Estimation of Numerical Answers

If you input the numbers correctly into your calculator, the answer will be correct. But will you recognize an incorrect answer? You will if you obtain an approximate answer by visual inspection. Especially important is the order of magnitude, represented by the location of the decimal point or the power of 10, which may go astray even though the digits are correct. For example, consider a calculation of the power required to raise a 639 kg mass 20.74 m in 2.120 minutes:

This example involves concepts and units which may be unfamiliar to you, so that you can't easily judge whether the result ''makes sense," so we'll check the answer by estimation. Write each term in exponential notation, using just one significant figure. Then mentally combine the powers of 10 and the multipliers separately to estimate the result:

The estimate agrees with the calculation to one significant figure, showing that the calculation is very

likely correct.