Estimating and Solving Applied Problems Using Decimals

  1. Doing Arithmetic of Decimals Using Estimation

    Since arithmetic can be cumbersome when it involves complicated numbers, it is convenient to know how to estimate to get a ball park figure.  A useful method for estimating is to round each number so that there is only one nonzero digit.  


    Example

    Estimate 23.487201 + 38.48291

    Solution

    We round each number and then add

            20 + 40  =  60


    Example

    Estimate 9.376 x 0.035912

    Solution

    We round each number and then multiply

            9 x 0.04  

     
    Since

            9 x 4  =  36

    and there are two total digits to the right of the decimal places, we get

            9 x 0.04  =  0.36


    Example

    Estimate 0.015 3.407

    Solution

    We round each number and then divide

            0.01 3  

    Since we are only keeping one nonzero digit, we only keep one nonzero digit for our estimation.

                .0033
            3| .0100
                     9 
                      10

    The solution is approximately 0.003 


    Exercises

    Use estimation to approximate the following.

    1. 143.2153 + 255.91829
      400

    2. 56.09812 - 31.2516
      25

    3. 8.98102 x 3.25175
      27

    4. 0.00354 0.04218
      0.1

     

  2. Applications

    Example


    The total snowfall was 37.3 inches in January, 41.5 inches in February, and 18.7 inches in March.  What was the average monthly snowfall during these three months?

    Solution

    By definition, to find the average we add up all three numbers and divide by 3.

               37.3
               41.5
            + 18.7
                97.5

    Now divide by 3

                32.5
            3| 97.5
                9 
                07
                  6    
                   15

    The average monthly snowfall was 32.5 inches.


    Example

    You make $8.75 per hour at your job for regular work and time and a half for work over 40 hours.  If you work 48 hours this week, how much will you earn?

    Solution

    First find the amount for the first 40 hours.  This is a multiplication problem.

            8.75
          x   40
                  0
          35000
          350.00

    Now compute the overtime wages

            8.75
          x   1.5
            4375
            8750
          13.125

    Now find the earnings for 8 hours of overtime by multiplying

           13.125
          x        8
          105.000

    Now add the regular wages and the overtime wages

              350
          +  105
               455

    You made $455 for the week.

 



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