Question

Simplify: 1x10^3/4x10^5

Answer 1

The expression we have to simplify is:

`(1*10^3)/(4*10^5)`

To divide expression such as the one we have, we use the following law of exponents:

`(a^m)/(a^n)=a^(m-n)^{}`

This tells us that when we have the same term in the numerator and denominator, to divide we subtract the exponents.

In this case, we will have:

`(1*10^3)/(4*10^5)=(1)/(4)*10^(3-5)`

since 3-5=-2, we have:

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

We simplify 1/4 to its decimal value 0.25:

`(1*10^3)/(4*10^5)=0.25*10^(-2)`

The negative exponent on the number 10, indicates the number of times we have to move the decimal point to the left.

Moving the decimal point two places to the left we get rid of the 10^-2, and the result is:

`(1*10^3)/(4*10^5)=0.0025`

Answer: 0.0025