To convert the decimal \( 0.33 \) to a fraction, we can follow these steps:
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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).
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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.
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Conclusion: Therefore, the fraction \( \frac{33}{100} \) is already in its simplest form.
The simplest form of \( 0.33 \) as a fraction is:
\[ \frac{33}{100} \]