How to Convert Decimals to Fractions

Count digits after the decimal point. That count is the power of 10 in the denominator.

• 1 digit → tenths → denominator 10
• 2 digits → hundredths → denominator 100
• 3 digits → thousandths → denominator 1000

Examples

• 0.7 = 7/10
• 0.25 = 25/100 → simplify → 1/4
• 0.125 = 125/1000 → simplify → 1/8
• 0.4 = 4/10 → 2/5
• 2.75 = 275/100 → 11/4 or mixed 2 3/4

Leading zeros after the point still count as places: 0.05 = 5/100 = 1/20. The “5” sits in hundredths, so denominator 100, not 10.

Whole numbers alone are already fractions over 1 (6 = 6/1). Pure decimals between 0 and 1 start with numerator from the digits and denominator a power of 10 before simplifying.

After writing n / 10ᵏ, reduce to lowest terms:

1. Find GCD of numerator and denominator.
2. Divide both by that GCD.
3. Stop when GCD is 1.

Worked: 0.36

• 0.36 = 36/100
• GCD(36, 100) = 4
• 36÷4=9, 100÷4=25 → 9/25

Worked: 0.875

• 875/1000
• GCD(875, 1000) = 125
• 875÷125=7, 1000÷125=8 → 7/8

Euclidean algorithm for GCD is the reliable hand method; tools can show the steps. Full GCD/LCM methods live in the GCD and LCM guide and the free GCD and LCM calculator.

Same GCD skill simplifies ratios (12:18 → 2:3) — see how to simplify a ratio.

If the absolute value is greater than 1, separate the whole part from the fractional part.

Example: 3.4

• Whole = 3; fractional = 0.4 = 4/10 = 2/5
• Mixed = 3 2/5
• Improper: 3 2/5 = 17/5

Example: 5.125

• 0.125 = 125/1000 = 1/8
• Mixed = 5 1/8; improper = 41/8

Negatives

−2.5 = −(2 + 1/2) = −2 1/2 or −5/2. Keep the sign on the whole mixed form or on the improper fraction, not on both pieces inconsistently.

Choose mixed form for measurements people read aloud (“two and a half cups”); choose improper form for algebra multiplication and division of fractions.

Repeating decimals need a short algebra trick, not place value alone.

Single digit repeat: 0.3̅

1. Let x = 0.333…
2. 10x = 3.333…
3. 10x − x = 3 → 9x = 3 → x = 1/3

Two digit repeat: 0.18̅

1. x = 0.181818…
2. 100x = 18.1818…
3. 100x − x = 18 → 99x = 18 → x = 18/99 = 2/11

Repeat after a non-repeating part: 0.16̅

1. x = 0.1666…
2. 10x = 1.666…
3. 100x = 16.666…
4. 100x − 10x = 15 → 90x = 15 → x = 15/90 = 1/6

Rule of thumb: multiply by 10^r to shift one full repeat block of length r, subtract, then simplify. For exact homework answers, prefer the fraction over a rounded decimal like 0.17.

Going the other direction (1/6 → 0.16̅) is covered in how to convert fractions to decimals.

All three describe rational amounts with different scaling.

• Decimal → percent: × 100 (0.375 → 37.5%)
• Percent → decimal: ÷ 100 (37.5% → 0.375)
• Decimal → fraction: place value + GCD (0.375 = 375/1000 = 3/8)
• Fraction → percent: (a/b)×100 or decimal first then ×100

Example chain

0.2 = 1/5 = 20%. 0.125 = 1/8 = 12.5%. 0.3̅ = 1/3 ≈ 33.3̅%.

When the question is “what percent is 12 of 80?”, you may never write a decimal explicitly — use (12÷80)×100. The free percentage calculator and percentage guide cover those modes with everyday money and grade examples.

Ratios like 2:3 are not automatically “0.666…” of a whole until you pick a total of parts; convert carefully.

Use a converter for speed, then verify with place value and GCD so you still own the method.

1. Open the free decimal to fraction converter.
2. Enter a terminating decimal (and repeating form if the tool supports it).
3. Read the simplified proper or improper fraction.
4. Note mixed-number form when |value| > 1.
5. Confirm by dividing numerator ÷ denominator back to the decimal.
6. For hand checks, rewrite via /10, /100, or /1000 and cancel the GCD.
7. For repeating input, confirm the algebraic subtraction method matches the tool.
8. Convert to percent if your context needs % labels.

Cooking often wants mixed numbers; algebra worksheets often want improper fractions in lowest terms — match the form to the audience.

Common traps:

• Wrong denominator — 0.05 is 5/100, not 5/10
• Skipping simplify — leaving 25/100 instead of 1/4
• Treating 0.333 as 333/1000 forever when the intent was repeating 1/3
• Dropping the whole number when converting 2.5 → writing only 1/2
• Rounding then converting — 1/3 rounded to 0.33 becomes 33/100, which is not 1/3
• Sign errors on negative decimals

Sanity checks: 0.5=1/2, 0.25=1/4, 0.75=3/4, 0.2=1/5, 0.125=1/8, 0.3̅=1/3. If those fail, fix place value before harder cases.

Practice five terminating decimals and one repeating decimal by hand, then confirm with the converter.