Convert Ratio to Decimal

Calculator and formulas to convert a ratio into a decimal number

Ratio to Decimal Calculator

What is calculated?

This function converts a ratio into a decimal number. The ratio is interpreted as a division and the first value is divided by the second value.

Enter ratio

:
Represents: a ÷ b

Result
Decimal value of the ratio
The result shows the quotient a ÷ b rounded to the chosen number of decimal places

Ratio to Decimal Info

Conversion logic

The conversion is done by division:

  • a : b = a ÷ b
  • First number = Dividend
  • Second number = Divisor
  • Result = Quotient

Interpretation: The decimal result shows how many times the second value is contained in the first.

Quick examples
1:2 = 0.5
One half
3:4 = 0.75
Three quarters
2:1 = 2.0
Double
1:3 ≈ 0.333
One third
Decimal types

Terminating: 1:4 = 0.25
Repeating: 1:3 = 0.333...
Greater than 1: 5:2 = 2.5

Mathematical formulas for ratio to decimal

Basic formula
\[a:b = \frac{a}{b} = a \div b\] Division as decimal
Decimal representation
\[a:b = d.d_1d_2d_3...\] With fractional digits
Repeating decimal
\[a:b = d.\overline{p}\] When division does not terminate
Percent form
\[a:b \times 100 = p\%\] As percentage
Reciprocal
\[\frac{1}{a:b} = \frac{b}{a} = b:a\] Inverse ratio
Rounding
\[\text{round}(a:b, n) = r\] To n decimal places

Step-by-step example

Example: convert 50:120 to decimal

1Write ratio as division

\[50:120 = 50 \div 120 = \frac{50}{120}\]

50 divided by 120

2Perform division

50.000000 ÷ 120 = 0.416666...

Repeating decimal

3Round to desired decimal places

\[50:120 = 0.\overline{416} \approx \color{blue}{0.417}\]

Result: 0.417 (rounded to 3 decimal places)

Different division types

Terminating decimals
1:2 = 1 ÷ 2 = 0.5
\[1:2 = 0.5\]
3:4 = 3 ÷ 4 = 0.75
\[3:4 = 0.75\]
7:8 = 7 ÷ 8 = 0.875
\[7:8 = 0.875\]
Repeating decimals
1:3 = 1 ÷ 3 = 0.333...
\[1:3 = 0.\overline{3}\]
2:3 = 2 ÷ 3 = 0.666...
\[2:3 = 0.\overline{6}\]
1:7 = 1 ÷ 7 = 0.142857...
\[1:7 = 0.\overline{142857}\]
Greater than 1
3:2 = 3 ÷ 2 = 1.5
\[3:2 = 1.5\]
5:4 = 5 ÷ 4 = 1.25
\[5:4 = 1.25\]
7:3 = 7 ÷ 3 = 2.333...
\[7:3 = 2.\overline{3}\]

Practical applications

Speed

Example: distance to time

150 km in 2 hours

\[150:2 = 75 \text{ km/h}\]

Average speed

Density

Example: mass to volume

250 g at 100 ml

\[250:100 = 2.5 \text{ g/ml}\]

Density of the substance

Price-performance

10 Euro for 3 kg apples
10:3 ≈ 3.33 Euro/kg

Grades and scoring

85 out of 100 points
85:100 = 0.85 = 85%

Special cases and tips

Division by zero
\[a:0 = \text{undefined}\]

Warning: Division by 0 is not possible!

Very small ratios
\[1:1000 = 0.001\]

Scientific notation: 1×10⁻³

Rounding tips
  • For percentages: 2-3 decimal places
  • For money: 2 decimal places
  • For measurements: Depending on accuracy
  • For grades: 1-2 decimal places

Mathematical foundations

Division and decimal numbers

Division is one of the four basic arithmetic operations. When we convert a ratio a:b to a decimal number, we perform the division a ÷ b. The result can be terminating, repeating or non-terminating non-repeating.

Decimal expansion

Rational numbers (fractions) always have a terminating or repeating decimal expansion. The length of the period depends on the prime factors of the denominator.

Key concepts
  • Dividend: The number to be divided (a)
  • Divisor: The number by which we divide (b)
  • Quotient: The result of the division
  • Rounding: Limiting to n decimal places

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  •