Question
6. \( 0.125 \div 8000 \)
Ask by Fleming Macdonald. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The answer is \( \frac{1}{64000} \).
Solution
1. First, rewrite the division as a fraction:
\[
0.125 \div 8000 = \frac{0.125}{8000}.
\]
2. Express \(0.125\) as a fraction. Since
\[
0.125 = \frac{125}{1000} = \frac{1}{8},
\]
the expression becomes
\[
\frac{1}{8} \div 8000.
\]
3. Dividing by \(8000\) is the same as multiplying by its reciprocal:
\[
\frac{1}{8} \times \frac{1}{8000} = \frac{1}{8 \times 8000} = \frac{1}{64000}.
\]
4. Thus, the final answer is:
\[
\boxed{\frac{1}{64000}}.
\]
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Simplify this solution The Deep Dive
Did you know that dividing decimals by whole numbers can be fun? When you divide \( 0.125 \) by \( 8000 \), you essentially move the decimal point to the left! So, \( 0.125 \) becomes \( 0.000015625 \) when divided by \( 8000 \). Just a little mathematical magic to make those pesky decimals dance! And for those who often stumble upon division with zeros, remember the key: simplify first if you can! It makes calculations easier. In this case, you could first convert \( 0.125 \) into a fraction, \( \frac{1}{8} \), then divide by \( 8000 \) or multiply by its reciprocal, which can often clarify the process and avoid common mistakes. Happy calculating!
