Free Fraction Calculator — Decimal to Fraction

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Quick answer: 5.5 = 11/2 — write it over 10 (55/10) and divide top and bottom by 5. 0.8333… = 5/6, 15/2 = 7½, and 2/3 = 0.666… The calculator above converts any decimal, repeating decimal, or fraction between all five forms — with the exact working shown, never floating-point guesses.

Last updated: October 2026

How to write 5.5 as a fraction

Short answer: 5.5 = 11/2 (or 5½). Put 5.5 over a power of 10 — one decimal place means ÷10, giving 55/10 — then divide the top and bottom by their greatest common divisor, 5. That gives 11/2.

The method is the same for any terminating decimal: count the decimal places, write the number over 10, 100, 1000, … and reduce. 0.75 has two decimal places → 75/100 → divide by 25 → 3/4. 1.005 has three → 1005/1000 → divide by 5 → 201/200. Type any decimal into the "Decimal → Fraction" mode above and the calculator shows the reduction step it used.

How to convert a repeating decimal to a fraction

Short answer: 0.8333… = 5/6. Let x = 0.8333…, multiply by 10 to shift the repeat (10x = 8.333…), then subtract: 10x − x = 7.5, so 9x = 75/10 = 75/90 after clearing the decimal — divide top and bottom by 15 → 5/6.

This shift-and-subtract trick works for any repeating decimal: 0.333… → x = 3/9 = 1/3; 0.142857142857… → x = 142857/999999 = 1/7; 0.1666… → (16 − 1)/90 = 15/90 = 1/6. The classic edge case falls out naturally too: 0.999… = 9/9 = 1. Use the "Repeating → Fraction" mode above — type the non-repeating part (e.g. 0.8) and the repeating digit(s) (e.g. 3) — and it shows the algebra.

How to write 15/2 as a mixed number

Short answer: 15/2 = 7½. Divide 15 by 2: 7 fits with a remainder of 1. The whole number is 7, and the leftover 1 stays over the denominator 2.

Any improper fraction (top bigger than bottom) converts the same way: divide, keep the whole part, and put the remainder over the original denominator — 11/2 becomes 5½, 23/4 becomes 5¾, 9/3 is just 3. Going the other direction is the reverse: multiply the whole number by the denominator and add the numerator, 5¾ = (5 × 4 + 3)/4 = 23/4. The calculator accepts mixed numbers like "7 1/2" as input too.

How to write 2/3 as a decimal

Short answer: 2/3 = 0.666…, with the 6 repeating forever — written 0.(6). Divide 2 by 3: the remainder 2 keeps returning, so the digit 6 repeats without end.

Fractions divide into two kinds: terminating (1/2 = 0.5, 3/4 = 0.75) and repeating (1/3 = 0.(3), 1/7 = 0.(142857), 5/6 = 0.8(3)). A fraction terminates exactly when its denominator, in lowest terms, has no prime factors other than 2 and 5. The "Fraction → Decimal" mode marks which kind you got and shows the repeating block in parentheses.

How to simplify a fraction

Short answer: 18/24 = 3/4. Find the greatest common divisor of 18 and 24 (it's 6) and divide both by it: 18 ÷ 6 = 3, 24 ÷ 6 = 4.

A fraction is in lowest terms when the top and bottom share no common factor. Big ones reduce the same way — 150/225 divides by 75 → 2/3, 1024/2048 divides by 1024 → 1/2. Because this calculator uses exact integer arithmetic (not floating point), even very large numerators and denominators reduce correctly. Try the "Simplify" mode with your own fraction.

One value, every form

Short answer: every rational number has four faces — decimal, fraction, mixed number, and (sometimes) a repeating decimal. Here is 0.75 shown all four ways; the calculator gives you all of them at once for any input.

Form	0.75	5.5	0.8333…
Decimal	0.75	5.5	0.8(3)
Fraction	3/4	11/2	5/6
Mixed number	3/4	5 1/2	5/6

Notice the middle column: 5.5 and 11/2 and 5½ are the same number wearing different clothes. Homework usually wants the fraction, recipes want the mixed number, and spreadsheets want the decimal — the tool answers whichever one you were actually asked for.

Frequently asked questions

What is 5.5 as a fraction?

11/2, or 5½. Write 5.5 over 10 to get 55/10, then divide top and bottom by their greatest common divisor, 5.

What is 0.8333… (repeating) as a fraction?

5/6. Let x = 0.8333…, then 10x = 8.333…; subtracting gives 9x = 7.5, so x = 75/90, which simplifies to 5/6.

What is 15/2 as a mixed number?

7½. 15 ÷ 2 = 7 with a remainder of 1 — the whole number is 7 and the leftover 1 stays over the denominator 2.

What is 2/3 as a decimal?

0.666…, with the 6 repeating forever (written 0.(6)). Divide 2 by 3 and the remainder 2 keeps coming back, so the 6 repeats without end.

How do you simplify 18/24?

Divide both by their greatest common divisor, 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4, so 18/24 = 3/4.