A percentage expresses a quantity per hundred: p%= p100. To express one quantity as a percentage of another, divide by the reference quantity, then multiply by 100%. Use the same units first. Example 4530 x 100%=150%: 45 is 150% of 30. It is 50% greater than 30, not 150% greater. In the reverse comparison, 45-3045 x 100%=33 13%, so 30 is 33 13% less than 45. The comparison base changed. Conversions preserve value: 38=0.375=37.5%. A percentage above 100% is valid when the compared quantity exceeds the reference quantity.

A percentage expresses a quantity per hundred: \(p\%=\dfrac p{100}\). To express one quantity as a percentage of another, divide by the reference quantity, then multiply by \(100\%\). Use the same units first.

\(\dfrac{45}{30}\times100\%=150\%\): \(45\) is \(150\%\) of \(30\). It is \(50\%\) greater than \(30\), not \(150\%\) greater.

In the reverse comparison, \(\dfrac{45-30}{45}\times100\%=33\dfrac13\%\), so \(30\) is \(33\dfrac13\%\) less than \(45\). The comparison base changed.

Conversions preserve value: \(\dfrac38=0.375=37.5\%\). A percentage above \(100\%\) is valid when the compared quantity exceeds the reference quantity.

Percentages and the comparison base

Percentages and the comparison base