Convert Fraction to Decimal

Convert fractions to decimals with selectable precision

Fraction → Decimal Calculator

What is calculated?

This tool converts a fraction to a decimal number. Optionally include a whole number part. The number of decimal places can be chosen.

Enter fraction
Example: 3/4 = 0.75
Result
Fraction will be converted to a decimal with chosen precision

Fraction → Decimal Info

Properties

Conversion rules:

Perform division Selectable precision Mixed numbers Automatic rounding

Note: For negative mixed numbers the sign applies to the whole value.

Examples
Simple: 3/4 = 0.75
Repeating: 1/3 = 0.333...
Mixed: 2 3/4 = 2.75
Negative: -1 2/3 = -1.667


Formulas & Rules for Fraction → Decimal Conversion

Main formula
\[\frac{a}{b} = a \div b\] Divide numerator by denominator
Mixed number
\[n\frac{a}{b} = n + \frac{a}{b}\] Integer part plus fraction
Negative numbers
\[-n\frac{a}{b} = -(n + \frac{a}{b})\] Sign applies to whole value
Rounding
\[\text{to n places}\] Automatic rounding
Finite decimals
\[\frac{1}{2^m \cdot 5^n}\] Denominator factors only 2 and 5
Repeating decimals
\[\frac{1}{3} = 0.\overline{3}\] Infinite repetition
Place-value notation
\[0.75 = \frac{7}{10} + \frac{5}{100}\] Sum of powers of ten
Percent form
\[0.75 = 75\%\] Decimal × 100

Step-by-step Examples

Example 1: Simple fraction 3/4
Step 1: Perform division
\[\frac{3}{4} = 3 \div 4 = 0.75\]

Divide numerator by denominator.

Step 2: Result
\[\frac{3}{4} = \color{blue}{0.75}\]
Example 2: Mixed number 2 2/3
Step 1: Convert fraction
\[\frac{2}{3} = 2 \div 3 = 0.6666...\]
Step 2: Add whole part
\[2\frac{2}{3} = 2 + 0.6666... = \color{blue}{2.6667}\] (rounded to 4 decimal places)
More examples
Half:
\[\frac{1}{2} = 0.5\]
Eighth:
\[\frac{5}{8} = 0.625\]
Repeating:
\[\frac{1}{6} = 0.1666...\]
Negative:
\[-\frac{3}{4} = -0.75\]
Practical tip
Negative mixed numbers:
\[-2\frac{2}{3}\] is interpreted as \[-(2\frac{2}{3})\]
The sign applies to the entire value.
Steps for fraction → decimal conversion
1. Divide numerator by denominator
2. Add whole number
3. Round to desired precision
4. Observe sign

Dividing the numerator by the denominator yields the decimal form of the fraction.

Applications of fraction → decimal conversion

Decimals are used across many everyday contexts:

Finance & Trade
  • Prices and currencies
  • Interest rates and returns
  • Discounts and taxes
  • Exchange rates
Engineering & Measurement
  • Precise dimensions
  • Tolerances and deviations
  • Engineering applications
  • Scientific data
Statistics & Analysis
  • Averages
  • Probabilities
  • Percentages
  • Trends and comparisons
Everyday math
  • Recipes and portions
  • Time calculations
  • Calculator input
  • Computer programs

Mathematical context

Description

Converting fractions to decimals is a fundamental operation that maps rational numbers to their decimal representation. This transformation simplifies comparisons and numeric computations. Some fractions yield finite decimals, others produce repeating decimals — a rich area of number theory.

Summary

Decimals bridge exact fractional arithmetic and practical numerical work. They enable precise calculations in science and engineering, simplify comparisons, and are essential for digital computation. Understanding fraction-to-decimal conversion is key to mathematical fluency and real-world problem solving.




More Fraction Calculators

Add Fractions  •  Compare Fractions  •  Decimal to Fraction  •  Divide Fractions  •  Fraction to Decimal  •  Fraction to Percent  •  Egyptian Fraction  •  Mixed number to improper Fraction  •  Multiply Fractions  •  Percent to Fraction  •  Simplify Fraction  •  Subtract Fractions  •