Percentages Less Than 1 or Greater Than 100

Girl BikeProblem 1: Glosser Grade School has an enrollment of 400 students. Only one_half_small.gif% 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 one_half_small.gif = 0.5, then one_half_small.gif% = 0.5%, and 0.5% =.005. Thus we get one_half_small.gif% = .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:     two_fifths_1.gif%,    1.8%,    0.32%,    235%

Since two_fifths_1.gif = 0.4, we get two_fifths_1.gif% = 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 forty_two_10000ths_1.gif twenty1_5000ths_1.gif
395%       3.95      3 ninety5_100ths.gif 3nineteen_20ths_1.gif
    0.07% 0.0007 seven_10000ths.gif seven_10000ths.gif

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%?
 
      

      190.0

      19.0

      1.90

      None of the above.

      RESULTS BOX:
          

2.  Which of the following is equal to 0.37%?
 
      

      0.0037

      0.037

      0.37

      None of the above.

      RESULTS BOX:
          

3.  Which of the following is equal to 0.00319?
 
      

      3.19%

      0.319%

      0.0319%

      None of the above.

      RESULTS BOX:
          

4.  Which of the following is equal to 29.348?
 
      

      2,934.8%

      293.48%

      29.348%

      None of the above.

      RESULTS BOX:
          

5.  Which number has the least value?
 
      

      0.0056

      0.56%

       fifty6_10000ths_1.gif

      All have the same value.

      RESULTS BOX: