Question

obtain an estimate for the following 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{0.19965 \times 102}{0.206}\\)
which of the following is a good estimate of the quotient \\(\frac{0.19965 \times 102}{0.206}\\)?
\\(\bigcirc\\) a. 33
\\(\bigcirc\\) b. 67
\\(\bigcirc\\) c. 50
\\(\bigcirc\\) d. 100
the actual quotient is \\(98.86\\). (round to two decimal places as needed.)
how reasonable is your estimate when compared to the actual answer? select the correct answer below and fill in the answer box to complete your choice.
(round to two decimal places as needed.)
\\(\bigcirc\\) a. the estimate is a little lower than the actual result. the difference is \\(\square\\).
\\(\bigcirc\\) b. the estimate is a little higher than the actual result. the difference is \\(\square\\).

Explanation:

Step1: Estimate the quotient

We can approximate \(0.19965\) as \(0.2\) and \(0.206\) as \(0.2\) (or notice that \(0.19965\times102\approx0.2\times100 = 20\), but wait, no, the expression is \(\frac{0.19965\times102}{0.206}\). Let's simplify the estimation:

First, approximate \(0.19965\approx0.2\), \(102\approx100\), \(0.206\approx0.2\). Then the estimate is \(\frac{0.2\times100}{0.2}=\frac{20}{0.2} = 100\). So the estimate is \(100\) (option D).

Step2: Compare estimate and actual

The actual quotient is \(98.86\). The estimate (\(100\)) is higher than the actual result (\(98.86\)). The difference is \(100 - 98.86=1.14\).

Answer:

For the estimate choice: D. 100
For the reasonability: B. The estimate is a little higher than the actual result. The difference is \(1.14\)