9514 1404 393
Answer:
49,000
Step-by-step explanation:
The divisor is 4.084. When it is rounded to the nearest whole number, it is 4.
Then the division problem becomes ...
196,900/4 ≈ 49,000 . . . . . . showing just 2 significant digits for the estimate
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The point of an estimate is to obtain an approximate answer that is within a few percent of the actual answer. Here, rounding 4.084 to 4.000 gives an error on the order of .084/4 ≈ 2.1%. Because we're using a smaller divisor, the value we obtain for our estimate will be too large by about that amount.
Often, an estimate that has 1 or 2 significant digits is "close enough" for the purpose. Because a change in our estimated value of 1 in the least significant digit is a change of about 2%, we judge this estimate to be "close enough", given the rounding we did to start. Keeping 3 significant digits in our estimate would claim an accuracy that it does not have.
