The place value of any digit can be found by following the format in the chart above.

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1 SECTION. Place Value, Rounding, and Estimations 6. PLACE VALUE, ROUNDING, AND ESTIMATIONS Textbook Reference Section. CLAST OBJECTIVES Recognize the role of the base number in the base ten numeration system Identify a reasonable estimate of sum, average, or product Place Value hundred hundred thousands thousands ten ten thousands thousands thousands thousands hundreds hundreds tens tens ones ones (decimal (decimal point) point) tenth tenth hundredth hundredth ten ten thousandth thousandth hundred thousandth 0 0 The place value of any digit can be found by following the format in the chart above. a) What is the place value of 8 in 5.897? The 8 is two places right of the decimal point. Thus, the place value of 8 is 0. b) What is the place value of in 7,9.? The is three places left of the decimal point. Thus, the place value of is 0. c) Write the expanded form of Consider the place values of the, 7, and. 0 ( ) ( ) d) Write the numeral for ( 0 ) + ( 0) is four places left of the decimal point. is two places left of the decimal point. 5 is one place right of the decimal point..5 Place zeroes in the hundreds place and the ones place. Result: 00.5

ten thousands thousands thousands thousands hundreds hundreds tens tens ones ones 0 5 0 0 0 0 0 0.

2 6 CHAPTER Arithmetic Check Your Progress. For Questions, give the place value of the underlined digit.. 8, , , ,9.56 For Questions 5 7, write the numeral in expanded form , For Questions 8 0, write the numeral ( ) ( ) ( 9 0 ) ( 0 ) ( ) 0 Rounding Note the digit x that is specified. If the digit after x is 5 or greater than 5, increase x by one and replace all the digits after x with zeroes. If the digit after x is less than 5, leave x as it is and replace all the digits after x with zeroes. Note that some zeroes will be insignificant. e) Round 7.59 to the nearest tenth. The is in the tenth place. The digit after is 5, so increase to. Result: 7.00 or 7. f) Round 7.59 to the nearest one. The is in the ones place. The digit after is which is less than 5, so do not increase. Result: or 7

If the digit after x is 5 or greater than 5, increase x by one and replace all the digits after x with zeroes.

3 SECTION. Place Value, Rounding, and Estimations 65 Check Your Progress.. Round 8,90.7 to the nearest hundredth.. Round 8,9.7 to the nearest one.. Round 8,90.7 to the nearest hundred.. Round 8,90.7 to the nearest tenth. Estimation: A rough calculation using rounded numbers. g) Gas is sold at $.89 a gallon and Tom s car takes 9 gallons. What is a reasonable estimate of Tom s gas bill? h) Jenny bought perfume for $.99, nail polish for $.5, lipstick for $7.95, and earrings for $7.9. About how much money did Jenny spend? Round $.89 to $.00 Round 9 gallons to 0 gallons Estimate: ($)(0) = $0 Round $.99 to $.00 Round $.5 to $.00 Round $7.95 to $8.00 Round $7.9 to $7.00 Estimate: $ + $ + $8 + $7 = $ i) Three hundred students took an English examination. All of the students scored less than 9, but more than 6. What is a reasonable estimate of the average score of the students? j) A music store has 0 employees. The largest gross pay is $00 per week, and the lowest is $00 per week. Estimate the weekly payroll at the music store Estimate: = = Average pay: = = 50 Estimate: 0($50) = $7,500 Check Your Progress. 5. Bill owns.87 shares of a mutual fund valued at $0.7 per share. Find a reasonable estimate of the value of Bill s stock to the nearest hundred dollars. 6. A unit of water costs $.09 and 60. units are used. Find a reasonable estimate of the bill to the nearest hundred dollars.

99, nail polish for $.5, lipstick for $7.95, and earrings for $7.9. About how much money did Jenny spend? Round $.89 to $.00 Round 9 gallons to 0 gallons Estimate: ($)(0) = $0 Round $.99 to $.

4 66 CHAPTER Arithmetic 7. Seventy students took a test. If the highest score was 96 and the lowest score was 7, what was the class average. 8. On a certain day, the college cafeteria sold 70 lunch specials. The lowest special was $ and the highest was $7. What is the estimate of income from lunch specials that day? 9. A bag of fertilizer covers.75 acres. What is a reasonable estimate of the number of acres that could be covered with 59.5 bags of fertilizer? 0. Below are the prices of the four most active stocks on a certain Exchange and their closing prices per share in dollar. Tallar Corp Paxin Inc Fun NY Aninus 5 8 What would be a reasonable estimate of the average closing price per share for these stocks? See If You Remember SECTIONS (.8)(.)

A bag of fertilizer covers.75 acres. What is a reasonable estimate of the number of acres that could be covered with 59.5 bags of fertilizer? 0.

5 SECTION. Place Value, Rounding, and Estimations Change 0.5 % to decimal. 6. Change 8 7 to decimal. 7. Write as a fraction is 0 % of what number? 9. 7 is what percent of 5? 0. If is decreased to, what is the percent decrease?. If you increase 60 by 50 %, what is the result?. Peter weighed 60 pounds. After the vacation, his weight increased by 0 %. What is his new weight?. A car that originally cost $5, has now depreciated by 0%. What is the present value of the car?

. If you increase 60 by 50 %, what is the result?. Peter weighed 60 pounds. After the vacation, his weight increased by 0 %.

DIVISION OF DECIMALS. 1503 9. We then we multiply by the

DIVISION OF DECIMALS. 1503 9. We then we multiply by the Tallahassee Community College 0 DIVISION OF DECIMALS To divide 9, we write these fractions: reciprocal of the divisor 0 9. We then we multiply by the 0 67 67 = = 9 67 67 The decimal equivalent of is. 67.