Explainer: Percentages to Decimals

In this explainer, we will learn how to convert percents to decimals for a set of rational numbers.

Proportions are particular ratios that compare a part, π‘Ž, to a whole, 𝑏. They are usually written as the fraction π‘Žπ‘.

A percentage is a way to express a given proportion: it gives the number, 𝑝, that relates to 100 the same way as π‘Ž relates to 𝑏 (or: π‘Ž is the same fraction of 𝑏 as 𝑝 is of 100). Both (equivalent) proportions can then be represented on a double line diagram.

The ratio of π‘Ž to 𝑏 compares a part, π‘Ž, to a whole, 𝑏. It can be expressed as the fraction π‘Žπ‘. The equivalent fraction to π‘Žπ‘, where the whole (which is the denominator of the fraction) is 100, is a percentage. We have π‘Žπ‘=𝑝100=𝑝%, and we can say that π‘Ž is 𝑝% of 𝑏.

When we are asked to express percentages as decimals, it means that we need to find this percentage of the unit (1). The result is then expressed as a decimal. However, as it comes from a percentage, this decimal is not to be understood like any number, since it is still a proportion: it is the part when the whole is 1. For instance, expressing 63% as 0.63 only makes sense if 0.63 is understood as 0.631, that is, comparing a part, 0.63, to a whole, 1. This is visualized on the diagram below.

We see that, to find the equivalent fraction to 63100 with 1 as the denominator, we simply need to divide both the numerator and the denominator by 100: 63Γ·100100Γ·100=0.631.

The numbers 0.63 and 1 relate to each other in the same way as 63 and 100. When the decimal number 0.63 is to be understood as a proportion, where 0.63 is the part and 1 is the whole, then we can say it is equivalent to 63%.

Let’s look at some questions to check our understanding.

Example 1: Expressing Percentages as Decimals

Express 44% as a decimal.

Answer

The proportion given, expressed as a percentage, is 44%, that is, 44100. The equivalent fraction with 1 as a whole is then 44Γ·100100Γ·100=0.441. So the answer is 0.44.

Example 2: Expressing Percentages as Decimals

Convert 32.89% into a decimal.

Answer

We are given here a percentage: 32.89%. The percentage is a decimal, which means it is a fraction where the numerator is a decimal: 32.89100. The equivalent fraction with 1 as a whole is then 32.89Γ·100100Γ·100=0.32891. So, the answer is 0.3289.

Example 3: Expressing Percentages as Decimals

Express 574% as a decimal.

Answer

The proportion given, expressed as a percentage, is 574%, that is, 574100. The percentage is greater than 100, which means that we are comparing a part that is bigger than the whole. The equivalent fraction with 1 as a whole is then 574Γ·100100Γ·100=5.741. So the answer is 5.74. This means that the part is 5.74 times bigger than the whole.

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