In the previous section, you used models to show how the same part of a whole can be represented with both a fraction and a decimal. In this part of the lesson, you will focus on how you can represent the same part of a whole with equivalent decimal numbers or percents. Recall that a percent is a rational number that describes the number of parts per 100. For example, the Texas state sales tax rate is 6.25%. This means that for every dollar—or 100 cents—of a sale, 6.25 cents are added to the purchase total in order to pay a state sales tax.

Use the sliders in the interactive below to show the relationship between a number written as a percent and the number written as a decimal. Click on the horizontal slider to change the tens digit in the percent and the vertical slide to change the ones digit in the percent.

Use the interactive to create a model for the given percents. Copy and paste the table below into a word processing or spreadsheet program or app. Record the equivalent decimal number in the table. Use your table to answer the questions that follow.

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Percent	Decimal Number
25%	0.25
63%	0.63
78%	0.78
18%	0.18

• What patterns do you notice in the completed table?

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  The decimal number has the same digits as the percent, but instead of a percent sign, there is a decimal point in front of the digit that was in the tens place of the percent.

• What relationship is there between the tens digit of the percent and the tenths digit of the decimal number?

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  The tens digit of the percent is the same as the tenths digit of the decimal number.

• What relationship is there between the ones digit of the percent and the hundredths digit of the decimal number?

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  The ones digit of the percent is the same as the hundredths digit of the decimal number.

• What number could you multiply or divide the percent by (without the percent sign) to obtain the decimal number?

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  Divide the percent by 100 to obtain the equivalent decimal.

• What number could you multiply or divide the decimal number by to obtain the percent?

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  Multiply the decimal number by 100 to obtain the equivalent percent.

Pause and Reflect

A percent is a part of the whole given in terms of the number of parts per 100. How does the definition of a percent appear in the relationship between a percent and its equivalent decimal number?

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The decimal number is found by dividing the percent by 100. The percent is found by multiplying the decimal number by 100.

If the percent is greater than 100%, such as 245%, how will you convert the percent to a decimal number?

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Divide the percent, without the percent sign, by 100. 245% is equivalent to 245 ÷ 100 = 2.45.

Practice

1. In a recent year, the cost of gasoline showed a 29.6% increase in price. What is this number represented as a decimal?

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   Need a hint?

   To generate an equivalent decimal number from a percent, divide the percent by 100 (remember that a percent is the number of parts per 100).
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   29.6 ÷ 100 = 0.296
2. A grocery store is advertising produce at a 20% discount and milk for 0.9 times the original price. Which item is being sold for a greater portion of its original price?

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   If produce is being sold at a 20% discount, then the sale price will be 80% of the original price. Generate an equivalent decimal number for 80%, and then compare it to the decimal number for the sale price of milk, 0.9.
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   Check Your Answer

   A 20% discount means that produce is being sold at 100% − 20% = 80% of the original price.
   80 ÷ 100 = 0.80 or 0.8
   0.8 < 0.9
   
   Milk is being sold for a greater portion of its original price.
3. In a local toy store, a radio-controlled car costs 1.25 as much as a car that is not radio-controlled. What is the relationship between the cost of the radio-controlled car and car that is not radio-controlled, 1.25, written as a percent?

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   Need a hint?

   To generate an equivalent percent from a decimal number, multiply by 100.
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   Check Your Answer

   1.25 × 100 = 125%