To convert the decimal 0.836 into a fraction, follow these steps:
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Recognize that 0.836 can be written as \(\frac{836}{1000}\) since there are three decimal places.
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Now, simplify the fraction \(\frac{836}{1000}\). To do this, find the greatest common divisor (GCD) of 836 and 1000.
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The prime factorization of 836 is \(2^2 \times 11 \times 19\). The prime factorization of 1000 is \(2^3 \times 5^3\).
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The GCD of 836 and 1000 is 4.
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Now, divide both the numerator and the denominator by their GCD: \[ \frac{836 \div 4}{1000 \div 4} = \frac{209}{250} \]
Thus, the decimal 0.836 as a fraction in simplest form is \(\frac{209}{250}\).
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