Part 1: Decimal to Percent. Part 2: Fraction to Percent

Size: px

Start display at page:

Download "Part 1: Decimal to Percent. Part 2: Fraction to Percent"

Gabriella Doyle
5 years ago
Views:

1 Lecture Notes Review of Fractions and Percents page Part : Decimal to Percent Turning a decimal to a percent is easy if we know what percents mean. A percent is a standardized fraction, with denominator 00: For example, 4% is exactly the same thing as Example Convert 0:6 We rst obtain a fraction by "growing a ". We can check mentally: any number divided by results in the original number. 0:6 0:6 Now we want to turn this fraction into one with denominator 00: The only thing we can do to a fraction without changing its value is to multiply upstairs and downstairs by the same number. Since our goal is to turn the denominator into 00, we will use 00: Thus 0:6 60%. 0:6 0:6 0: % Example 2 Convert :209 We rst obtain a fraction by "growing a ". Then we turn this fraction into one with denominator 00: The only thing we can do to a fraction without changing its value is to multiply upstairs and downstairs by the same number. Since our goal is to turn the denominator into 00, we will use 00. :209 :209 : : :9% Thus :209 20:9%. The percent we obtained is larger than 00%; indicating that we have started with a decimal that is larger than. Part 2: Fraction to Percent Again, the process is simple if we know what percents mean. A percent is a standardized fraction, with denominator 00: For example, 4% is exactly the same thing as Case. If we are lucky, we have a fraction whose denominator is a factor of 00: Example 3 Convert 20 same number. Since our goal is to turn the denominator into 00, we will use 5: Thus 20 35% % c copyright Hidegkuti, Powell, 200 Last revised: December 20, 203

2 Lecture Notes Review of Fractions and Percents page 2 Example 4 Convert 3 4 same number. Since our goal is to turn the denominator into 00, we will use 25: Thus 3 4 5%. Example 5 Convert % same number. Since our goal is to turn the denominator into 00, we will use 0: % Thus 0%. The percent we obtained is larger than 00%, indicating that we have started with a fraction 0 that is larger than. Case 2. If we are given a fraction whose denominator is not a factor of 00, we can not apply the method used above. The process is still simple: we convert the fraction to a decimal, and then convert the decimal to a percent. Fraction! Decimal! Percent Example 6 Convert Step. We convert to a decimal by division :3625 The result is a terminating decimal. To preserve accuracy, we will carry all digits after the decimal point. Step 2. We convert the decimal to a percent as described in Part. Thus :25%. 0:3625 0:3625 0: : :25% Example Convert 4 Step. We convert 4 to a decimal by division. 4 0: :::::: The result is a non-terminating repeating decimal. To preserve accuracy, we will carry ve (or more) digits after the decimal point. Step 2. We convert the decimal to a percent as described in Part. 0: : : : We round the result according to the accuracy requested in the particular problem. 5:4285% For now, we will round to three decimals after the decimal point. The result is 4 5:43%. The sign means "approximately equal". c copyright Hidegkuti, Powell, 200 Last revised: December 20, 203

3 Lecture Notes Review of Fractions and Percents page 3 Example 8 Convert 43 5 Step. We convert 43 5 to a decimal by division :866666:::::: The result is a non-terminating repeating decimal. To preserve accuracy, we will carry ve (or more) digits after the decimal point. Step 2. We convert the decimal to a percent as described in Part. 2: : : : :6666% We round the result according to the accuracy requested in the particular problem. For now, we will round to three decimals after the decimal point. The result is :66%. The sign means "approximately 5 equal". The result is a percent larger than 00%, indicating that we have started with a fraction larger than. Part 3: Percent to Decimal Example 9 Convert 64% to a decimal. 64% :64 Thus 64% 0:64. Example 0 Convert 50% to a decimal. 50% :5 Thus 50% :5. Example Convert 8:5% to a decimal. 8:5% 8:5 00 0:085 Thus 8:5% 0:085 c copyright Hidegkuti, Powell, 200 Last revised: December 20, 203

4 Lecture Notes Review of Fractions and Percents page 4 Part 4: Percent to Fraction We have left the easiest one for last. Percents already are fractions, with denominator 00. Example 2 Convert 55% to a reduced fraction. We rewrite the percent as a fraction and simplify. Example 3 Convert 240% to a reduced fraction. We rewrite the percent as a fraction and simplify. 55% 55 /5 00 / % Thus 240% 2 2. The result is a mixed number, indicating that we started with a percent larger than 00%. 5 Example 4 Convert 3:5% to a reduced fraction. When we rewrite the percent as a fraction, the numerator is not an integer. numerator and denominator by 0. The rest is as before. Thus 3:5% :5% 3:5 00 Compute the missing values in the table shown below. 3: Exercises We x this by multiplying both c copyright Hidegkuti, Powell, 200 Last revised: December 20, 203

5 Lecture Notes Review of Fractions and Percents page 5 Answers for Exercises For more documents like this, visit our page at and click on Lecture Notes. questions or comments to mhidegkuti@ccc.edu. c copyright Hidegkuti, Powell, 200 Last revised: December 20, 203

Classwork. Exercises Use long division to determine the decimal expansion of. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 6 8 7

Classwork. Exercises Use long division to determine the decimal expansion of. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 6 8 7 Classwork Exercises 1 5 1. Use long division to determine the decimal expansion of. 2. Use long division to determine the decimal expansion of. 3. Use long division to determine the decimal expansion of.