Question

How do you evaluate `(4.2 times 10^2)(4.2 times 10^5)`?

Answer 1

`1.764` x `10^8`

Explanation:

Easiest way is to separate the coefficients and the powers of 10.

(`4.2` x `10^2`)(`4.2` x `10^5`)

`(4.2)(4.2)(10^2)(10^5)`

`4.2^2` `(10^7)`

`17.64` x `10^7`

This answer is correct, but it is not in its simplest form. Since 17.64 > 10, we can divide it by 10 repeatedly and multiply those additional powers to the power of 10 term.

`17.64 / 10 = 1.764` This is 1 additional power of 10

Since 1.764 this is less than 10, we have no more powers of 10 left to gather.

So the final answer is:

`1.764` x `10^8`