Changing Percents to Decimals

Need some basic practice with decimals and percents first? Changing Decimals to Fractions and Multiplying and Dividing Decimals by Powers of Ten and Changing Decimals to Percents

Whenever computations need to be done with percents, the percents are first renamed as decimals.

Here are examples of changing percents to decimals. Notice that the $\,\%\,$ symbol is replaced with a factor of $\,\frac{1}{100}\,$:

Examples

$3.5\% = 3.5\cdot\frac{1}{100} = \frac{3.5}{100} = 0.035$

$25\% = 25\cdot \frac{1}{100} = \frac{25}{100} = 0.25$

$50\% = 50\cdot \frac{1}{100} = \frac{50}{100} = 0.5$

$100\% = 100\cdot \frac{1}{100} = \frac{100}{100} = 1$

$250\% = 250\cdot \frac{1}{100} = \frac{250}{100} = 2.5$

As these examples illustrate, the percent symbol instructs multiplication by $\,\frac{1}{100}\,$ (or, equivalently, division by $\,100\,$), which is accomplished by moving the decimal point two places to the left. Remember that if you don't see a decimal point, then it gets inserted just to the right of the ones place.

Now, you can go from percents to decimals in one easy step, by moving the decimal point two places to the left:

Examples

$3\% = 0.03$

$2.37\% = 0.0237$

$0.01\% = 0.0001$

$5032\% = 50.32$

Some of my students find this memory device helpful: PuDdLe DiPpeR (Imagine a little kid, barefoot, dipping piggy-toes in puddles!)

Percent to Decimal, two places to the Left

Decimal to Percent, two places to the Right

Practice

Here, you will practice renaming percents as decimals. For example, $\,54\%\,$ gets renamed as $\,0.54\,.$