Percentages Less Than 1 or Greater Than 100
Problem 1: Glosser Grade School has an enrollment of 400 students. Only % of students ride their bicycles to school each day. How many students is this?
We know from previous lessons how to write a percent as a decimal by moving the decimal point two places to the left. So we get the following:
If = 0.5, then % = 0.5%, and 0.5% =.005. Thus we get % = .005
Going back to our original problem, we get: .005 of 400 = .005 x 400 = 2
Solution: 2 students ride their bicycle to school each day.
Problem 2: This year, enrollment at Glosser Grade school is 150% of last year. How many students are enrolled now?
Writing 150% as a decimal, we get: 150% = 1.50 = 1.5
1.5 of 400 = 1.5 x 400 = 600
Solution: 600 students are now enrolled at Glosser Grade School.
In Problem 1, we were asked to work with a percent less than 1, and in Problem 2, we were asked to work with a percent greater than 100. When working with percents less than 1 and greater than 100, we follow the same rules that we learned for percents between 1 to 100. Let’s look at some examples.
Example 1: Write each percent as a decimal: %, 1.8%, 0.32%, 235%
Since = 0.4, we get % = 0.4%
Solution | |||
Percent | Decimal | ||
0.4% | 0.004 | ||
1.8% | 0.018 | ||
0.32% | 0.0032 | ||
235% | 2.35 |
Note that instead of writing .32% we write 0.32% The leading zero reminds us that this number is between 0 and 1 percent. Let’s look at some more examples.
Example 2: Write each percent as a fraction in lowest terms: 0.42%, 395%, 0.07%
Solution | |||
Percent | Decimal | Fraction | Lowest Terms |
0.42% | 0.0042 | ||
395% | 3.95 | 3 | 3 |
0.07% | 0.0007 |
Example 3: Write each decimal as a percent: 12.2, 0.00459, 1.2765
Solution | ||
Decimal | Percent | |
12.2 | 1,220% | |
0.00459 | 0.459% | |
1.2765 | 127.65% |
Summary: When working with percents less than 1 and greater than 100 (special percents), we follow the same rules that we learned for percents between 1 and 100. In this lesson, we applied these rules to help us make conversions between fractions, decimals and special percents.
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 190%? |
2. Which of the following is equal to 0.37%? |
3. Which of the following is equal to 0.00319? |
4. Which of the following is equal to 29.348? |
5. Which number has the least value? |