To convert the decimal 0.195 to a fraction, follow these steps:
- Write the decimal as a fraction with the numerator and denominator. Since 0.195 has three decimal places, you can write it as:
\[ \frac{195}{1000} \]
- 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.
- Divide both the numerator and the denominator by their GCD (5):
\[ \frac{195 \div 5}{1000 \div 5} = \frac{39}{200} \]
- 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:
\[ \frac{39}{200} \]