Question

Convert 0, point, 5, 1, 30.513 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 0.513 to a fraction in simplest form and a percent, let's break this down step by step.

### Step 1: Converting to a Fraction

The decimal 0.513 can be expressed as:

\[
0.513 = \frac{513}{1000}
\]

To simplify this fraction, we need to find the greatest common divisor (GCD) of 513 and 1000.

The prime factorization of 513 is:
- 513 = 3 × 171
- 171 = 3 × 57
- 57 = 3 × 19
Thus, the prime factorization of 513 is \(3^3 \times 19\).

The prime factorization of 1000 is:
- 1000 = \(10^3 = (2 \times 5)^3 = 2^3 \times 5^3\)

Since there are no common factors (other than 1), the GCD is 1. Therefore, the fraction \(\frac{513}{1000}\) is already in simplest form.

### Step 2: Converting to Percent

To convert a decimal to a percent, we multiply by 100:

\[
0.513 \times 100 = 51.3\%
\]

**Final Answers**:

- **Fraction:** \(\frac{513}{1000}\)
- **Percent:** \(51.3\%\)