Decimal Place Values The decimal point separates the whole numbers from the fractional part of a number. 8.09 In a whole number the decimal point is all the way to the right, even if it is not shown in a problem. =. The place values of the number 8.09 are shown below: ones tenths hundreds tens hundredths thousandths thousands 8.09 ten-thousandths In word problems you will be asked to translate numbers from English. The word and is where the decimal point will go. Write the following numbers: Fifty-eight = 8 One-hundred twenty-five thousandths =. One hundred and twenty-five thousandths = 00.0 Eleven and three hundredths =.0 Six thousand forty and nine tenths = 6,040.9 Revised @009 MLC Page of
In the number 09.876, what digit is in the tenths place? 8 In the number 09.876, what digit is in the ones place? 9 In the number 09.876, what digit is in the tens place? In the number 09.876, what digit is in the thousandths place? 6 Exercise (answer key starts on page 9) ) In the number 78.9, what digit (number) is in the tenths place? ) In the number 78.9, what digit (number) is in the ones place? ) In the number 78.9, what digit (number) is in the tens place? 4) In the number 674.90, what digit is in the thousands place? ) In the number 674.90, what digit is in the thousandths place? 6) In the number 674.90, what digit is in the hundredths place? 7) In the number 674.90, what digit is in the tenths place? 8) In the number 674.90, what digit is in the ones place? 9) In the number 674.90, what digit is in the tens place? 0) In the number 674.90, what digit is in the hundreds place? Exercise Directions: translate the following numbers from English into decimal numbers. Twenty-nine. Eighty-one hundredths. Nine thousand thirty-four and seven tenths 4. One and four thousandths. One hundred and sixty-two thousandths 6. Forty-five hundredths 7. Four thousand three hundred twenty-one ten-thousandths 8. One hundred twenty and five tenths 9. Seventeen thousandths 0. One and seven tenths Revised @009 MLC Page of
Rounding Decimal Numbers When rounding decimal numbers, first look at the number place you are asked to round to. Then look at the digit (number) just to its right. If that digit is smaller than (0,,,, or 4), then do not round up. If the digit is or larger (, 6, 7, 8, 9), then round up. Round.69 to the nearest thousandth The place to round to.69 The digit is small..69 is the answer Do not round up. Round 8.067 to the nearest thousandth The place to round to 8.067 8.0 is the answer Drop everything to the right The digit 6 is large. Round up. Round.09999 to the nearest tenth The place to round to.09999. is the answer The digit 9 is large. Round up. Drop everything to the right Round.04999 to the nearest tenth The place to round to The digit 4 is small. Do not round up..04999 Drop everything to the right.0 is the answer Round 99.99 to the nearest whole (ones) number The place to round to 99.99 The digit 9 is large. Round up. 00 is the answer Drop everything to the right Revised @009 MLC Page of
Exercise Directions: Round the following decimal numbers to the place indicated ). to thousandths ).009 to thousandths ).096 to thousandths 4).4 to thousandths ) 6.6666 to thousandths 6) 40.6884 to thousandths 7).99999 to thousandths 8). to hundredths 9).009 to hundredths 0). to hundredths ).67 to hundredths ) 48.00 to hundredths ) 7.987 to tenths 4).666 to tenths ). to tenths 6) 99.99 to tenths 7). to whole (ones) number 8).99 to whole (ones) number 9) 499 to the nearest hundred 0) 999 to the nearest thousand Revised @009 MLC Page 4 of
Decimal/Fraction Conversion Changing fractions and mixed numbers to decimal numbers simply by dividing the denominator (bottom number) into the numerator (top number)...0 0.6 4.0 4 = 4.6 0. = 0..000 = 0. 9 0 9 0 The whole number in front of the fraction will also be in front of the decimal. 9 Rounded to the nearest thousandth or Use repeating dash over the first =. Changing decimal numbers into fractions and mixed numbers is as easy as saying the number as a fraction then writing it down. Remember to reduce and simplify.. = two tenths = = 0 7.7 = thirty-seven hundredths = 00.40 = four hundred twenty thousandths = 8. = eighteen and thirty-two hundredths = 40 = 000 0 8 = 8 00 8 Revised @009 MLC Page of
Exercise 4 Directions: Change the following fractions and mixed numbers to decimal numbers. Round answers to the nearest thousandth, if necessary. ) ) 9) 8 4 8 ) 7 6) 0 0) ) 7) 6 7 ) 8 6 4) 6 8) 0 8 ) 6 Exercise Directions: Change the following decimal numbers to fractions or mixed numbers. Reduce answers, if possible. ). ).6 9).07 ). 6).6 0).87 ).8 7) 6. ) 4. 4).7 8). ) 7.7 Revised @009 MLC Page 6 of
Exercise 6 Directions: Fill in the chart below with equivalent fractions and decimal numbers. Reduce fraction answers, if possible. Round decimal answers to the nearest hundredth, if necessary. Fraction Decimal Fraction Decimal ) 6).00 4 ) 7).0 9 4 ) 8).8 0 6 4) 9) 7. 68 ) 0) 9. Arranging decimal numbers by size When comparing decimal numbers and arranging them in order it is usually easiest to line up the numbers vertically with the decimal points in a vertical line. If a number doesn t have a decimal point, place the decimal at the end. You may fill in blanks with zeroes to make the columns easier to line up. The same Which is larger.06 or.00899?.0600.00899 added zeros is larger than 0; therefore,.06 is larger than.00899.06 is the answer Revised @009 MLC Page 7 of
Arrange from the smallest to the largest:.08.8..08.8 The only clue here is that.8 does not have a whole number; therefore, it is the smallest..08.80.00.080 0.8 In the tenths place.08 and.080 have zeroes; therefore, they are the next smallest numbers. Since.08 has a in the hundredths place, it is smaller. The two largest numbers are left over. Compare.80 and.00 by looking at hundredths place. Since.00 has a zero there, it is smaller and.80 is the largest of all the numbers. from smallest to largest, they are:.8.08.08..8 Exercise 7 Directions: arrange these numbers from largest to smallest: ).6.06.6 0.66 6. ) 4.0 40..40 4. 4. ).0067.007.0068.0070.006 4)..0..09 )..0.09.9 Revised @009 MLC Page 8 of
Exercise 8 Directions: arrange these numbers from smallest to largest: ) 7.8 8.7 8. 7.96 8.04 ) 0..0..00.00 ) 94 9.999 9.909 9.9990 94.000 4) 6.8 6.8 6. 6.8 6 ).49.489.4899.48999.48989 Adding and Subtracting Decimal Numbers When adding and subtracting decimal numbers, line up the decimal point of all the numbers. If a number does not show a decimal point, place one to the right of the whole number. You may add zeroes to keep the columns lined up. Add.6 and 4.8 Add 47 and.000.60 + 4.8.78 47.0000 +.000 47.000 Add a zero Add zeroes Subtract 4.69 from.06.06 4.69 98.7 The wording here can be confusing. Notice how subtract 4.69 from.06 means.06 4.69 46.98 46.000.98 4.80 Add zeroes Revised @009 MLC Page 9 of
Exercise 9 Directions: add or subtract the following ) ) 74.906 +.0 + 4 = ) 846 +.8 +.489 = 8.7 +.4 4) 8.64 8.87 ) 46. = 6) 6.00 -.984 = 7). +.9 + = 8) 0 4.8 -.08 = 9) 6 +.89 = 0) 46.89 9.98764 ).0000.4 ) 4..4 ) 4.8 +.79 8.96 4) Subtract 6.8 from 4. ) Subtract 8.97 from 9 6) Add.00 to 87 7) Add 000 to.086 8).40.80 6.9 + 87.89 9) 4.0 + 98.764 0) Subtract.00 from.0 Revised @009 MLC Page 0 of
Multiplying Decimal Numbers When multiplying decimal numbers, set up the problem like regular multiplication. When you get your answer, add up the total number of digits to the right of the decimals in both the numbers you are multiplying and place the decimal in your answer that many places from the right end..0.008 0.8.008 three digits.0.0006 is the answer.0006 two digits 0 five digits.8 6.0 is the answer 6.0 When multiplying three numbers together, multiply any two to get an answer; then multiply that answer by the third number...0 46.0..06.06 46 86 4 4.076 two digits one digit three digits 4.076 is the answer Revised @009 MLC Page of
Exercise 0 Directions: Multiply the following ).67. ) 84.78.6 ) 98.47.7 4).884 ).76.00. 6) 8.04 7) 8.4 8) 4.09 9).4 0) 6.004.6.006 8. ).00 ) 8.88 ).4 4) ).00.88 4.....7 8..004 Revised @009 MLC Page of
Dividing Decimal Numbers Here are the three ways you will see division problems; they all mean the same thing: 46.8. 46.8 46.8.. When dividing decimal numbers, move the decimal point in the divisor (number you re dividing by) to the right end of the divisor. Then move the decimal point in the dividend (the number you re dividing into) the same number of places to the right as you moved it in the divisor... 46.8.00 8.00. 4. 6..8..0 Once you have placed the decimal point correctly in your quotient (answer), divide like you would in whole numbers. Rounded to hundredth. 4.6 4 6 6 0.6 0..0 0 9.47.7.7 6.00000 = 9.4.600 =.7 70 0 68 0 0 0 4 7 0 7 0 9 Revised @009 MLC Page of
Exercise Directions: Divide. Round answers to hundredths, if necessary )..69 ).8 6.4 ).00 4 4).4 80 ) 4 6) 7.68 7).66.8 8).87.96 9) 9.0 0).64.408 ) 0. ). 8 ).86 0 4).789.6 ).8 7.006 Revised @009 MLC Page 4 of
Word Problems using Decimal Numbers Definitions: Sum the answer from adding numbers Difference the answer from subtracting numbers Product the answer from multiplying numbers Quotient the answer from dividing numbers In solving word problems, try to understand the whole situation being described. Some numbers may not even be involved in answering the question. Sometimes you will have to do extra steps to get the numbers you need to solve the problem. If the annual rainfall for a town near Santa Fe was. inches in 960,. inches in 96, and. in 96, what was the total rainfall for the three years?. Total means to add. +. 7.0 inches is the answer 7.0 What is the difference between David s salary of $.86 per month and Robert s monthly salary, which is $8.90? Difference means to subtract.86 8.90 04.96 $04.96 is the answer If you have a car that used 9. gallons of gas to go 8 miles, how many miles per gallon (mpg) did the car get? (round your answer to the nearest tenth.) miles 8 miles mpg = = ; so divide 9. into 8 gallon 9. gallon 4.84 9. 8.000 4.8 mpg is the answer Revised @009 MLC Page of
You need to order three hinges for each of doors. Each hinge costs $.7. How much will the hinges cost? The total number of hinges is = 4 Multiply 4.7 =.7 $.7 is the answer Exercise ) During five days, you drive.4 miles, 4. miles, 0.4 miles, 8.7 miles, and 7. miles. How many miles did you drive during those five days? ) If you are given checks, one for $6.98, another for $7.7, and a third for $60, how much is the total of all checks? ) If a car gets 4. mpg on the highway, how many gallons of fuel will it use by traveling 40 highway miles? (round answer to tenths) 4) If you need to cut pieces of glass from a 4 feet length, how long should each piece be? ) If you purchase a TV and pay $40 down and $.60 a month for 8 months, what was the purchase price of the TV? 6) If the revenues from the extra ¼ % sales tax amounted to $48,6.47 in 98 and is to be divided equally among 7 different departments within the city of Albuquerque, how much will each department receive? (round to the nearest cent) 7) If the total precipitation (rainfall and snow) for the year at a mountain town is expected to be 7.9 inches and it has already rained 6.8 inches, how many more inches of precipitation are expected? Revised @009 MLC Page 6 of
Decimals Practice Test Change to decimals. (round to hundredths) ) ) ) 6 8 4) Change to fractions (reduce, if possible) ). 6).66 7).4 8) 4.87 Add 9).7 + 8.9 0) 7.006..86 + 46.9 ) 8. + 68 + 49.64 Subtract ).6 -.87 ) 6.8 46.96 4) Subtract.97 from. Multiply ).8 x.78 6).6 x 74 7).0 x.67 x.9 Divide (round answers to hundredths) 8).7.49 9) 8..7 0).7 Revised @009 MLC Page 7 of
) Arrange from largest to smallest.808,.8,.809,.807.8 ) Arrange from smallest to largest.6,.6,.06,.6,.66 ) Subtract four and three-tenths from eleven and eighty-one hundredths. 4) If you ran. miles on Monday,.9 miles on Wednesday, and 4.7 miles on Friday, how many miles did you run, total, for the three days? ) If you divided $6.6 evenly among five children, how much would each child get? 6) If you bought.6 gallons of gasoline at $.0 per gallon, how much did the gasoline cost? Revised @009 MLC Page 8 of
Answer Key Exercise Exercise Exercise ) 9 ) 9 ). ) 8 ).8 ).009 ) 7 ) 904.7 ).00 4) 6 4).004 4). ) ) 00.06 ) 6.667 6) 0 6).4 6) 40.69 7) 9 7).4 7).000 8) 4 8) 0. 8). 9) 7 9).07 9).0 0) 0).7 0). ).7 Exercise 4 Exercise ) 48.00 ). ) 8.0 ) 4 ).86 ).67 4).88 ).7 6). ) 4).7 ) 4 ). 4) 4 6) 00.0 ) 4 7) 6) 8 8) 7).87 8) 8.667 9).6 0).667 ).06 ) 6.6 7) 6 00 7 8) 0 7 9) 00 0) 6 ) 4 40 7 ) 7 00 9) 00 0) 000 Revised @009 MLC Page 9 of
Exercise 6 Fraction Decimal Fraction Decimal ). 6).00 00 4 ).44 7).0 9 0 ). 4 8).8 4 0 4) 0.06 9) 7 7. 6 0 68 ) 68.4 0) 9 9. 8 Exercise 7 Exercise 8 Exercise 9 ) 6.,.6,.6,.06, 0.66 ) 7.8, 7.96, 8.04, 8., 8.7 ) 4. ) 40., 4., 4., 4.0,.40 ).00,.0,.00,.,. ) 6.96 ) 847.769 ).0070,.007,.0067,.0068,.006 ) 9.909, 9.999, 9.9990, 94, 94.000 4).,,.,.09,.0 4) 6, 6., 6.8, 6.8, 6.8 4) 8.77 ).9,.,.09,.0, ).489,.48989,.4899,.48999,.49 ) 40.8 6).07 7) 8).8 9) 8.89 0) 6.906 ) 9.88767 ).8766 ) 9.6 4) 7.4 ) 0.0 6) 87.00 7) 000.086 8) 69 9) 4.776 0).009 Revised @009 MLC Page 0 of
Exercise 0 Exercise Exercise ).44 ). ) 76. miles ).886 ) 0 ) $4. ) 68.99 ) 000 ) 8. gallons 4).007684 4) 00 4).8 feet ).44 ).6 ) $00.80 6).06 6).0 6) $6876.64 7).04 7) 7).08 inches 8).047 8). 9) 0. 9).0 0) 9.6 0). ).00000 ).0 ) 7.844 ) 8. ).4 ) 4.66 4).00 4) 400 ).074 ).0 Practice Test ).4 ).84 ) $.7 ).7 4). 6) $. ).8 ) 4.96 4). 6). ) 4 7).000 6) 0 8).70 7) 9).0 8) 4 7 8 0).6 9).6 ).8,.808,.807,.809,.8 0) 40.069 ).06,.6,.6,.6,.66 ).74 ) 7. ).9 4).9 miles Revised @009 MLC Page of