Fractions, Decimals and Percentages

Fractions, decimals and percentages are three languages for the same idea: a part of a whole. You can always translate between them.

• Fraction → decimal: divide top by bottom. $\dfrac{3}{5} = 3 \div 5 = 0.6$.
• Decimal → percentage: multiply by $100$. $0.6 \times 100 = 60\%$.
• Percentage → fraction: put it over $100$ and simplify. $35\% = \dfrac{35}{100} = \dfrac{7}{20}$.

So $\dfrac{3}{5} = 0.6 = 60\%$ are three ways to write one quantity. Knowing all three lets you compare numbers that look different at a glance.

Exam checkpoint

A fraction, decimal and percentage can describe the same amount. A decimal is based on tenths, hundredths or thousandths; a percent is ‘out of 100’. Convert a fraction to a decimal by division, and convert a decimal to a percent by multiplying by 100. Use the form that makes the question easiest.

Short worked example. $\frac{7}{10}=0.7=70\%$. The denominator 10 becomes tenths in the decimal, then 70 hundredths in the percent.