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Chapter 1: Problem 35

In Exercises 35-36, obtain an estimate for each computation without using a calculator. Then use a calculator to perform the computation. How reasonable is your estimate when compared to the actual answer? \(\frac{0.19996 \times 107}{0.509}\)

Short Answer

Expert verified
The result of the manual estimate calculation \(\frac{0.2 \times 100}{0.5}\) is \(40\). The actual computation \(\frac{0.19996 \times 107}{0.509}\) done with a calculator gives approx. \(39.4886\). The estimation result, thus, is very close and reasonably accurate.

Step by step solution

01

Estimation

Firstly, we need to estimate the calculation in exercise. The numbers can be slightly rounded to simplify the process. We can round \(0.19996\) to \(0.2\), round \(107\) to \(100\) and round \(0.509\) to \(0.5\). Our new simpler computation becomes \(\frac{0.2 \times 100}{0.5}\).
02

Performing the Simplified Computation

Next, carry out the calculation with the simplified numbers. The computation becomes \(\frac{20}{0.5}\), which gives you \(40\) as a result. This is the estimate of the computation.
03

Actual computation

Perform the actual computation using the original numbers, \(\frac{0.19996 \times 107}{0.509}\), on a calculator. This should give an outcome of approximately \(39.4886\).
04

Comparison

Compare the actual computation result with your earlier estimate. In this case, the estimate of \(40\) is very close to the actual computation result of \(39.4886\), which shows that the estimation worked reasonably well.

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