3.1: Expressing Numbers as Percentages

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Percentages and decimals are commonly used in waterworks mathematics. Whether you are working with financial budgets, chemical percent concentrations, or water quality results, decimals and percentages are used often. Therefore, knowing how to convert to percentages from decimals is important and vice versa.

When expressing numbers as a percent they need to be whole numbers or decimals. Therefore, fractions must be converted first. Percent (%) simply means per hundred. Understanding that percent means per hundred indicates that 2 decimal places are involved.

When a number needs to be converted to a percent you multiply the number by 100 and put a percent sign (%) at the end.

Example \(\PageIndex{1}\)

The number 1 written as a percent is

1 × 100 = 100%

The number 5 written as a percent is

5 × 100 = 500%

When a decimal is written as a percent do the same thing.

1.4 × 100 = 40%

Note that the decimal moves two places to the right.

When a percent is written as a decimal, you simply divide the number by 100. Dividing by 100 moves the decimal two places to the left.

Example \(\PageIndex{2}\)

If 100% is to be written as a number, divide by 100.

\[100 \% \div 100=1\nonumber \]

\[8.25 \% \div 100=0.0825\nonumber \]

\[2,500 \% \div 100=25\nonumber \]

Exercise 3.1

Convert the following numbers to percentages and percentages to numbers (round all numbers to the nearest hundredth place.

1 =
30 =
0.5 =
0.75 =
1.02 =
35.5 =
0.004 =
5.005 =
102% =
2.3% =
0.45% =
1,570% =
8% =
0.9% =
65% =
12.5% =