Question

What is `(8.96 * 10^6)*(8.46*10^-5)`?

Answer 1

758

Explanation:

This is scientific notation; the number has one digit, then a decimal point, then the rest of the number, times ten raised to a power. The power shows how many places the decimal point has been moved.
`10^6` is a 1 with six zeroes, so `10^6` is another way of saying 'a million'.

Multiply the digits: `8.96*8.46=75.8016`

Add the powers of 10: `6+(-5)=1`

You now have `75.8016*10^1=758.016` but the original numbers had only three significant digits, so you can only report three significant digits in your answer `=758`

If your answer is supposed to be in scientific notation, move the decimal point two places to the left and put `10^2` on the end
`=7.58*10^2`

Answer 2

`=7.58016 xx 10^2`

Explanation:

In Algebra. `3x^4 xx 5x^6 = 15x^10`

In scientific notation you do the same:

Multiply the numbers and add the indices of 10.

`8.96 xx 10^6 xx 8.46 xx 10^-5`

`= 75.8016 xx 10^(6-5)`

`=75.8016 xx 10^1`

Adjust the number to have one digit before the decimal, increase the index of 10.

`=7.58016 xx 10^2`