What is 4.65 converted to a fraction? The answer should be simplest form.

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

To convert the decimal \( 4.65 \) to a fraction, we can follow these steps:

1. **Express the decimal as a fraction**:
\[
4.65 = \frac{465}{100}
\]

2. **Simplify the fraction**:
First, we need to find the greatest common divisor (GCD) of 465 and 100.

- The prime factorization of \( 465 \) is \( 3 \times 5 \times 31 \).
- The prime factorization of \( 100 \) is \( 2^2 \times 5^2 \).

The only common factor is \( 5 \).

3. **Divide both the numerator and the denominator by their GCD**:
\[
\frac{465 \div 5}{100 \div 5} = \frac{93}{20}
\]

Thus, the decimal \( 4.65 \) converted to the simplest form of a fraction is:

\[
\frac{93}{20}
\]