Decimal to Ratio Converter

Calculator and formulas to convert a decimal value to a ratio

Decimal to Ratio Calculator

What is calculated?

This function converts a decimal number into a ratio. The decimal is first converted to a fraction, simplified and then displayed as a ratio in the format a:b.

Enter decimal number

Examples: 0.5, 0.75, 1.25, 0.125

Result
Ratio: :
The ratio is displayed in simplified form automatically

Decimal to Ratio Info

Conversion process

The conversion is performed in three steps:

  1. Decimal → Fraction
  2. Simplify fraction
  3. Fraction → Ratio

Tip: Decimals are especially useful for converting percentages and probabilities to ratios.

Quick examples
0.5 = 1:2
One half corresponds to 1 to 2
0.25 = 1:4
One quarter corresponds to 1 to 4
0.75 = 3:4
Three quarters corresponds to 3 to 4
1.5 = 3:2
One and a half corresponds to 3 to 2
Special cases

Repeating decimals: Numbers like 0.333... (= 1/3) result in exact ratios.
Whole numbers: 2.0 becomes 2:1


Formulas for Decimal to Ratio

Basic formula
\[d = \frac{a}{b} \Rightarrow a:b\] Decimal to ratio
Decimal to fraction
\[0.d_1d_2...d_n = \frac{d_1d_2...d_n}{10^n}\] n decimal places
Simplify
\[\frac{a}{b} = \frac{a \div \gcd(a,b)}{b \div \gcd(a,b)}\] Simplify using gcd
Repeating decimal
\[0.\overline{d} = \frac{d}{9}, \quad 0.\overline{dd} = \frac{dd}{99}\] Periodic fractions
Mixed numbers
\[n.d = n + 0.d = \frac{n \cdot 10^k + d}{10^k}\] Integer part + decimal part
Percent to ratio
\[p\% = \frac{p}{100} = p:100\] Direct conversion

Step-by-step example

Example: convert 0.6 to a ratio

1Decimal to fraction

\[0.6 = \frac{6}{10}\]

6 over 10 (one decimal place)

2Simplify fraction

\[\frac{6}{10} = \frac{6 \div 2}{10 \div 2} = \frac{3}{5}\]

gcd(6, 10) = 2

3Write as ratio

\[\frac{3}{5} = \color{blue}{3:5}\]

Meaning: 3 parts to 5 parts

Result: 0.6 corresponds to the ratio 3:5

Advanced examples

Example: 0.125 (1/8)
\[0.125 = \frac{125}{1000}\] \[\frac{125}{1000} = \frac{1}{8} = \color{blue}{1:8}\]

gcd(125, 1000) = 125

Interpretation: 1 part to 8 parts

Example: 1.25 (1¼)
\[1.25 = \frac{125}{100}\] \[\frac{125}{100} = \frac{5}{4} = \color{blue}{5:4}\]

gcd(125, 100) = 25

Interpretation: 5 parts to 4 parts

Repeating decimals

Examples with repeating decimals
0.333... = ⅓
\[0.\overline{3} = \frac{1}{3} = \color{blue}{1:3}\]
0.666... = 2/3
\[0.\overline{6} = \frac{2}{3} = \color{blue}{2:3}\]
0.090909... = 1/11
\[0.\overline{09} = \frac{1}{11} = \color{blue}{1:11}\]

Rule: 0.\overline{d} = d/9, 0.\overline{dd} = dd/99, 0.\overline{ddd} = ddd/999, etc.

Practical applications

Probabilities

Example: coin toss

Probability for heads: 0.5 = 1:2

\[P(\text{Heads}) = 0.5 = \frac{1}{2} = 1:2\]
Percentages

Example: 25% discount

25% = 0.25 = 1:4 (1 part discount to 4 parts total)

\[25\% = 0.25 = \frac{1}{4} = 1:4\]
Chemistry: concentrations

0.1 M solution means 0.1 mol/L = 1:10 ratio to standard concentration

Finance: interest rates

3.5% interest = 0.035 = 35:1000 = 7:200 (simplified)

Mathematical background

Understanding decimals

Decimal numbers are a representation for fractions with powers of ten in the denominator. Every finite decimal can be represented exactly as a fraction and thus as a ratio.

Conversion logic

The conversion process uses the place value logic of the decimal system. Each decimal place corresponds to a power of ten in the denominator.

Key properties
  • Uniqueness: Each decimal has exactly one simplified ratio
  • Reversibility: Ratio → Decimal by division
  • Periodicity: Rational numbers produce repeating or terminating decimals
  • Simplifiability: Result is always fully simplified




More Ratio Functions

Aspect Ratio  •  Compare Ratios  •  Decimal to Ratio  •  Fraction to Ratio  •  Ratio-Calculator  •  Ratio Simplifier  •  Ratio to Decimal  •  Ratio to Fraction  •  Scale Ratio  •