Changing a Decimal or Fraction to a Percent

Transcription

1 6. Changing a Decimal or Fraction to a Percent 6. OBJECTIVES. Change a decimal to a percent. Change a fraction to a percent. Change a mixed number to a percent Changing a decimal to a percent is the opposite of changing from a percent to a decimal. We reverse the process of Section 6.. Here is the rule: Rules and Properties: To change a decimal to a percent, move the decimal point two places to the right and attach the percent symbol. Example NOTE 0. % % CHECK YOURSELF 0.7 Example NOTE 0.0 % % CHECK YOURSELF 0.0 Example 00 McGraw-Hill Companies NOTE. % A decimal greater than always gives a percent greater than % CHECK YOURSELF. If the percent still includes a decimal after the decimal point is moved two places to the right, the fractional portion can be written as a decimal or as a fraction.

2 CHAPTER 6 PERCENTS NOTE % % Example (a) 0.0.% or (b) % or % 0 % CHECK YOURSELF 0.07 The following rule allows us to change fractions to percents. Rules and Properties: NOTE You may want to review Section.6 on writing decimal equivalents. To change a fraction to a percent, write the decimal equivalent of the fraction. Then use the previous rule to change the decimal to a percent. Example NOTE Move the decimal point two places to the right and attach the percent symbol. First write the decimal equivalent To find the decimal equivalent, just divide the denominator into the numerator. Now write the percent % CHECK YOURSELF Again, you will find both decimals and fractions used in writing percents. Consider the following. Example % or % 00 McGraw-Hill Companies

3 CHANGING A DECIMAL OR FRACTION TO A PERCENT SECTION 6. CHECK YOURSELF 6 Units Analysis When computing a percentage note that, in the result, the units are rarely expressed. Each time we say percent we are essentially saying, numerator units per 00 denominator units. Examples Of 00 students, 00 were boys. What percent of the students were boys? 00 boys 0. % 00 students But what happened to our units? At the decimal, the units boys/student (0. boys per student) wouldn t make much sense, but we can read the % as boys per 00 students and have a reasonable unit phrase. Of 00 computers sold, 0 were equipped with a scanner. What percent were equipped with a scanner? % 00 6 were equipped with a scanner for each (per) 00 computers sold. To write a mixed number as a percent, we use exactly the same steps. Example 7 Changing a Mixed Number to a Percent NOTE Notice that the resulting percent must be greater than 00 because the original mixed number was greater than.. % 00 McGraw-Hill Companies CHECK YOURSELF 7

4 CHAPTER 6 PERCENTS Some fractions have repeating-decimal equivalents. In writing these as percents, we will either round to some indicated place or use a fractional remainder form. Example NOTE Here we use the fractional remainder in writing the decimal equivalent. 0. % CHECK YOURSELF Example 9 NOTE In this case, we round the decimal equivalent. Then we write the percent % (to the nearest thousandth) (to the nearest tenth of a percent) CHECK YOURSELF 9 9 to the nearest tenth of a percent. CHECK YOURSELF ANSWERS. 7%. 0.0 %. 0%. 7.% or 7 % % 6. 7.% or 7 % 7.. 0%. 66 % 9..% 00 McGraw-Hill Companies

5 Name 6. Exercises Section Date each decimal ANSWERS each fraction McGraw-Hill Companies

6 ANSWERS (to nearest tenth of a percent) 0. (to nearest tenth of a percent) 9 In exercises to, partially shaded decimal squares are given. Express the partially shaded region as (a) a decimal (b) a fraction, and (c) a percent McGraw-Hill Companies 6

7 ANSWERS Between 97 and 990, the average fuel efficiency of new U.S. cars increased from 6. to.9 kilometers per liter (km/l). During this same time, the average fuel efficiency for the entire fleet of U.S. cars rose from. to. km/l. For exercises 9 and 0, solve the applications involving fuel efficiency. 9. Fuel efficiency. The percentage increase in fuel efficiency for new cars is given by (.9 6.) the fraction. Change this fraction to a percent Fuel efficiency. The percentage increase in fuel efficiency for the fleet of U.S. cars (..) is given by the fraction. Change this fraction to a percent... Complete the following table of equivalents. Round decimals to the nearest ten thousandth. Round percents to the nearest hundredth of a percent. Fraction Decimal Percent McGraw-Hill Companies 0.6 % % 7

8 ANSWERS.... Business travelers were asked how much they spent on different items during a business trip. The circle below shows the results for every $000 spent. Use this information to answer exercises to. Lodging $00 Car $00 Miscellaneous $00 Food $0 Entertainment $0. What percent was spent on car expenses?. What percent was spent on food?. Where was the least amount of money spent? What percent was this?. What percent was spent on food and lodging together? Answers. %. %. % 7. 6% 9. 0%. 70%. 0%. 0% 7. 6.% or 6 % 9..% or %. 0.% or %. 0.% or %. 0. % 7. 0% 9. 0% %..%. 0% 7. 6 % %. 0.,, % ,, 7%. 0.77,, 77% ,, % %. Fractions: decimals: 0., 0., 0.0,, 7 0, 00, 7 60 ; 0.6; percents:.%, %, 6.%, 6.%. %. % 00 McGraw-Hill Companies