Represent probabilities as fractions / decimals / percentages
Theory
The same probability can be written as a fraction, a decimal or a percentage — three names for one value. Build an equivalent fraction with \(100\) on the bottom and both other forms follow: \(\dfrac{1}{4}=0.25=25\%\).
A probability can be shown as a fraction, a decimal or a percentage. They are three ways of writing one value.
Build an equivalent fraction with \(100\) on the bottom. The hundredths give the percentage straight away.
The same hundredths read as a decimal in the second decimal place: \(\dfrac{25}{100}=0.25=25\%\).
Common probabilities written all three ways.
| Fraction | Decimal | Percentage |
|---|---|---|
| \(\dfrac{1}{4}\) | \(0.25\) | \(25\%\) |
| \(\dfrac{1}{2}\) | \(0.5\) | \(50\%\) |
| \(\dfrac{3}{4}\) | \(0.75\) | \(75\%\) |
| \(\dfrac{2}{5}\) | \(0.4\) | \(40\%\) |
| \(\dfrac{1}{5}\) | \(0.2\) | \(20\%\) |
How to convert a probability
- Build an equivalent fraction with \(100\) on the bottom.
- Read the top number as the percentage.
- Write the hundredths as a decimal in the second decimal place.
| \(\dfrac{1}{4}\) | \(=\) | \(\dfrac{25}{100}\) |
| \(=\) | \(0.25=25\%\) |
| \(\dfrac{3}{4}\) | \(=\) | \(\dfrac{75}{100}\) |
| \(=\) | \(0.75=75\%\) |
| \(\dfrac{2}{5}\) | \(=\) | \(\dfrac{40}{100}\) |
| \(=\) | \(0.4=40\%\) |
| \(\dfrac{1}{5}\) | \(=\) | \(\dfrac{20}{100}\) |
| \(=\) | \(20\%\) |
No — it is \(20\%\), not \(15\%\).
Common pitfalls
Frequently asked questions
How do I turn a fraction into a percentage?
Build an equivalent fraction with \(100\) on the bottom. The top number is the percentage, so \(\dfrac{3}{4}=\dfrac{75}{100}=75\%\).
How do I turn a fraction into a decimal?
Make hundredths (or tenths), then read the place value. \(\dfrac{1}{4}=\dfrac{25}{100}=0.25\).
Why is \(\dfrac{1}{5}\) not \(15\%\)?
The digits of a fraction are not the digits of a percentage. Change to hundredths: \(\dfrac{1}{5}=\dfrac{20}{100}=20\%\).
Are the three forms really equal?
Yes. \(\dfrac{1}{2}\), \(0.5\) and \(50\%\) are the same value written three different ways.