SD 581- Hargrove CHAPTER 4: DECIMALS

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					       Math 581- Hargrove                       CHAPTER 4: DECIMALS
4.1, Reading & Writing Decimals
I.     Decimal Notation & Word Names
       A. Place Value Chart

                                . .




       B. Writing Word Names: page 268

          1) 35.3 ________________________________________________________

          2) 2.45678______________________________________________________

                     ______________________________________________________

          3) 0.0032 ______________________________________________________

          4) Write a check for the amount of $3,214.34. __________________________

             ____________________________________________________dollars
II.    Changing decimals in words to standard notation.
       A. Eight and twelve hundredths ________________________________________

       B. One hundred and eleven ten thousandths ______________________________

       C. Thirty-five thousand two hundred four hundred thousandths

          ________________________________________________________________

III.   Naming the decimal places for decimal numerals
       A. 234,560.00123



       B. 0.98765



       C. 9.99810



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IV.   From Decimal Notation to Fractional Notation
      A. Remember that we can think of decimals in terms of fractions.
                  3 7       4     2       1
         3.7421                   
                  1 10 100 1000 10000
                  30000 7000         400     20      1
                                             
                  10000 10000 10000 10000 10000
                   37421
                =
                   10000
      B. Process of converting from decimal to fractional notation.
         1. The digits to the right of the decimal point is the numerator of the fraction.
          2. The denominator is 10 for tenths, 100 for hundredths, 1000 for thousandths, and so on.
          3. If the decimal point has a whole number, it will be written as a mixed number with the
              same whole number part.
      C. Another Process
         1. Read the decimal.      (three and twenty-four hundredths)           3.24
                                                                                   24
          2. Write as a mixed numeral.                                          3
                                                                                  100
      D. Examples (don’t simplify)
         1) 24.003

          2) 0.34251

          3) 5.093

4.2, Rounding Decimals
I.     A. Use the same method as with whole numbers.
       B. Using the number line, round 1.34 to the nearest tenth.

               1.30                            1.40
      C. Without the number line:
          1. Locate the digits place.
          2. Look at the number to the right. If it is 4 or smaller, it stays the same. If it is 5 or larger,
             it rounds up.
      D. Examples: Round each number to the nearest tenth, hundredth, & thousandth.

                                    Tenth               Hundredth                  Thousandth
                 1) 45.2491

                 2) 47892

                 3) 0.99874




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II.Rounding Money Amounts:
    A. Place Value for Money




      II.      Rounding Money
            A. To the nearest cent
               1) $2.345                      2) $0.695                  3) $0.995

            B. To the nearest dollar
               1) $345.35                     2) $456.98                 3) $0.789


4.3, Adding & Subtracting Decimals
I.     Addition
       A. Make sure to line-up the decimal points.

            B. Examples
               1) 34.298 + 127.93 =           2)7.45 + 0.241 + 27.8 =         3) 23.4 + 0.098 +34 =




II.         Subtraction
            A. Similar to addition but must use zeroes for missing places.
            B. Examples
               1) 38.213 – 12.87 =            2) 18.03 – 8.203 =              3) 2210 – 28.9876 =



 4.4, Multiplying Decimals
I.     Process for multiplying and examples
       A. Process
           1. Multiply the numbers (the factors) as if they were whole numbers.              24.1
                                                                                           X.008
               2. After multiplying count the number of decimal places in the factors.
               3. Use that sum to find the decimal’s place. Start at the far right and count
                  the decimal places to the left.
               4. You may need to add extra zeroes on the left side to get the correct number of decimal
                  places.
                                                                                                       3
      B. Examples
         1) 0.093 x 0.008                 2) 0.032 x 0.00081               3) (0.11)(0.00025)




4.5, Dividing Decimals
I.     Whole-Number Divisors
       A. Process
           1. Place the decimal point directly above the decimal point in the dividend.

                                                               32 81.92
          2. Divide as you would a whole number.

      B. Examples

          1) 82 38.54                                  2)      15 22.5



      C. Writing extra zeroes to divide
         1) 30  8                                     2)      78




II.   Division that are not whole numbers
      A. Consider this:            0.83 406.7
         1. If you multiply the divisor by 100 you get a whole number. You must also multiply
             the dividend and end up with 83 406.7
         2. Simpler method
             a. Move the decimal point in the divisor to make a whole number.
             b. Move the decimal point in the dividend the same number of places as the divisor.
                            .83 406.7
             c. Place the decimal point right above and divide.
      B. Examples

        1)    5.848  8.6                2)    0.64 12                    3)      25 1.6




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       D. Dividing and rounding the quotient
          1) Divide as you normally would.
          2) Occasionally, the quotient will either repeat or go on for a very long time. Check the
             directions to see if you have been instructed to round your answer to a particular place.
          3) Remember to go one more than you are asked to round so that you will know the
             correct rounding. Example: If you are round to the nearest hundredth, you must go out
             to the thousandths in order to round.
          4) Try these and round to the nearest hundredth:
             a) 7 ÷ 1.3                                 b) 5.3091 ÷ 6.2




III. Order of operations
        A. Rules
           1. P
           2. E
           3. M/D
           4. A/S
        B. Examples
           1) 5  0.006  2  3.42  0.1                                                          
                                                      2) 102   3  0.24   2.4   0.21  0.092 
                                                                                 




4.6, Writing Fractions as Decimals
I.    Fractional Notation to Decimal Notation
      A. When the denominator can be changed to a power of 10.
              2                                9                                        12
           1)                         2)                                      3)          
              5                               10                                        25

       B. Also use division.
                  1                                                       1
          1) Write as a decimal.                              2) Write       as a decimal.
                  8                                                       20




                                                                                                         5
                   3
         3) Write 3 as a decimal
                   4




      C. Repeating decimals
            1                                 5                            3
         1)                             2)                            3)
            6                                11                            7




II.   Rounding in Problem Solving
      Round each to the nearest:

                              Tenth                      Hundredth             Thousandth
       1) 0.83
       2) 0.09
       3) 0.59


III. Order of Decimals
        A. To compare decimals the decimals must be taken to the same decimal place, so add
           zeroes.
        B. Compare
           1) 2.109 and 2.1            2)    0.9 and 0.908             3)     0.875 and 0.83


      C. Arrange in order from the smallest to largest.
                                                             3               1 2 3
         1) 6.39, 6.309, 6.4, 6.401               2) 1.085, 1 , 0.9        3) , , , 0.428
                                                             4               4 5 7




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IV. Solving decimals is just like solving whole numbers.
       A. Formulas to remember:
           1. Area of rectangles = length x width                  4.3 in.
           2. Perimeter is the distance around a figure.
       B. Examples                                                          1.4 in.
           1. Find the area of the rectangle:            2. Find the perimeter of the rectangle




V.    Remember
      A. Key words: page 91

      B. Steps to take to solve: three-step method

      C. In a recent year, the IRS allowed a tax deduction of 55¢ per mile for mileage driven for
         business purposes. What deduction, in dollars, would be allowed for driving 127 miles?




      D. A car loan of $7382.52 is to be paid off in 36 monthly payments. How much is each
         payment?




      E. A driver filled the gasoline tank and noted that the odometer read 67,507.8.
         After the next filling, the odometer read 68,006.1. It took 16.5 gallons to fill the tank. How
         many miles per gallon did the driver get?




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Money Conversions
        1. From dollars to cents:

              a. $25.43                  b.   $0.35              c. $2.999



           2. From cents to dollars:

              a.    45¢                  b.   345¢               c. 385.9¢


Math 581                                              Name _________________________

Hargrove                                              Class _________________________




                                       Homework:
Convert from dollars to cents.
1)  $28.88 = ________________                 2).     $0.66 = _____________

3)    $67.43 = ________________               4).     $1.785 = ____________




Convert from cents to dollars.
5). 34¢ = ___________________                 6).     95¢ = ______________

7).   3445¢ = _________________               8).     24.9¢ = _____________




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