Writing Percents as Decimals

Problem: What is 35 percent of one dollar?

We know from the previous lesson that .35 = 35%. The word "of" means multiply. So we get the following:

35% x $1.00 = .35 x $1.00

since $1.00 = 1, we get .35 x $1.00 = .35 x 1 = .35

35% of $1.00 is $.35

Solution: 35% of one dollar is $.35, or 35 cents.

The solution to the above problem is not surprising, since percents, dollars and cents are all based on the number 100. To convert a percent to a decimal, first remove the percent symbol, then move the decimal point two places to the left. Look at the Example 1 below.

Example 1: Write each percent as a decimal:     18%,    7%,    82%,    55%

In Example 1, it was easy to convert each percent to a decimal since each percent had two digits. (The exception to this was 7% for which we needed to add in a zero in order to make the conversion.) Thus, we need a procedure to follow for consistency.

To write a percent as a decimal, follow these steps:

1. Remove the percent symbol.
2. Move the decimal point two places to the left, adding in zeros as needed.

Why do we move the decimal point 2 places to the left?

Remember that percent means parts per hundred, so 18% = 

From your knowledge of decimal place value, you know that  = 0.18  (eighteen hundredths).

Thus, 18% must also equal 0.18.

Let's take another look at Example 1, this time including the fractional equivalents of each percent.

Example 1: Write each percent as a decimal:     18%,    7%,    82%,    55%

Solution
Percent	Fraction	Decimal
18%		.18
07%		.07
82%		.82
55%		.55

Let's look at another example of writing percents as decimals.

Example 2: Write each percent as a decimal:     12.5%,    89.19%,    39.2%,    71.935%

Summary: To write a percent as a decimal, remove the percent symbol, then move the decimal point two places to the left, adding in zeros as needed.

Exercises

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