To perform the prime factorization of \(0.008\), we first convert the decimal into a fraction:

\[
0.008 = \frac{8}{1000}
\]

Next, simplify the fraction:

\[
\frac{8}{1000} = \frac{8 \div 8}{1000 \div 8} = \frac{1}{125}
\]

Now, factor \(125\):

\[
125 = 5^3
\]

Thus:

\[
\frac{1}{125} = \frac{1}{5^3}
\]

Therefore, the prime factorization of \(0.008\) is:

\[
\frac{1}{5^3}
\]

This means that \(0.008\) is equivalent to \(1\) divided by \(5^3\).

Would you like more details or have any questions?

Here are five related questions to explore:
1. How do you find the prime factorization of larger decimals?
2. What is the prime factorization of \(125\)?
3. How do you express other fractions in terms of prime factors?
4. How does prime factorization help simplify fractions?
5. What is the prime factorization of \(1000\)?

**Tip:** Always start by converting decimals to fractions when doing prime factorizations.

Learn how to perform the prime factorization of 0.008 by converting the decimal into a fraction and simplifying it step-by-step. Understand key concepts of prime factorization and fraction simplification. Suitable for students in Grades 6-8.

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