to decimals:

1. 5/8
2. 2/5
3. 7/20
4. 4 3/4
5. 5/6

Answers: (1) 0.625 (2) 0.4 (3) 0.35 (4) 4.75 (5) 0.8333...

Need More Help?

If you want step-by-step walkthroughs for any fraction conversion, or need help with related topics like how fractions work or percentages, Mr Jarven AI Tutor is here for you.

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