| Chapter 6 Percents 6-2 Converting Between Percents, Decimals, and Fractions 6-2.1 Converting Between Percents to Decimals Procedures To convert a percent to a decimal: - Remove the percent sign.
- Divide by 100
| Example Convert 70% to its decimal form. | Problem | | 70% = ? | Remove the percent sign and divide by 100. | 70 / 100 = 0.7 | | | Solution | | 70% = 0.7 | More Examples | 1. 26% = 0.26 | 2. 100% = 1.00 | 3. 2.5% = 0.025 | 4. 1% = 0.01 | 5. 0.2% = 0.002 | Exercises Convert the given percents to decimal values.
Click the ? symbol to see the correct answer. | 1. 75% = ? | 2. 10% = ? | | 3. 100% = ? | 4. 35.5% = ? | | 5. 0.5 % = ? | | Procedures To convert a decimal to a percent: - Multiply by 100
- Add the percent sign.
| Example Convert 0.45 to its percent form. | Problem | | 0.45 = ? % | Multiply by 100 and add the percent sign. | 0.45 x 100 = 45% | | | Solution | | 0.45 = 45% | More Examples | 6. 0.34 = 34% | 7. 0.011 = 1.1% | 8. 0.4 = 40% | 9. 0.623 = 62.3% | 10. 0.0012 = 0.12% | Exercises Convert the given decimals to percent.
Click the ? symbol to see the correct answer. | 1. 0.78 = ? | 2. 0.12 = ? | | 3. 1 = ? | 4. 0.06 = ? | | 5. 0.0025 = ? | | 6-2.2 Converting Between Percents and Fractions Procedure To convert a percent to a fraction: - Remove the pecent sign and write the result as the numerator of the fraction.
- Write 100 as the denominator of the fraction.
- Simpify or reduce as necessary.
| Example Convert 24% to its fraction form. | Problem | | 24% = ? | - Remove the pecent sign and write the result as the numerator of the fraction.
- Write 100 as the denominator of the fraction.
| 24% = 24/100 | | - Simpify or reduce as necessary.
| 24/100 = 6/25 | | | Solution | | 24% = 6/25 | More Examples Convert these percents to fractions. Simplify or reduce as needed. | 1. 26% = 26/100 = 13/50 | 2. 100% = 100/100 = 1 | 3. 1% = 1/100 | 4. 90% = 90/100 = 9/10 | 5. 75% = 75/100 = 1/4 | Exercises Click the ? symbol to see the correct answer. | 1. 89% = ? | 2. 48% = ? | | 3. 34% = ? | 4. 3.7% = ? | | 5. 72% = ? | | 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 Convert 22.5% to a fraction | Problem | | 22.5% = ? | Step 1: Remove the pecent sign and write the result as the numerator of the fraction. Write 100 as the denominator. | 22.5% = 22.5/100 | | Step 2: Multiply the numerator and denominator by a factor that changes the numerator to a whole-number value: | 22.5/100 x 2/2 = 45/200 | | Step 3: Simpify or reduce as necessary. | 45/200 = 9/40 | | | Solution | | 22.5% = 9/40 | 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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