Benchmark fraction / decimal / percentage equivalence
Theory
Percent means out of 100, so any percentage is a number of hundredths, and \(100\%\) is the whole. The same amount can be written three ways: \(\dfrac{3}{5} = 0.6 = 60\%\). This Year 6 maths page shows how to move between fractions, decimals and percentages for the benchmark amounts, and how to compare and order numbers written in different forms.
Percent (\(\%\)) means out of \(100\): \(35\% = \dfrac{35}{100} = 0.35\).
\(100\%\) is the whole amount. The part that is left is \(100\%\) minus the part you know.
Fraction to percentage: make an equivalent fraction with denominator \(100\): \(\dfrac{3}{5} = \dfrac{60}{100} = 60\%\).
Decimal to percentage: write the decimal in hundredths: \(0.6 = 0.60 = 60\%\); \(0.07 = 7\%\).
Percentage to fraction: write it over \(100\) and simplify: \(40\% = \dfrac{40}{100} = \dfrac{2}{5}\).
Benchmark equivalences to know:
| Fraction | Decimal | Percentage |
|---|---|---|
| \(\dfrac{1}{100}\) | \(0.01\) | \(1\%\) |
| \(\dfrac{1}{10}\) | \(0.1\) | \(10\%\) |
| \(\dfrac{1}{5}\) | \(0.2\) | \(20\%\) |
| \(\dfrac{1}{4}\) | \(0.25\) | \(25\%\) |
| \(\dfrac{1}{2}\) | \(0.5\) | \(50\%\) |
| \(\dfrac{3}{4}\) | \(0.75\) | \(75\%\) |
| \(1\) | \(1\) | \(100\%\) |
Changing between the forms
- Fraction to percentage: make the denominator \(100\); the numerator is the percentage.
- Decimal to percentage: write two decimal places and read the hundredths.
- Percentage to decimal: write the percentage as hundredths: \(35\% = 0.35\).
Ordering mixed forms
- Change every number to a percentage.
- Order the percentages, then write the original forms in that order.
| \(\dfrac{3}{5}\) | \(=\) | \(\dfrac{60}{100}\) |
\(0.6\) and \(60\%\).
(i) \(0.35\)
(ii) \(0.07\)
(iii) \(0.9\)
(i) \(35\%\)
(ii) \(7\%\)
(iii) \(90\%\) (\(0.9 = 0.90\))
| \(40\%\) | \(=\) | \(\dfrac{40}{100}\) |
| \(\dfrac{40}{100}\) | \(=\) | \(\dfrac{2}{5}\) |
\(\dfrac{2}{5}\), as in the first diagram.
As percentages: \(30\%\), \(25\%\), \(35\%\), \(20\%\).
\(\dfrac{1}{5}, \dfrac{1}{4}, 0.3, 35\%\).
(i) What percentage chose soccer?
(ii) What percentage chose netball?
(iii) What percentage chose something else?
| \(100 - 30 - 45\) | \(=\) | \(25\) |
(i) \(30\%\)
(ii) \(45\%\)
(iii) \(25\%\)
\(0.34\). It uses the digits \(3\) and \(4\) but is only \(34\%\).
\(\dfrac{7}{100} = 0.07 = 7\%\).
\(0.4 = 0.40\), which is \(40\) hundredths, so \(0.4 = 40\%\). \(4\%\) is \(0.04\).
Common pitfalls
Frequently asked questions
What does percent mean?
Out of \(100\). \(35\%\) means \(35\) out of \(100\).
What is 100% of 37?
\(37\), the whole amount.
How do you change a fraction to a percentage?
Make the denominator \(100\): \(\dfrac{3}{5} = \dfrac{60}{100} = 60\%\).
How do you change a decimal to a percentage?
Write it in hundredths: \(0.6 = 0.60 = 60\%\).
Is 0.4 the same as 4%?
No. \(0.4 = 40\%\); \(4\% = 0.04\).
What fraction is 40%?
\(\dfrac{40}{100} = \dfrac{2}{5}\).