Fraction & Decimal Converter

Convert between fractions and decimals seamlessly.

Fraction to Decimal Converter

How to Use

Choose conversion direction

Select fraction-to-decimal or decimal-to-fraction based on your starting value.

Enter numerator and denominator (or decimal)

For fractions, input both parts. For decimals, enter the decimal number including repeating forms.

View the converted result

See the decimal value or fully simplified fraction in lowest terms.

Check mixed number format if needed

For values greater than 1, see the result presented as an improper fraction and as a mixed number.

How to convert fractions to decimals

Divide the Numerator by the Denominator.

Real-World Examples & Use Cases

Cooking and Recipe Measurements

Recipes use fractions (1/3 cup, 2/3 teaspoon, 3/4 pound) while kitchen scales often display decimals. Converting 2/3 cup to a decimal for precise measuring: 2 ÷ 3 = 0.667 cups. Converting a decimal weight from a scale (0.375 pounds) back to a fraction: 0.375 = 3/8 pound. When scaling recipes or using digital kitchen scales, being able to move between fractions and decimals ensures measurements translate accurately between a recipe's format and the measuring tool being used.

Construction and Woodworking Measurements

Carpentry and construction use fractional measurements on measuring tapes (1/4 inch, 3/16 inch, 5/8 inch) while CAD software and digital calipers often use decimals. Converting 5/16 inch to decimal: 5 ÷ 16 = 0.3125 inches. Converting a caliper reading of 0.4375 inches back to a fraction: 0.4375 = 7/16. Building projects require moving between these formats constantly — fractional tape measures, decimal CNC specifications, and mixed measurement situations all benefit from instant conversion.

Student Math and Homework Help

Students learning fractions, decimals, and their relationships use this converter to check answers, understand equivalences, and develop number sense. Seeing that 1/8 = 0.125, 1/4 = 0.25, 3/8 = 0.375, 1/2 = 0.5 builds understanding of the decimal number system. Students converting 0.625 back to a fraction (625/1000 → 5/8) practice simplification using GCF. Mixed number conversions (changing 2.333... to 2 and 1/3) connect terminating and repeating decimal concepts to fractions.

Finance and Investment Calculations

While modern finance uses decimals, historical stock prices were quoted in fractions (1/8 = $0.125 per share increments before decimalization). Bond prices still use fractional notation: 99 31/32 means 99 + 31/32 = 99.96875. Interest rates in fractions (3 5/8% = 3.625%) appear in mortgage documents and bond prospectuses. Financial analysts working with historical data or international markets sometimes encounter fractional pricing that must be converted to decimals for calculations and spreadsheet input.

How It Works

Fraction-to-decimal conversion: Decimal = Numerator / Denominator Examples: 1/4 = 0.25 (terminates) 1/3 = 0.333... (repeating; written as 0.3̄) 5/6 = 0.8333... (repeating; written as 0.83̄) Decimal-to-fraction conversion: 1. Count decimal places (n) 2. Write: decimal_digits / 10^n 3. Simplify by dividing numerator and denominator by GCF Example: 0.375 = 375/1000 GCF(375, 1000) = 125 = 3/8 Repeating decimals to fractions: Let x = 0.333... 10x = 3.333... 10x - x = 3 → 9x = 3 → x = 3/9 = 1/3 For 0.142857142857... (repeating block of 6 digits): Let x = 0.142857... 1,000,000x - x = 142857 999,999x = 142857 → x = 142857/999999 = 1/7

Frequently Asked Questions

What is the difference between a terminating and a repeating decimal?▼

A terminating decimal has a finite number of digits after the decimal point: 1/4 = 0.25, 3/8 = 0.375. A repeating decimal has a pattern of digits that repeats infinitely: 1/3 = 0.3333..., 1/7 = 0.142857142857... A fraction produces a terminating decimal when its denominator (in lowest terms) has only factors of 2 and/or 5. Any other prime factor in the denominator produces a repeating decimal.

What fractions produce repeating vs. terminating decimals?▼

If the simplified fraction's denominator has only prime factors 2 and 5, the decimal terminates. Examples: 1/2 (2), 1/4 (2²), 1/5 (5), 3/8 (2³), 7/25 (5²) all terminate. If the denominator has any other prime factor, it repeats: 1/3, 1/6, 1/7, 1/9, 1/11, 1/12 all repeat. The number of repeating digits equals the length of the repeating cycle in the decimal expansion.

How do I convert a mixed number to a decimal?▼

A mixed number like 2 3/4 converts by treating the integer and fraction separately: the integer part (2) stays, and the fractional part (3/4 = 0.75) is added: 2 + 0.75 = 2.75. Alternatively, convert to an improper fraction first: 2 3/4 = 11/4, then divide: 11 ÷ 4 = 2.75. Both methods produce the same result.

Are all decimals convertible to fractions?▼

All terminating and repeating decimals can be expressed as exact fractions (rational numbers). Truly irrational numbers like π (3.14159...) and √2 (1.41421...) cannot be expressed as fractions — their decimal expansions never terminate and never repeat. Most practical measurements and calculations involve rational numbers (terminating or repeating decimals) that convert exactly to fractions.

How is 0.999... related to 1?▼

Mathematically, 0.999... (repeating nines) is exactly equal to 1, not just approximately equal. Proof: let x = 0.999...; then 10x = 9.999...; subtract: 10x - x = 9; therefore 9x = 9; x = 1. Another proof: 1/3 = 0.333..., multiply both sides by 3: 3/3 = 0.999..., but 3/3 = 1. This counterintuitive result is a consequence of how decimal notation works — different representations can encode the same real number.

Related Tools

Explore other tools in this category.

Number to Words Converter

Convert any number into its full English word representation.

Roman Numeral Converter

Convert between Arabic numbers and Roman numerals instantly in both directions.

Ohm's Law Calculator

Calculate voltage, current, resistance, and power using Ohm's Law and the power formula.

Percentage Calculator

Calculate percentages, increases, and decreases instantly.

LCM & GCF Calculator

Calculate the Least Common Multiple and Greatest Common Factor of numbers.

Prime Number Checker

Check if a number is prime or composite instantly.