Benchmark fraction / decimal / percentage equivalence
Theory
Benchmark fractions, decimals and percentages are three ways of writing the same amount out of one whole. Per cent means "out of 100", so writing an amount over \(100\) links the three forms.
Per cent means "out of 100", so \(25\%\) is \(\dfrac{25}{100}\).
Writing an amount with a denominator of \(100\) turns it into hundredths, which is both a decimal and a percentage: \(\dfrac{75}{100} = 0.75 = 75\%\).
The benchmarks to know are \(\dfrac{1}{2} = 0.5 = 50\%\), \(\dfrac{1}{4} = 0.25 = 25\%\), \(\dfrac{3}{4} = 0.75 = 75\%\) and \(\dfrac{1}{10} = 0.1 = 10\%\).
These benchmark amounts are worth learning by heart.
| Fraction | Decimal | Percentage |
|---|---|---|
| \(\dfrac{1}{2}\) | \(0.5\) | \(50\%\) |
| \(\dfrac{1}{4}\) | \(0.25\) | \(25\%\) |
| \(\dfrac{3}{4}\) | \(0.75\) | \(75\%\) |
| \(\dfrac{1}{10}\) | \(0.1\) | \(10\%\) |
How to move between the three forms
- Write the amount with a denominator of \(100\).
- Read the hundredths as a decimal.
- Read the same hundredths as a percentage.
Per cent means out of 100.
| \(50\%\) | \(=\) | \(0.5\) |
Write over 100 and simplify.
| \(25\%\) | \(=\) | \(\dfrac{1}{4}\) |
Scale the fraction to hundredths.
| \(\dfrac{3}{4}\) | \(=\) | \(75\%\) |
A quarter is 25 out of 100.
| \(\dfrac{1}{4}\) | \(=\) | \(25\%\) |
Common pitfalls
Frequently asked questions
What does per cent mean?
Per cent means "out of 100". \(25\%\) is \(25\) out of \(100\), or \(\dfrac{25}{100}\).
How do you turn a fraction into a percentage?
Write it with a denominator of \(100\). \(\dfrac{3}{4} = \dfrac{75}{100} = 75\%\).
Is 0.25 the same as 25%?
Yes. \(0.25\) is \(25\) hundredths, which is \(25\%\). Be careful: \(2.5\%\) is \(0.025\), not \(0.25\).
What are the main benchmarks to learn?
\(\dfrac{1}{2} = 0.5 = 50\%\), \(\dfrac{1}{4} = 0.25 = 25\%\), \(\dfrac{3}{4} = 0.75 = 75\%\) and \(\dfrac{1}{10} = 0.1 = 10\%\).