Step-by-step conversion rules with worked examples and practice exercises
This tutorial explains how to convert between percentages, fractions, and decimals. Each example is solved step by step, followed by practice exercises with answers.
| From → To | Rule | Example |
|---|---|---|
| Percent → Fraction | Write over 100, then reduce | \(20\% = \tfrac{20}{100} = \tfrac{1}{5}\) |
| Percent → Decimal | Divide by 100 | \(50\% = 0.5\) |
| Fraction → Decimal | Numerator ÷ denominator | \(\tfrac{3}{4} = 0.75\) |
| Fraction → Percent | Fraction → decimal → ×100 | \(\tfrac{3}{4} = 75\%\) |
| Decimal → Percent | ×100 | \(0.1 = 10\%\) |
| Decimal → Fraction | Use a power-of-ten denominator, then reduce | \(0.06 = \tfrac{6}{100} = \tfrac{3}{50}\) |
Convert \(20\%\) to an equivalent fraction in reduced form.
A percentage is already a fraction with denominator \(100\):
\[ 20\% = \frac{20}{100} \]Divide numerator and denominator by \(20\):
\[ \frac{20}{100} = \frac{1}{5} \]So \(20\% = \dfrac{1}{5}\).
Convert \( \dfrac{3}{4} \) to a percentage.
Convert to a decimal by dividing numerator by denominator:
\[ \frac{3}{4} = 0.75 \]Multiply by \(100\):
\[ 0.75 = 75\% \]Convert \(0.06\) to a fraction in reduced form.
Write over \(100\):
\[ 0.06 = \frac{6}{100} \]Divide numerator and denominator by \(2\):
\[ \frac{6}{100} = \frac{3}{50} \]Convert \(0.1\) to a percentage.
Multiply by \(100\):
\[ 0.1 = \frac{10}{100} = 10\% \]Convert \( \dfrac{3}{5} \) to a decimal and a percentage.
Decimal: divide numerator by denominator:
\[ \frac{3}{5} = 0.6 \]Percentage: multiply by \(100\):
\[ 0.6 = 60\% \]Convert \(0.08\) to a percentage and a reduced fraction.
Percentage:
\[ 0.08 = \frac{8}{100} = 8\% \]Reduced fraction:
\[ \frac{8}{100} = \frac{2}{25} \]Try each conversion, then expand Answer to check your work.
Convert \(2.3\) into a percentage.
Convert \( \dfrac{4}{5} \) into a percentage and a decimal.
Convert \(50\%\) into a fraction and a decimal.
Convert \(0.8\) into a percentage and a reduced fraction.
Convert \( \dfrac{1}{3} \) into a percentage and a decimal.
Exact:
\[ \frac{1}{3} = 33.\overline{3}\% = 0.\overline{3} \]Rounded to two decimal places:
\[ \approx 33.33\%, \quad \approx 0.33 \]Convert \(0.7\) into a percentage and a reduced fraction.
Convert \(210\%\) into a decimal and a reduced fraction.
Write the percentage over \(100\) and reduce. For example, \(20\% = \tfrac{20}{100} = \tfrac{1}{5}\).
Divide the numerator by the denominator to get a decimal, then multiply by \(100\). For example, \(\tfrac{3}{4} = 0.75 = 75\%\).
Multiply the decimal by \(100\) and add the percent sign. For example, \(0.1 = 10\%\).
Write the decimal as a fraction with a power-of-ten denominator, then reduce. For example, \(0.06 = \tfrac{6}{100} = \tfrac{3}{50}\).
Divide the percentage by \(100\). For example, \(50\% = 0.5\) and \(210\% = 2.1\).
Last updated: October 17, 2026