Question

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

Answer 1

Recall that we want to solve this problem

$\frac{3.45\cdot10^{-2}}{2.03\cdot10^{-5}}$

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

$\frac{a^b}{a^c}=a^{b-c}$

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

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

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

$\frac{3.45}{2.03}=1.6995073$

So we have

$\frac{3.45\cdot10^{-2}}{2.03\cdot10^{-5}}=1.6995073\cdot10^3=1699.5073$