Estimating and Solving Applied Problems Using Decimals 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. 143.2153 + 255.91829 56.09812 - 31.2516 8.98102 x 3.25175 0.00354 ÷ 0.04218   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.   Back to the Decimals page Back to the Math 187A page Back to the Math Department page