To convert the decimal \( 0.492 \) to a fraction, follow these steps:
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Write the decimal as a fraction: \[ 0.492 = \frac{492}{1000} \] Here, we place \( 492 \) over \( 1000 \) because there are three digits after the decimal point.
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Simplify the fraction: To simplify \( \frac{492}{1000} \), we need to find the greatest common divisor (GCD) of \( 492 \) and \( 1000 \).
First, we can factor \( 492 \) and \( 1000 \):
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\( 492 \) can be factored: \[ 492 = 2 \times 246 = 2 \times 2 \times 123 = 2^2 \times 3 \times 41 \]
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\( 1000 \) can be factored: \[ 1000 = 10^3 = (2 \times 5)^3 = 2^3 \times 5^3 \]
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Find the GCD: The common prime factors of \( 492 \) and \( 1000 \) are:
- The factor \( 2 \), where the minimum power is \( 2^2 \) from \( 492 \).
Therefore, the GCD is: \[ GCD(492, 1000) = 2^2 = 4 \]
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Divide both the numerator and denominator by the GCD: \[ \frac{492 \div 4}{1000 \div 4} = \frac{123}{250} \]
Thus, the decimal \( 0.492 \) as a fraction in simplest form is: \[ \frac{123}{250} \]