To convert the decimal 0.65 to a fraction, follow these steps:
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Write 0.65 as a fraction: \[ 0.65 = \frac{65}{100} \]
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Next, simplify the fraction. Find the greatest common divisor (GCD) of 65 and 100. The factors of 65 are 1, 5, 13, and 65, and the factors of 100 are 1, 2, 4, 5, 10, 20, 25, and 100. The greatest common factor is 5.
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Divide both the numerator and the denominator by their GCD: \[ \frac{65 \div 5}{100 \div 5} = \frac{13}{20} \]
Thus, the decimal 0.65 as a fraction in lowest terms is \[ \frac{13}{20} \]
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