Decimal to Fraction and Fraction to Decimal Calculator

Convert a decimal such as 0.75 or 2.125 into a fraction in its simplest form — and recurring decimals too: type 0.(3) for 0.333… or 0.1(6) for 0.1666…, and see the NCERT Class 9 algebra method (let x = …, multiply by 10, subtract). Switch direction to turn any fraction into a decimal by long division and see where the digits start repeating.

Decimal

Recurring: put the repeating digits in brackets — 0.(3) = 0.333…, 0.1(6) = 0.1666…

Fraction (simplest form)

1/6

Mixed number

1/6

Percentage

16.6667%

Step-by-step solution

Let x = 0.1666666… (6 repeats, 1 does not)
Multiply by 10 to move the non-repeating part before the point: 10x = 1.666666…
Multiply by 10² to move one full repeating block too: 100x = 16.666666…
Subtract (the repeating tails cancel): 90x = 16 − 1 = 15
x = 15/90
Simplify: HCF(15, 90) = 15 → 1/6

How to use the decimal to fraction calculator

Choose “Decimal → fraction” or “Fraction → decimal”.
Type the decimal. For a recurring decimal, put the repeating digits in brackets: 0.(3), 0.1(6), 2.(142857).
Or type a fraction such as 3/8, 1/7 or 2 1/3 and choose the decimal places for the rounded value.
Read the simplest fraction (and mixed number), or the exact decimal with its repeating block, plus the steps.

Formulas

Terminating decimal	`0.abc = abc / 1000, then simplify by the HCF`
Pure recurring	`0.(ab) = ab / 99` one 9 for each repeating digit: 0.(3) = 3/9 = 1/3
Mixed recurring	`0.a(b) = (ab − a) / 90` one 9 per repeating digit, one 0 per non-repeating digit: 0.1(6) = 15/90 = 1/6
Fraction → decimal	`divide numerator by denominator (long division)`
Terminating test	`p/q (simplest) terminates ⇔ q = 2ᵐ × 5ⁿ`

Solved examples

Example 1: Convert 0.375 to a fraction.

3 decimal places → 375/1000
HCF(375, 1000) = 125

Answer: 3/8

Example 2: Convert 0.1666… to a fraction.

Let x = 0.1666…
10x = 1.666…, 100x = 16.666…
100x − 10x = 16 − 1 → 90x = 15

Answer: x = 15/90 = 1/6

Example 3: Write 5/11 as a decimal.

50 ÷ 11 = 4 r 6
60 ÷ 11 = 5 r 5
50 ÷ 11 = 4 r 6 — remainder 6 repeats

Answer: 0.454545… = 0.(45)

Why some decimals repeat for ever

When you divide by the denominator, each remainder is smaller than it, so only a limited number of different remainders are possible. As soon as one comes back, the same digits repeat. That is why every fraction gives either a terminating decimal or a recurring one — and why every recurring decimal can be turned back into a fraction (it is rational).

Whether it stops depends only on the denominator in simplest form: 3/8 terminates because 8 = 2³, but 1/6 recurs because 6 = 2 × 3 has the factor 3.

Writing recurring decimals

Textbooks put a bar over the repeating digits: 0.16̅ means 0.1666… and 0.4̅5̅ means 0.4545…. You cannot type a bar easily, so this calculator uses brackets — 0.1(6) and 0.(45) — and shows the bar form in the answer. Note that 0.(9) = 1 exactly.

🎯 Asked in competitive exams

This topic regularly appears in the quantitative aptitude section of:

SSC CGL & CHSL
RRB NTPC & Group D

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Frequently asked questions

How do I convert a decimal to a fraction?

Write the digits after the point over 1 followed by as many zeros as there are decimal places, then simplify: 0.75 = 75/100 = 3/4.

What is 0.333… as a fraction?

1/3. Let x = 0.333…, then 10x = 3.333…; subtracting, 9x = 3, so x = 3/9 = 1/3. Type it here as 0.(3).

How do I enter a recurring decimal?

Put the repeating digits in brackets: 0.(3) for 0.333…, 0.1(6) for 0.1666…, 1.2(45) for 1.24545…. Typing “0.333…” is not accepted because the calculator cannot know which digits repeat.

How do I know if a fraction will have a terminating decimal?

Simplify it and factorise the denominator. If it has no prime factors other than 2 and 5, the decimal terminates (7/20 = 0.35); otherwise it recurs (7/30 = 0.2333…).

Is 0.999… equal to 1?

Yes. Let x = 0.999…; 10x = 9.999…; subtracting gives 9x = 9, so x = 1. The calculator shows 0.(9) = 1.