CHAPTER 2 PERCENTAGE 3. General a. Definition. Percentage is the process of computation in which the basis of comparison is a hundred. The term percent-from per, by, and centum, hundred-means by or on the hundred. Thus, 2 percent of a quantity means two parts of every hundred parts of the quantity. b. Symbol. The symbol of percentage is %. Percent may also be indicated by a fraction or 5 a decimal. Thus, 5% = = .05. Figure 1 100 shows the relationship between fractions, decimals, and percentage. c. Base, Rate, and Percentage. (1) The base is the number on which the percentage is computed. (2) The rate is the amount (in hun dredths) of the base to be estimated. (3) The percentage is a part or propor tion of a whole expressed as so many per hundred. Percentage is the portion of the base determined by the rate. 4. Conversion of Decimal to Percent To change a decimal to percent, move the decimal point two places to the right and add the percent symbol. Example: Chance .375 to percent. Move decimal point two places to right: 37.5 Add percent symbol: 37.5% 5. Conversion of Fraction to Percent To convert a fraction to percent, divide the numerator by the denominator and convert to a decimal. Then, convert the decimal to percent (par. CHAPTER 2 PERCENTAGE 3. General a. Definition. Percentage is the process of computation in which the basis of comparison is a hundred. The term percent-from per, by, and centum, hundred-means by or on the hundred. Thus, 2 percent of a quantity means two parts of every hundred parts of the quantity. b. Symbol. The symbol of percentage is %. Percent may also be indicated by a fraction or 5 a decimal. Thus, 5% .05. Figure 1 100 shows the relationship between fractions, deci mals, and percentage. = c. Base, Rate, and Percentage. (1) The base is the number on which the percentage is computed. (2) The rate is the amount (in hun dredths) of the base to be estimated. (3) The percentage is a part or propor tion of a whole expressed as so many per hundred. Percentage is the portion of the base determined by the rate. 4. Conversion of Decimal to Percent To change a decimal to percent, move the decimal point two places to the right and add the percent symbol. Example: Chance .375 to percent. Move decimal point two places to right: 37.5 Add percent symbol: 37.5% 5. Conversion of Fraction to Percent To convert a fraction to percent, divide the numerator by the denominator and convert to a decimal. Then, convert the decimal to percent (par. 6. Conversion of Percent to Decimal To change a percent to a decimal, omit the percent symbol and move the decimal point two places to the left. Example 1: Change 15% to a decimal. Omit percent symbol: 15% becomes 15 Move decimal point two places to the left: 15 becomes .15 Thus, 15%.15. Example 2: Change 110% to a decimal. Move the decimal point two Thus, 110% = 1.10. 7. Conversion of Percent to Fraction To change a percent to a fraction, first change the percent to a decimal (par. 6) and then to a fraction. Reduce the fraction to its lowest terms. Example 1: Change 25% to a fraction. Change to a decimal: 25% = .25 25 Change to a fraction: .25 = 100 Reduce fraction to lowest terms: 25 1 - 100 4 Thus, 25% = 1. 11. Expressing Accuracy of Measurements in Percent a. Relative error is the accuracy of a measurement expressed in percent of the total measurement. In determining the relative error, it is first necessary to establish the limit of error. b. The limit of error is the difference between the true value and the measured value. Assume that the reading on a scale, to the nearest tenth of an inch, is 2.2 inches. If the true value is 2.15 inches, the limit of error is the difference between 2.15 and 2.20, or .05 inch. (18) 371% (19) 105% (20) 4% b. Evaluate the following: (4) 225% of 400 c. What percent of a number is (1) 1.5 times the number? |