UNIT 3: DECIMAL FRACTIONS

Unit 3Decimal Fractions2123456 7UNITSTENTHSHUNDREDTHSTHOUSANDTHS TENTHOUSANDTHS HUNDREDTHOUSANDTHSMILLIONTHSDECIMAL FRACTIONSWritten with a decimal pointEquivalent to common fractions having denominators which are multiples of 10 The chart below gives the place value for each digit in the number 1.2345673READING DECIMAL FRACTIONSTo read a decimal, read number as whole number.Say name of place value of last digit to right.0.567 is read five hundred sixty-seven thousandthsTo read a mixed decimal (a whole number and a decimal fraction), read whole number, read word and at decimal point, and read decimal.45.00753 is read forty-five and seven hundred fifty-three hundred thousandths4ROUNDING DECIMAL FRACTIONSRounding rules:Determine place value to which number is to be roundedLook at digit immediately to its rightIf digit is less than 5, drop it and all digits to its rightIf digit is 5 or more, add 1 to digit in place to which you are rounding. Then drop all digits to its right5ROUNDING EXAMPLESRound 14.763 to the nearest hundredth6 is in the hundredths place value, so look at 3. Since 3 is less than 5, leave 6 alone and drop 3.Ans: 14.76Round 0.0065789 to the nearest ten thousandth5 is in the ten thousandths place value, so look at 7. Since 7 is greater than 5, raise 5 to 6 and drop all digits to its right.Ans: 0.00666CONVERTING FRACTIONS TO DECIMALSFractions can be converted to decimals by dividing the numerator by the denominatorExpress 5/8 as a decimal fraction:Place a decimal point after the 5 and add zeros to the right of the decimal point. Bring the decimal point straight up in the answer. Divide.

Ans 8 20 16 40 40 7CONVERTING DECIMALS TO FRACTIONSTo change a decimal to a fraction, use the number as the numerator and the place value of the last digit as the denominatorChange 0.015 to a common fraction:0.015 is read as fifteen thousandths

8ADDITION AND SUBTRACTIONTo add and subtract decimals, arrange numbers so that decimal points are directly under each other. Add or subtract as with whole numbers Place decimal point in answer directly under the other decimal points9Perform the following operations: 13.475 + 6.367 19.842 Ans 3.537 1.476 2.061 AnsADDITION AND SUBTRACTION10MULTIPLICATIONMultiply decimals using same procedures as with whole numbersCount total number of digits to right of decimal points in both numbers being multipliedBegin counting from last digit on right in answer and place decimal point same number of places as there are total in both of the numbers being multiplied11MULTIPLICATIONSince 62.4 has 1 digit to right of decimal and 1.73 has two points to right of decimal, answer should have 3 digits to right of decimal point 62.4 1.73 1 872 43 68 62 4 107 952= 107.952 AnsMultiply 62.4 1.73:12DIVISIONDivide using the same procedure as with whole numbersMove the decimal point of the divisor as many places as necessary to make it a whole numberMove the decimal point in the dividend the same number of places to the rightDivide and place the decimal point in the answer directly above the decimal point in the dividend13DIVISIONDivide 2.432 by 6.4:Move decimal point 1 place to right in 6.4Move decimal point 1 place to right in 2.432Place decimal point straight up in the answerDivide

2 5 12 5 12 .38 Ans14POWERSProduct of two or more equal factors

Appear slightly smaller

Located above and to right of number being multiplied15POWERSEvaluate each of the following powers:.43

(2.5 3)2

The power 3 means to multiply .4 by itself 3 times.43 = .4 .4 .4 = .064 AnsParentheses first: 2.5 .3 = .75(.75)2 = .75 .75 = .5625 Ans16ROOTSA quantity that is taken two or more times as an equal factor of a numberFinding a root is opposite operation of finding a powerRadical symbol () is used to indicate root of a numberIndex indicates number of times a root is to be taken as an equal factor to produce the given number

Note: Index 2 for square root is usually omitted

17FINDING ROOTSDetermine the following roots:

This means to find the number that can be multiplied by itself to equal 64. Since 8 8 = 64, the = 8 Ans

This means to find the number that can be multiplied by itself three times to equal 27. Since 3 3 3 = 27, = 3 Ans

Note: Roots that are not whole numbers can easily be computed using a calculator

18ORDER OF OPERATIONSOrder of operations including powers and roots is:ParenthesesFraction bar and radical symbol are used as grouping symbolsFor parentheses within parentheses, do innermost parentheses firstPowers and RootsMultiplication and division from left to rightAddition and subtraction from left to right19ORDER OF OPERATIONSParentheses and grouping symbols (square root) first:(1.2)2 + 6 2 Powers next:1.44 + 6 2Divide:1.44 + 3Add:4.44 Ans

20PRACTICE PROBLEMSWrite the following numbers as words. a. 0.0027 b. 143.45 c. 1.007368Round 10.2364579 to each of the following place values: TENTHSHUNDREDTHSTHOUSANDTHSTENTHOUSANDTHSHUNDREDTHOUSANDTHS MILLIONTHS

21PRACTICE PROBLEMS (Cont)Express each of the following as decimal fractions:

4. Express each of the following as fractions in lowest terms: a. 0.16 b. 0.1204 c. 0.6355. Perform the indicated operations: a. 0.0027 + 0.249 + 0.47 b. 6.45 + 2.576 c. 3.672 1.569 d. 45.3 16.97

22PRACTICE PROBLEMS (Cont)e. 1.54 2.7f. 25.63 3.46g. 0.12 .4h. 15.325 2.5i. 0.33j. (12.2 .2)2

23SolutionsWritingTwenty-seven ten thousandthsOne hundred forty-three and forty-five hundredthsOne and seven thousand three hundred sixty-eight millionthsRounding10.210.2410.23610.236510.2364610.23645824SolutionsConvert to decimal0.50.8750.9375Decimal to Fractiona

b

c

25SolutionsOrder of operations0.72179.0262.10328.334.15888.67980.036.130.027

5.953645.323.82