How do you estimate to check that your answer is reasonable?

Answer 1

To estimate an answer the numbers are rounded and the calculation done. It is often suggested to round to 1 sig fig as this will give a general indication of how big the answer should be.

eg 1234 ÷ 31 → 1000 ÷ 30 ≈ 33.33 so an answer in the region of about 30 to 40 is expected.

A slight variation from this can make the calculation easier, eg rounding the 1234 above to 2 sig fig gives 1200 ÷ 30 which is easier as 1200 is a multiple of 30 (and actually much closer to the real answer) giving 1200 ÷ 30 = 40; the real answer is approx 39.81.

Answer 2

It really depends on the specific problem. But the general idea is to round off the numbers involved, perhaps to a single significant digit, so you can easily do the calculation in your head. Then you do whatever calculations are involved (you may want to do additional rounding for intermediate results), and verify whether the exact answer is reasonably close to the answer based on estimates.

Answer 3

Round the numbers which are used in the calculation and then repeat the calculation. See if this answer tallies approximately with the answer.