Question

Convert 0, point, 0, 9, 30.093 to a fraction in simplest form and a percent.
Answer
Attempt 1 out of 2

Fraction:
Percent (Edit the repeating and non-repeating part):

Answer 1

To convert the decimal \( 0.093 \) to a fraction, we can follow these steps:

1. **Identify the decimal:** Here, we have \( 0.093 \).
2. **Express it as a fraction:**
\[
0.093 = \frac{93}{1000}
\]
(since there are three decimal places, \( 10^3 = 1000 \)).

3. **Simplify the fraction:**
We need to find the greatest common divisor (GCD) of 93 and 1000.
The prime factorization of \( 93 \) is \( 3 \times 31 \), and for \( 1000 \) it is \( 2^3 \times 5^3 \). The GCD is \( 1 \), so:
\[
\frac{93}{1000} \text{ is already in simplest form.}
\]

Next, we convert the decimal to a percentage:

1. **Convert to percentage:**
\[
0.093 \times 100 = 9.3\%
\]

Thus, putting it all together:

- **Fraction:** \( \frac{93}{1000} \)
- **Percent:** \( 9.3\% \)

**Final Answer:**
- **Fraction:** \( \frac{93}{1000} \)
- **Percent:** \( 9.3\% \)