In a previous lesson, you represented fractions and their equivalent decimals, and vice versa.

For fractions with a denominator that is a power of 10, such as 10, 100, or 1,000, you can also use a decimal number to represent the fraction.

Decimal numbers use place value to represent a fractional quantity. For example, the place value chart below shows the value of each digit in the number 410.75.

In this section, you will represent fractions and decimals using their equivalent percents. Remember that a percent is a ratio of the number of parts per 100.

The interactive below uses a 10 by 10 grid to visualize the relationships among percents, fractions, and decimals. When you click on the image, the interactive will open in a new web browser tab or window. Use the interactive to determine the fraction, decimal, and percent equivalents for the percents given in the table. Then, use your table to answer the questions that follow.

• For each percent in the table, first identify a pair of factors that you can use to represent the length and width of a rectangle (e.g., 56 = 7 × 8, so the base length is 7 and the height is 8).
• Create a rectangle using the dimensions from the factor pair.
• Record the fraction equivalent given in the interactive, fraction equivalent with a denominator of 100, and decimal equivalent in a table like the one shown.
• Use the Check Your Answer popup to see a completed table and check your work.

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Use the interactive to complete the table below. Copy and paste the table into a word processing or spreadsheet program or app.

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Check Your Answer

Possible Answers:

Percent	Factor Pair	Fraction Equivalent	Fraction Equivalent (denominator of 100)	Decimal Equivalent
54%	9 × 6	27 over 50 27 50	54 over 100 54 100	0.54
36%	9 × 4	9 over 25 9 25	36 over 100 36 100	0.36
50%	10 × 5	1 over 2 1 2	50 over 100 50 100	0.50
24%	3 × 8	6 over 25 6 25	24 over 100 24 100	0.24
70%	7 × 10	7 over 10 7 10	70 over 100 70 100	0.70

Use your completed table to answer the questions below.

• How does the fraction equivalent with a denominator of 100 compare to the percent?

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  Check Your Answer

  The numerator of the fraction equivalent with a denominator of 100 is the same as the percent.

• Knowing that a percent is a ratio of the number of parts per 100, generalize how you can write a fraction when you know the percent. Explain why this is the case.

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  Check Your Answer

  Write a fraction with a denominator of 100 and a numerator that is equal to the given percent. This method will work because a percent is a ratio of parts per 100, so by definition the numerator is the number of parts and the denominator is 100. Simplify the fraction if necessary.

• How does the decimal equivalent compare to the percent?

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  The tenths and hundredths digits in the decimal match the tens and ones digit in the percent.

• Knowing that a percent is a ratio of the number of parts per 100, generalize how you can write a decimal when you know the percent. Explain why this is the case.

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  Check Your Answer

  Divide the percent by 100, because the percent is a ratio of the number of parts per 100. Remember from previous courses with patterns in division by powers of 10 that dividing by 100 generates a quotient that has the same digits with the decimal place moved two places to the left.

Pause and Reflect

Sometimes, you will see a percent that is greater than 100%, such as 140%. How would you write a percent greater than 100% as a fraction or as a decimal?

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Follow the same techniques as you would with a percent between 0% and 100%. To write a fraction, the number portion of the percent becomes the numerator and 100 becomes the denominator. The fraction will be improper, so simplify as needed, including rewriting the improper fraction as a mixed number if necessary. To write a decimal, divide the percent by 100. There will be digits in the ones or tens place of the quotient.

Sometimes, you will see a percent that includes a decimal point, such as 16.5%. How would you write such a percent as a fraction or a decimal?

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Check Your Answer

Follow the same techniques as you would with a percent between 0% and 100%. To write a fraction, the number portion of the percent becomes the numerator and 100 becomes the denominator. Multiply both the numerator and denominator by the same power of 10 in order to clear the decimal point, and then simplify the fraction as needed. To write a decimal, divide the percent by 100. There will be digits in the thousandths place or beyond, depending on the number of digits to the right of the decimal point in the original percent.

Practice

1. In a recent volleyball tournament, Ian’s team played 20 games and won 65% of them. What decimal represents the percent of games that Ian’s team won?

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   Percent means the number of parts per 100. What number would you divide 65 by in order to write the percent as a decimal?
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   Check Your Answer

   0.65
2. On a recent day, an airline had an 80% on-time departure rate from a local airport. What fraction represents the percent of flights that departed on time?

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   Need a hint?

   Percent means the number of parts per 100. Write the percent as a fraction with a denominator of 100 and then simplify the fraction.
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   Check Your Answer

   4 over 5 4 5
3. The sales tax rate in some cities in Texas is 8.25%. What decimal represents the sales tax rate?

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   Percent means the number of parts per 100. What number would you divide 8.25 by in order to write the percent as a decimal?
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   Check Your Answer

   0.0825