Decimal Calculator

Convert decimals to fractions and fractions to decimals instantly. Automatically simplifies fractions and shows the percentage equivalent.

⚡ Quick Calculator Get a fast estimate

Decimal Number

0.75 as a fraction

3/4

Numerator

Denominator

As percentage

75%

Verification

3 ÷ 4 = 0.7500000000

Mixed number

3/4

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How to Use

Choose a tab: "Decimal to Fraction" or "Fraction to Decimal". Enter your number(s) and the calculator instantly converts and simplifies, showing all equivalent forms.

The Extended Calculator adds a number line visualization, a place value chart, and a repeating decimals reference table. The Professional Calculator shows long division steps for repeating decimals, continued fraction expansions, and multi-base conversion.

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📊 Extended Calculator More options, charts, and scenario comparison

Decimal number

As Fraction

5/8

Numerator

Denominator

Decimal places

Conversion Methods

Decimal to Fraction: Multiply by 10ⁿ (where n = decimal places), simplify by GCD.

Fraction to Decimal: Divide numerator by denominator.

Terminating decimal: Denominator (simplified) has only factors of 2 and 5.

Repeating decimal: Denominator has prime factors other than 2 and 5.

Repeating → fraction: Multiply by 10^period, subtract, solve for x.

Worked Example

0.625 to fraction: 0.625 = 625/1000; GCD(625,1000)=125 → 5/8

7/8 to decimal: 7 ÷ 8 = 0.875 (terminating)

1/3 to decimal: 1 ÷ 3 = 0.333... (repeating)

0.272727... to fraction: 100x − x = 27 → 99x = 27 → x = 3/11

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🔬 Professional Calculator Complete parameters, sensitivity analysis, and detailed breakdown

Decimal Expansion of 1/7

0.142857

Type

Repeating

Non-repeating part

(none)

Repeating block

142857

Period length

Long division: 1 ÷ 7 = 0.[142857]

Frequently Asked Questions

Set x = 0.333..., then 10x = 3.333... Subtract: 9x = 3, x = 1/3. For two-digit repeating (0.272727...): 100x − x = 27; 99x = 27; x = 27/99 = 3/11.

A fraction p/q (in lowest terms) produces a terminating decimal only if q has no prime factors other than 2 and 5. Since 3 is a prime factor of the denominator, 1/3 repeats.

Yes. 0.999... (repeating forever) equals exactly 1. Proof: x = 0.999..., 10x = 9.999..., 10x − x = 9, 9x = 9, x = 1. This is a mathematical fact, not an approximation.

A mixed number combines a whole number and a proper fraction. 7/4 = 1¾. To convert: divide to get the whole part; the remainder over the denominator gives the fractional part.

Decimal Calculator

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Conversion Methods

Worked Example

Frequently Asked Questions

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