Question

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

Answer 1

Answer:

3.2 x 10⁶

Explanation:

Given the quotient:

$\frac{1.232\times10^8}{3.85\times10}$

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

$=\frac{1232\times10^{-3}\times10^8}{385\times10^{-2}\times10}$

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

$\begin{gathered} =\frac{1232}{385}\times\frac{(10^{-2}\times10^{-1})\times(10\times10^7)}{10^{-2}\times10} \\ \frac{1232}{385}\times10^{-1}\times10^7 \end{gathered}$

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

$\begin{gathered} =\frac{16\times77}{5\times77}\times10^{-1}\times10^7 \\ =\frac{16}{5}\times10^{-1}\times10^7 \\ =3.2\times10^{-1+7} \\ =3.2\times10^6 \end{gathered}$

The quotient expressed in scientific notation is 3.2 x 10⁶.