Converting Decimals and Percentages

In everyday life, we often use percentages to express the amount of something relative to the whole. A percent is a ratio expressed as a fraction of 100, so the whole is equal to "100%". In math and science, however, decimals are more frequently used to express portions. When using decimals, we consider "1" as the whole. Therefore we have 1=100%, and we come to a formula that gives the relation between decimals and percentages:

$$\begin{aligned} a&=100\times a\text{ \%},\\ b\text{ \%}&=b\times0.01, \end{aligned}$$

where $0\leq a\leq1$ and $0\leq b\leq100$. Thus, the percentage is expressed as a number 100 times larger than the decimal. Now let's take a look at a few examples.

Convert 75% into decimals.

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Using the formula above, we have

$$75\text{ \%}=75\times0.01=0.75.\ _\square$$

How can we express 'half' using decimals? What is this in percentage?

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When we use decimals, we consider "1" as whole. Therefore "0.5" would be equal to half.

When using percentages, we consider "100%" as whole. Hence "50%" would be equal to half.

Using the conversion formula above, we can verify this as shown below:

$$0.5=100\times0.5\text{ \%}=50\text{ \%}.\ _\square$$

Consider a baseball player whose batting average is 0.3. This means that his probability to hit the ball successfully is __%.

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A batting average of 0.3 indicates that the player successfully hits an average of 3 balls out of 10. Using the formula above to convert the decimal into percentage gives

$$0.3=100\times0.3\text{ \%}=30\text{ \%}.\ _\square$$

The interest rate of a bank loan is 4%. Express this in decimals.

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Using the formula above we have

$$4\text{ \%}=4\times0.01=0.04.\ _\square$$