Question

change 5.5% to a fraction in simplest form
SHOW YOUR WORK

Answer 1

To convert 5.5% to a fraction in simplest form, follow these steps:

1. **Convert the percentage to a decimal**:
\[
5.5\% = \frac{5.5}{100} = \frac{55}{1000} \quad \text{(since } 5.5 = \frac{55}{10})
\]

2. **Convert the decimal fraction to a simpler fraction**:
\[
\frac{55}{1000}
\]

3. **Simplify the fraction**:
To simplify, find the greatest common divisor (GCD) of the numerator (55) and the denominator (1000).
- The factors of 55 are: 1, 5, 11, 55
- The factors of 1000 are: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000
- The GCD of 55 and 1000 is 5.

Divide both the numerator and the denominator by their GCD:
\[
\frac{55 \div 5}{1000 \div 5} = \frac{11}{200}
\]

Thus, the fraction representing 5.5% in simplest form is:
\[
\boxed{\frac{11}{200}}
\]