Question

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

Answer 1

To convert the decimal 4.65 to a fraction, follow these steps:

1. **Separate the whole number and the decimal part**:
The whole number is 4, and the decimal part is 0.65.

2. **Convert the decimal to a fraction**:
The decimal 0.65 can be expressed as:
\[
0.65 = \frac{65}{100}
\]

3. **Simplify the fraction**:
To simplify \(\frac{65}{100}\), find the greatest common divisor (GCD) of 65 and 100. The GCD is 5. Now, divide both the numerator and the denominator by 5:
\[
\frac{65 \div 5}{100 \div 5} = \frac{13}{20}
\]

4. **Combine the whole number and the fraction**:
The number 4.65 can be expressed as:
\[
4.65 = 4 + 0.65 = 4 + \frac{13}{20}
\]

5. **Convert to a single fraction**:
To add \(4\) (which is the same as \(\frac{4 \times 20}{20} = \frac{80}{20}\)) and \(\frac{13}{20}\):
\[
4.65 = \frac{80}{20} + \frac{13}{20} = \frac{80 + 13}{20} = \frac{93}{20}
\]

Thus, the simplest form of 4.65 as a fraction is:
\[
\frac{93}{20}
\]