Question

Find the quotient of 4.13 x 10^-8 and 0.04 x 10^5

. In two or more complete sentences, explain each step in your calculations. Include the quotient as part of your final answer.

Answer 1

To find the quotient of \( 4.13 \times 10^{-8} \) and \( 0.04 \times 10^{5} \), we start by rewriting the numbers in a form that makes the calculations easier.

First, we can express \( 0.04 \) as \( 4.0 \times 10^{-2} \) so that both numbers are in a similar scientific notation format. Therefore, we now have:

\[
4.13 \times 10^{-8} \div (4.0 \times 10^{-2} \times 10^{5})
\]

Next, we can combine the terms inside the second coefficient:

\[
4.0 \times 10^{-2} \times 10^{5} = 4.0 \times 10^{3}
\]

Now, we have the expression:

\[
\frac{4.13 \times 10^{-8}}{4.0 \times 10^{3}}
\]

This can be separated into the numerical part and the exponential part:

\[
\frac{4.13}{4.0} \times \frac{10^{-8}}{10^{3}}
\]

Calculating the numerical part:

\[
\frac{4.13}{4.0} = 1.0325
\]

For the exponential part, we use the property of exponents:

\[
\frac{10^{-8}}{10^{3}} = 10^{-8 - 3} = 10^{-11}
\]

Now we combine the results:

\[
1.0325 \times 10^{-11}
\]

Thus, the final answer for the quotient of \( 4.13 \times 10^{-8} \) and \( 0.04 \times 10^{5} \) is:

\[
1.0325 \times 10^{-11}
\]