Writing Percents as Decimals

Writing Percents as Decimals

Dollars centsProblem: 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%

Solution
Percent Decimal
18% .18
07% .07
82% .82
55% .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% = [IMAGE]

From your knowledge of decimal place value, you know that [IMAGE] = 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% [IMAGE] .18
07% [IMAGE] .07
82% [IMAGE] .82
55% [IMAGE] .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%

Solution
Percent Decimal
12.5%       .12500
89.19%    .89190
39.2%       .39200
71.935% .71935

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

Directions: Read each question below. Select your answer by clicking on its button. Immediate feedback is provided in the RESULTS BOX. If you make a mistake, choose a different button.

1.  Which of the following is equal to 64%?
 
      .064
      .64
      6.74
      None of the above.

      RESULTS BOX:
          

2.  Which of the following is equal to 7.27%?
 
      7.27
      .727
      .0727
      None of the above.

      RESULTS BOX:
          

3.  Which of the following is equal to 91.4763%?
 
      .914763
      9.14673
      91.4763
      None of the above.

      RESULTS BOX:
          

4.  Which number has the greatest value?
 
      19.72%
      1.972
      $19.72
      20 cents

      RESULTS BOX:
          

5.  Which number has the least value?
 
      1.039%
      1.39
      $1.39
      139 cents

      RESULTS BOX: