Question

How do you simplify `(91.2\cdot 10^ { 2} ) \cdot ( 3.972\cdot 10^ { 11})`?

Answer 1

`=3.622464 *10^15`

Explanation:

To simplify this equation, we do three steps. Since multiplication is commutative ( which means `a*b=b*a`), we shuffle around the equation so it looks the first step looks like this
`(91.2*3.972)(10^2*10^11)`

Next we solve the brackets, remembering that `a^m * a^n= a^(m+n)`, which leaves us with
`(362.2464)(color(red)(10^(2+11)))`
`=(362.2464)(10^13)`
`= 362.2464 * 10^13`

The last step is to simplify the equation. When multiplying a number by a power of 10, the standard thing to do is get that number into the single digits. Remembering that when you add `n` onto `10^x`, the deimal place moves `n` spots to the left on the number in front of 10 and vice-versa, we get
`362.2464 * 10^13 = color(red)(36).color(red)(22464) *10^color(red)(14)=color(green)(3).color(green)(622464)*10^color(green)(15)`

I hope I helped!