# 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:

\[\begin{align} a&=100\times a\text{ %},\\ b\text{ %}&=b\times0.01, \end{align}\]

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.

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?

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

__%.

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.

Using the formula above we have

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

**Cite as:**Converting Decimals and Percentages.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/decimals-percentages/