Last updated: 2026-05-25

Three ways to write the same number

A single number can be written in three equivalent ways depending on context: as a fraction (precise ratio), a decimal (positional notation), or a percentage (ratio per hundred). This converter shows all three forms at once, so the most suitable representation is always available for the situation at hand.

How to use

All three fields accept input. Entering a value in any field updates the other two:

• Decimal → enter 0.5 to see 1/2 and 50%.
• Fraction → enter a decimal like 0.75 to work backwards to the fraction display 3/4.
• Percent → enter 75 to set 75%, seeing 0.75 and 3/4.

The Fraction field shows:

• Proper fractions (1/2) for values between −1 and 1.
• Mixed numbers (1 3/4) or whole numbers for values outside that range.

The Percent field shows the decimal multiplied by 100, with up to four significant digits.

The three representations

Fractions

A fraction $\frac{p}{q}$ expresses an exact ratio of two integers. It is the canonical form for values that repeat infinitely in decimal (like $\frac{1}{3} = 0.\overline{3}$) and for values where precision matters more than scale — measurements, recipes, and music theory.

Decimals

Decimal notation places digits after the decimal point to represent values less than 1. It is convenient for arithmetic but loses information for repeating decimals (you must round or truncate). The decimal form is the input here because it is the most portable format between calculators and spreadsheets.

Percentages

Percent means "per hundred". To convert a decimal to percent, multiply by 100:

$$p\% = \text{decimal} \times 100$$

Percentages are intuitive for comparisons — "75% pass rate" is more readable than "0.75" for most audiences.

Conversion table

Fraction	Decimal	Percent
1/2	0.5	50%
1/3	0.3333…	33.3333%
1/4	0.25	25%
3/4	0.75	75%
5/8	0.625	62.5%
7/16	0.4375	43.75%
1 1/2	1.5	150%

Fraction approximation

The calculator approximates the fraction using the Stern–Brocot tree or a mediants algorithm capped at a maximum denominator of 1,000. This means:

• Common fractions (1/2, 3/4, 5/8) are found exactly.
• Irrational decimals (like 0.7071… for $\frac{1}{\sqrt{2}}$) get the closest rational approximation within the denominator limit — in that case 707/1000.
• Repeating decimals typed with enough digits (e.g. 0.333333) surface the exact fraction 1/3.

Applications

Teaching — showing students that 0.5, 1/2, and 50% are the same number is a cornerstone of numeracy.

Finance — interest rates are quoted as percentages, but compound-interest formulas use decimals, and some ratio analysis uses fractions. Moving fluidly between forms avoids rounding errors.

Cooking — a recipe might call for 3/4 cup while a kitchen scale reads grams. Converting to a decimal first, then to a weight percentage of the whole recipe, ties the forms together.

Frequently Asked Questions (FAQ)

What happens with a value greater than 1?

The fraction output shows a mixed number — for example, 1.75 → 1 3/4. The percent output shows the corresponding value above 100%, e.g. 175%.

Why does the fraction sometimes differ slightly from the expected value?

The denominator is capped at 1,000. A decimal that needs a larger denominator for an exact representation shows the closest approximation instead. For example, 0.142857 (which is 1/7) requires recognizing the repeat; entering 0.142857142857 gives the fraction 1/7 exactly.

Can a percentage be entered directly?

Yes. The Percent field is editable: entering 75 sets 75%, and the Decimal and Fraction fields update accordingly. All three fields accept input.