How to Convert Decimals to Fractions: A Complete Guide
Converting between decimals and fractions is a fundamental math skill used in cooking, construction, finance, and science. This guide walks you through every type of conversion — from simple terminating decimals to tricky repeating decimals — with step-by-step examples.
Converting Terminating Decimals
A terminating decimal has a finite number of digits after the decimal point. Converting these is straightforward:
- Count the decimal places — how many digits are after the decimal point?
- Write the decimal digits as the numerator (ignore the decimal point)
- The denominator is 10 raised to the number of decimal places
- Simplify by dividing both by their greatest common factor (GCF)
Example: Convert 0.75 to a Fraction
| Step | Result |
|---|---|
| 2 decimal places | Denominator = 10² = 100 |
| Write as fraction | 75/100 |
| GCF of 75 and 100 = 25 | 75÷25 / 100÷25 |
| Simplified | 3/4 |
Common Conversions to Memorize
| Decimal | Fraction | Percentage |
|---|---|---|
| 0.5 | 1/2 | 50% |
| 0.25 | 1/4 | 25% |
| 0.75 | 3/4 | 75% |
| 0.2 | 1/5 | 20% |
| 0.125 | 1/8 | 12.5% |
| 0.333... | 1/3 | 33.33% |
Converting Repeating Decimals
A repeating decimal has digits that repeat infinitely (e.g., 0.333..., 0.142857142857...). To convert these, use algebra:
- Let x = the repeating decimal
- Multiply x by 10 raised to the number of repeating digits
- Subtract the original x from the multiplied value
- Solve for x and simplify
Example: Convert 0.333... to a Fraction
x = 0.333...
10x = 3.333...
10x - x = 3.333... - 0.333...
9x = 3
x = 3/9 = 1/3
Example: Convert 0.1666... to a Fraction
x = 0.1666...
10x = 1.666...
100x = 16.666...
100x - 10x = 16.666... - 1.666...
90x = 15
x = 15/90 = 1/6
What About Irrational Numbers?
Some decimals cannot be expressed as exact fractions. These are called irrational numbers:
- π (pi) = 3.14159... — cannot be expressed as a fraction. Common approximations: 22/7 or 355/113
- √2 = 1.41421... — the diagonal of a unit square. No exact fraction exists
- e = 2.71828... — Euler's number, the base of natural logarithms
Important: For irrational numbers, calculators provide the closest rational approximation. The more decimal places you use, the more accurate the fraction.
Converting Fractions to Decimals
The reverse is simpler: divide the numerator by the denominator.
- 3/4 = 3 ÷ 4 = 0.75
- 2/3 = 2 ÷ 3 = 0.666...
- 7/8 = 7 ÷ 8 = 0.875
Why This Matters in Real Life
- Cooking: Recipes use fractions (1/2 cup, 3/4 tsp) but digital scales show decimals (0.5 cup)
- Construction: Measurements are often in fractions (1/16 inch) but calculators output decimals
- Finance: Interest rates may be quoted as decimals but need fractions for certain calculations
- Education: Standardized tests frequently test decimal-fraction conversion
Key Takeaways
- Terminating decimals: count places, write over power of 10, simplify
- Repeating decimals: use algebra (multiply, subtract, solve)
- Irrational numbers: no exact fraction exists — use approximations
- Fraction to decimal: just divide numerator by denominator
- Use our Decimal to Fraction Calculator for instant conversions with step-by-step breakdowns