# Writing Percentages as Decimals Lesson

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%

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:**

- Remove the percent symbol.
- 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%

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%? |

2. Which of the following is equal to 7.27%? |

3. Which of the following is equal to 91.4763%? |

4. Which number has the greatest value? |

5. Which number has the least value? |