Question

A human hair was measured to be 8.0×10−4 inch thick. A cat hair was measured to be 4.0×10−1 inch thick. How much greater is the thickness of the cat hair than the human hair? Write the answer in standard form.

Answer 1

So, since we want to know how much thicker the cat hair is to the human hair, we just have to divide them:

`(4.0*10^(-1))/(8.0*10^(-4)) = (10^3)/(2)=.5*10^3`

Answer 2

500 times thicker.

Explanation:

We have been given that a human hair was measured to be
`8.0*10^(-4)` inch thick. A cat hair was measured to be
`4.0*10^(-1)` inch thick.

To find the thickness of cat hair is how many times greater than human hair, we will divide thickness of cat hair by thickness of human hair as:

`(4.0*10^(-1))/(8.0*10^(-4))`

Using exponent property
`(a^m)/(a^n)=a^(m-n)`, we will get:

`(4.0*10^(-1))/(8.0*10^(-4))=(4.0)/(8.0)* 10^(-1-(-4))`

`(4.0*10^(-1))/(8.0*10^(-4))=(1)/(2)*10^(-1+4)`

`(4.0*10^(-1))/(8.0*10^(-4))=0.5* 10^(3)`

`(4.0*10^(-1))/(8.0*10^(-4))=0.5* 1000`

`(4.0*10^(-1))/(8.0*10^(-4))=500`

Therefore, the cat hair is 500 times thicker than human hair.