Question

How many times larger is 9 x 10-4 than 3 x 10-10? A) 3 x 10^5 B) 3 x 10^6 C) 6 x 10^5 D) 6 x 10^6

Answer 1

The correct option is B.

Explanation:

We need to find how many times larger is
`9* 10^(-4)` than
`3* 10^(-10)`.

Let
`9* 10^(-4)` is x times larger than
`3* 10^(-10)`.

`x* 3* 10^(-10)=9* 10^(-4)`

Divide
`3* 10^(-10)` on both sides.

`x=(9* 10^(-4))/(3* 10^(-10))`

It can be written as

`x=(9)/(3)* (10^(-4))/(10^(-10))`

`x=3* (10^(-4))/(10^(-10))`

Using quotient property of exponent, we get

`x=3* 10^(-4-(-10))`
`[\because (a^m)/(a^n)=a^(m-n)]`

`x=3* 10^(-4+10)`

`x=3* 10^(6)`

`9* 10^(-4)` is
`3* 10^(6)` times larger than
`3* 10^(-10)`.

Therefore the correct option is B.

Answer 2

`(9\cdot10^(-4))/(3\cdot10^(-10))=(9)/(3)\cdot (10^(-4))/(10^(-10))=3\cdot10^((-4)-(-10))=3\cdot10^(-4+10)=\boxed{3\cdot10^6}`

Answer B.