Question

Simplify the expression: (3.45× 10-²) ÷ (2.03 x 10-⁵)

Answer 1

Recall that we want to solve this problem

`(3.45\cdot10^(-2))/(2.03\cdot10^(-5))`

We will use the following property, given a nonzero number a and numbers b,c we have that

`(a^b)/(a^c)=a^(b-c)`

So if we divide two numbers that have the same base, we can simply subtract their exponents.

So, using the properties of multiplication of fractions, we get

`(3.45\cdot10^(-2))/(2.03\cdot10^(-5))=(3.45)/(2.03)\cdot(10^(-2))/(10^(-5))=(3.45)/(2.03)\cdot10^(-2-(-5))=(3.45)/(2.03)\cdot10^3^{}`

With help of a calculator, we will calculate 3.45/2.03. By doing so, we get that

`(3.45)/(2.03)=1.6995073`

So we have

`(3.45\cdot10^(-2))/(2.03\cdot10^(-5))=1.6995073\cdot10^3=1699.5073`