Question
Find the quotient of 4.13 x 10exponent-8
and 0.04 x 10exponent5
. In two or more complete sentences, explain each step in your calculations. Include the quotient as part of your final answer.
and 0.04 x 10exponent5
. In two or more complete sentences, explain each step in your calculations. Include the quotient as part of your final answer.
Answers
Answer
can you make it less less advanced and less words
Answered by
GPT-4o mini
To find the quotient of \( 4.13 \times 10^{-8} \) and \( 0.04 \times 10^{5} \), we start by dividing the numerical coefficients and then handling the powers of ten.
First, we divide the coefficients:
\[ \frac{4.13}{0.04} = 103.25 \]
Next, we divide the powers of ten:
\[ \frac{10^{-8}}{10^{5}} = 10^{-8 - 5} = 10^{-13} \]
Now, we combine both parts to write the final answer:
\[ 103.25 \times 10^{-13} \]
For standard scientific notation, we need to express \( 103.25 \) as \( 1.0325 \) while increasing the exponent by 1 to account for the shift of the decimal point. Therefore, the answer can be rewritten as:
\[ 1.0325 \times 10^{-12} \]
Thus, the final quotient is:
\[ 1.0325 \times 10^{-12} \]
First, we divide the coefficients:
\[ \frac{4.13}{0.04} = 103.25 \]
Next, we divide the powers of ten:
\[ \frac{10^{-8}}{10^{5}} = 10^{-8 - 5} = 10^{-13} \]
Now, we combine both parts to write the final answer:
\[ 103.25 \times 10^{-13} \]
For standard scientific notation, we need to express \( 103.25 \) as \( 1.0325 \) while increasing the exponent by 1 to account for the shift of the decimal point. Therefore, the answer can be rewritten as:
\[ 1.0325 \times 10^{-12} \]
Thus, the final quotient is:
\[ 1.0325 \times 10^{-12} \]
Answered by
GPT-4o mini
Sure! Here’s a simpler breakdown:
1. First, divide the numbers:
\[
\frac{4.13}{0.04} = 103.25
\]
2. Next, divide the powers of ten:
\[
\frac{10^{-8}}{10^{5}} = 10^{-13}
\]
3. Now, combine these results:
\[
103.25 \times 10^{-13}
\]
4. Convert \( 103.25 \) to scientific notation:
\[
1.0325 \times 10^{-12}
\]
So, the final answer is:
\[
1.0325 \times 10^{-12}
\]
1. First, divide the numbers:
\[
\frac{4.13}{0.04} = 103.25
\]
2. Next, divide the powers of ten:
\[
\frac{10^{-8}}{10^{5}} = 10^{-13}
\]
3. Now, combine these results:
\[
103.25 \times 10^{-13}
\]
4. Convert \( 103.25 \) to scientific notation:
\[
1.0325 \times 10^{-12}
\]
So, the final answer is:
\[
1.0325 \times 10^{-12}
\]
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