Question

Convert the decimal below to a fraction in simplest form.
0, point, 1, 9, 5
0.195

Answer 1

To convert the decimal 0.195 to a fraction, follow these steps:

1. Write the decimal as a fraction with the numerator and denominator. Since 0.195 has three decimal places, you can write it as:

\[
\frac{195}{1000}
\]

2. Next, simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator.

The factors of 195 are:
- 1, 3, 5, 13, 15, 39, 65, 195

The factors of 1000 are:
- 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000

The common factors are 1 and 5. The GCD is 5.

3. Divide both the numerator and the denominator by their GCD (5):

\[
\frac{195 \div 5}{1000 \div 5} = \frac{39}{200}
\]

4. The fraction \(\frac{39}{200}\) is in simplest form because 39 and 200 have no common factors other than 1.

Thus, the decimal 0.195 converted to a fraction in simplest form is:

\[
\frac{39}{200}
\]