Explainer: Decimals to Percentages

In this explainer, we will learn how to convert decimals to percentages for the rational system of 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 decimals as percentages, it means that the decimal has to be understood as a proportion where the whole is 1. For instance, expressing 0.25 as a percentage only makes sense if 0.25 is understood as 0.251, that is, comparing a part, 0.25, to a whole, 1.

The fraction 0.251 can be visualized on the diagram shown. The number 0.25 relates to 1 as 1 relates to 4 (and is indeed the result of 1 divided by 4; it is one quarter of 1).

We see that to find the equivalent proportion to 0.251 with 100 as the denominator, we simply need to multiply both the numerator and denominator by 100: 0.25Γ—1001Γ—100=25100.

The numbers 0.25 and 1 relate to each other in the same way as 25 and 100. When the decimal number 0.25 is to be understood as a proportion where 0.25 is the part and 1 is the whole, then we can say it is equivalent to 25%.

Let us look at some questions to check our understanding.

Example 1: Expressing Decimals as Percentages

Write 7.5 as a percentage.

Answer

We are asked to write 7.5 as a percentage. It means that 7.5 is the part compared to 1 as a whole. As 7.5Γ—1001Γ—100=750100=750%, we find that 7.51, written as 7.5, is equivalent to 750%.

Example 2: Expressing Decimals as Percentages

Benjamin’s hit rate is 0.269. Write this decimal as a percent.

Answer

We are given a hit rate, 0.269, that is, the ratio of the number of times the target was hit to the number of trials. The rate is given as a decimal; this means that 0.269 is the actual result of dividing the number of times the target was hit by the number of trials.

We can therefore understand 0.269 as a fraction where the whole is 1: 0.2691. To find the equivalent fraction with 100 as a denominator, we multiply both the numerator and denominator by 100: 0.269Γ—1001Γ—100=26.9100=26.9%.

We find that 0.2691, written as 0.269, is equivalent to 26.9%.

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