Question

The estimated answer to a multiplication problem is 800,000. Which of the following expressions could result in this answer? Explain how you know.

8,146 x 12
81,467 x 121
8,146 x 121
81,477 x 1,217

Answer 1

Explanation:

88

Answer 2

8,146 x 121

Explanation:

This is a problem in which you need to measure your understading of "orders of magnitude."

If the estimated answer is
`800000` that means that we are looking at a multiplication in the "order of"
`8*10^5`

You need to look at the "orders of magnitude" of the things you're multiplying. In the first case, we have
`8146*12` that would be "of the order of"
`8*10^3` times
`10^1`. So the whole multiplication would "of the order of"
`8*10^4` or near
`80000`

The correct answer, 8,146 x 121, is because it's "of the order of"
`8*10^3` times
`10^2` and the gives us the
`8*10^5` we need.