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
      
      
      
   2. 56.09812 - 31.2516
      
      
      
   3. 8.98102 x 3.25175
      
      
      
   4. 0.00354 ÷ 0.04218
      
      

    

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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