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Make connections between equivalent fractions, decimals and percentages (ACMNA131)

Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies (ACMNA132)

Source: Australian Curriculum, Assessment and Reporting Authority (ACARA)


Percentages are another way of expressing fractions with denominators that are ten, 100, 1000 and so on.
Per centum is Latin, meaning 'out of 100'. So 45 per cent or 45% means 45 out of 100 and we write it as a fraction: \(\dfrac{45}{100}\).

If we tallied the colours of 100 cars that passed a point on the highway and 50 were white, we could say that 50 out of 100 or \(\dfrac{50}{100}\) or \(\dfrac{1}{2}\) or 0.5 or 50% of those cars were white.

It is useful to know some common percentage conversions. For more about the connection between decimals, fractions and percentages see Connecting fractions, decimals and percentages.

Percentage conversions

Fraction Decimal Percentage
\(\dfrac{1}{20}\) 0.05 5%
\(\dfrac{1}{10}\) 0.1 10%
\(\dfrac{1}{5}\) 0.2 20%
\(\dfrac{1}{4}\) 0.25 25%
\(\dfrac{1}{2}\) 0.5 50%
1 1 100%
2\(\dfrac{1}{2}\) 2.5 250%

You might notice that a decimal with two digits after the decimal point converts easily to a percentage. For example:

0.85&=85\%\\\\ 0.99&=99\%\end{align}