Convert the decimal below to a fraction in simplest form.

0, point, 3, 3
0.33

1 answer

To convert the decimal \( 0.33 \) to a fraction, we can follow these steps:

  1. Write the decimal as a fraction: \[ 0.33 = \frac{33}{100} \] This is because there are two decimal places, so we use \( 100 \) as the denominator (10 raised to the power of the number of decimal places).

  2. Simplify the fraction: We need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of \( 33 \) and \( 100 \) is \( 1 \), since \( 33 \) (which is \( 3 \times 11 \)) and \( 100 \) (which is \( 10 \times 10 \) or \( 2^2 \times 5^2 \)) have no common factors.

  3. Conclusion: Therefore, the fraction \( \frac{33}{100} \) is already in its simplest form.

The simplest form of \( 0.33 \) as a fraction is:

\[ \frac{33}{100} \]