Chapter 7—Percents
7-2 Converting Between Percents, Decimals, and Fractions
When you complete the work for this section, you should be able to: - Rewrite any percentage as a fraction and as a decimal value.
- Rewrite any fraction or decimal value as a percent..
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Converting Between Percents and Decimals
Procedures To convert a percent to decimal: Remove the percent sign and divide by 100 |
Example
Problem Convert 70% to its decimal form. | |
| Procedure | |
Remove the percent sign and divide by 100. | 70 / 100 = 0.7 |
Solution 70% = 0.7 | |
Example
Problem Convert 12.5% to its decimal form. | |
| Procedure | |
Remove the percent sign and divide by 100. | 12.5 / 100 = 0.125 |
Solution 12.5% = 0.125 | |
Examples and Exercises
Converting Percents to Decimals Convert the given percent to its decimal value. Use these interactive examples and exercises to strengthen your understanding and build your skills: | |
Procedures To convert a decimal to a percent: Multiply by 100 and attach the percent sign. |
Example
Problem Convert 0.45 to its percent form. | |
| Procedure | |
Multiply by 100 and attach the percent sign. | 0.45 x 100 = 45% |
Solution 0.45 = 45% | |
Example
Problem Convert 0.0025 to its percent form. | |
| Procedure | |
Multiply by 100 and attach the percent sign. | 0.0025 x 100 = 0.25% |
Solution 0.0025 = 0.25% | |
Examples and Exercises
Converting Decimals to Percents Convert the given percent to its decimal value. Use these interactive examples and exercises to strengthen your understanding and build your skills: | |
Converting Between Percents and Fractions
Procedure To convert a percent to a fraction: - Remove the percent sign and write the result as the numerator of the fraction.
- Write 100 as the denominator of the fraction.
- Simplify or reduce as necessary.
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Example
Problem Convert 24% to its fraction form. | |
| Procedure | |
- Remove the percent sign and write the result as the numerator of the fraction.
| 24% = 24/ |
- Write 100 as the denominator of the fraction.
| 24/100 |
- Simplify or reduce as necessary.
| 24/100 = 6/25 |
Solution 24% = 6/25 | |
Example
Problem Rewrite 112% as a fraction. | |
| Procedure | |
- Remove the percent sign and write the result as the numerator of the fraction.
| 112/ |
- Write 100 as the denominator of the fraction.
| 112/100 |
- Simplify or reduce
| 112/100 = 1 3/25 |
Solution 18% = 9 / 50 | |
Examples and Exercises
Converting Percents to Fractions Convert the given percent to a fraction. Reduce the fraction if necessary. Use these interactive examples and exercises to strengthen your understanding and build your skills: | |
Interest rates are sometimes expressed as a percent that looks like a mixed number such as 8½% or 5¾%. Converting these values to a fraction is a matter of converting the mixed numbers to improper fractions and dividing by 100.
8½% = 17/2 ÷ 100 = 17/2 x 1/100 = 17/200
5¾% = 23/4 ÷ 100 = 23/4 x 1/10 = 23/400
When a percent includes a portion that is less than 1%, the conversion procedure requires an additional step. Try converting 2.5% to a fraction.
Step 1: Remove the percent sign and write the result as the numerator of the fraction. Write 100 as the denominator.
2.5/100
You can see that this creates an unusual sort of fraction. It is necessary to get rid of the decimal fraction in the numerator -- to convert the numerator to a whole number. In this case, multiplying 2.5 x 2 = 5. That converts 2.5 to a whole number. But the rules of algebra require that you multiply the numerator and denominator by the same value. You multiplied the numerator by 2 to change it to a whole number, so you must also multiply the denominator by the same factor of 2:
Step 2: Multiply the numerator and denominator by a factor that changes the numerator to a whole-number value:
2.5/100 x 2/2 = 5/200
Step 3: Simpify or reduce as necessary.
5/200 = 1/40
So 2.5% expressed as a fraction is 1/40.
Example
Problem Convert 22.5% to a fraction | |
| Procedure | |
- Remove the percent sign and write the result as the numerator of the fraction. Write 100 as the denominator.
| 22.5% = 22.5/100 |
- Multiply the numerator and denominator by a factor that changes the numerator to a whole-number value:
| 22.5/100 x 2/2 = 5/200 |
- Simplify or reduce as necessary.
| 5/200 = 1/40 |
Solution 2.5% = 1/40 | |
Note If you cannot find a factor that converts the numerator to a whole number, use factors of 10, 100, 1000, or whatever multiple of 10 that is required to convert the numerator to a whole number. Remember to multiply the denominator by the same multiple of 10. Example: 3.3% = 3.3/100 = 3.3/100 x 10/10 = 33/1000 |
Exercises
Convert the given percents to fractions. Simplify or reduce as needed.
Click the ? symbol to see the correct answer.
| 1. 8.25% = ? | 2. 6½% = ? | 3. 50.25% = ? | 4. 0.45% = ? | 5. 78.56% = ? |
Procedure To convert a fraction to a percent: - Convert the fraction to a decimal.
- Multiply by 100
- Attach the percent sign
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Converting Fractions to Percents Convert the given fraction to a percent. Round the percent to the nearest tenth, if necessary. Use these interactive examples and exercises to strengthen your understanding and build your skills: | |
