How to Convert Fractions to Decimals
Converting a fraction to a decimal is straightforward: divide the numerator by the denominator.
Types of Decimal Results
Terminating Decimals
When the division ends exactly (no remainder), you get a terminating decimal. This happens when the denominator only has prime factors of 2 and/or 5.
- 1/2 = 0.5 (denominator = 2)
- 1/4 = 0.25 (denominator = 2^2)
- 1/5 = 0.2 (denominator = 5)
- 1/8 = 0.125 (denominator = 2^3)
Repeating Decimals
When the division never ends evenly, the decimal repeats. This happens when the denominator has prime factors other than 2 or 5.
- 1/3 = 0.333... (repeating 3)
- 1/6 = 0.1666... (repeating 6)
- 1/7 = 0.142857142857... (repeating 142857)
- 1/9 = 0.111... (repeating 1)
Examples
Example 1: Convert 3/4 to Decimal
Problem:
3/4 = ?
Divide 3 by 4
Long division: 3.00 / 4
4 goes into 3 zero times, add decimal point
4 goes into 30 seven times (4 × 7 = 28), remainder 2
4 goes into 20 five times (4 × 5 = 20), remainder 0
Result: 3/4 = 0.75 (terminating decimal)
Example 2: Convert 5/6 to Decimal
Problem:
5/6 = ?
Divide 5 by 6
Long division: 5.000... / 6
6 goes into 5 zero times, add decimal point
6 goes into 50 eight times (6 × 8 = 48), remainder 2
6 goes into 20 three times (6 × 3 = 18), remainder 2
Pattern repeats: always remainder 2
Result: 5/6 = 0.8333... (repeating decimal, 3 repeats)
Example 3: Convert 1/8 to Decimal
Problem:
1/8 = ?
Divide 1 by 8
Long division: 1.000 / 8
8 goes into 10 one time (8 × 1 = 8), remainder 2
8 goes into 20 two times (8 × 2 = 16), remainder 4
8 goes into 40 five times (8 × 5 = 40), remainder 0
Result: 1/8 = 0.125 (terminating decimal)
Example 4: Convert 2/3 to Decimal
Problem:
2/3 = ?
Divide 2 by 3
Long division: 2.000... / 3
3 goes into 2 zero times, add decimal point
3 goes into 20 six times (3 × 6 = 18), remainder 2
Pattern repeats: always remainder 2
Result: 2/3 = 0.666... (repeating decimal, 6 repeats)
Example 5: Convert 7/10 to Decimal
Problem:
7/10 = ?
When denominator is 10, 100, 1000...
Simply move the decimal point
7/10 = 0.7 (one decimal place)
7/100 = 0.07 (two decimal places)
Result: 7/10 = 0.7 (terminating decimal)