Question

(9.38) x (53201) = 499025.4 What is the answer express to the correct number of significant figures?

Answer 1

`4.990*10^5`

Explanation:

As a general rule, in a multiplication, we take the amount of significant figures of the number with the least significant figures.

To delve deeper in this, we need to discuss the precision of those numbers:
9.38 means that we know 9.38 with a precision of +/- 0.01. That means that the maximum error is 0.1%

53201 means that we know 53201 with a precision of +/- 1. That means that the maximum error is 0.002%

The error in a product is the sum of the relative errors. In this case, 0.1% + 0.002% = 0.1% approximately.
So the maximum error in 499025.4 will be 0.1% of that number, i.e. 499.02.

The last significant figure should be on par with the largest figure of the maximum error. Our maximum error is in the hundreds, so that should be the our last significant figure: `4990*10^2 +- 500` (it doesn't make much sense to give errors with more than 2 significant figures).
So we have `4990*10^2`, or better written, `4.990*10^5` or `4.99*10^5`

Answer 2

`9.38xx53201=499025.4=499000.0=4.99xx10^5`

Explanation:

When multiplying or dividing, the answer must be limited to the fewest number of significant figures (digits) in the numbers used in the calculation.

`9.38xx53201=4990254`

The number with the fewest significant figures is `9.38`, with three significant figures. Therefore, the answer must be rounded to three significant figures.

`9.38xx53201=499025.4=499000.0=4.99xx10^5`