Question

What is the quotient of 1.232 x 10⁸ and 3.85 x 10 expressed in scientific notation?

Answer 1

3.2 x 10⁶

Step-by-step explanation:

Given the quotient:

`(1.232*10^8)/(3.85*10)`

We can rewrite the expression by removing the decimals as follows:

`=(1232*10^(-3)*10^8)/(385*10^(-2)*10)`

Next, we rewrite the powers of 10 so we can cancel out common terms.

`\begin{gathered} =(1232)/(385)*((10^(-2)*10^(-1))*(10*10^7))/(10^(-2)*10) \\ (1232)/(385)*10^(-1)*10^7 \end{gathered}`

Next, express the first fraction in the lowest possible form:

`\begin{gathered} =(16*77)/(5*77)*10^(-1)*10^7 \\ =(16)/(5)*10^(-1)*10^7 \\ =3.2*10^(-1+7) \\ =3.2*10^6 \end{gathered}`

The quotient expressed in scientific notation is 3.2 x 10⁶.