To convert the decimal 6.42 to a fraction in lowest terms, follow these steps:
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Separate the whole number from the decimal: \[ 6.42 = 6 + 0.42 \]
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Convert the decimal (0.42) into a fraction: \[ 0.42 = \frac{42}{100} \]
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Simplify the fraction: Find the greatest common divisor (GCD) of 42 and 100. The GCD is 2. \[ \frac{42 \div 2}{100 \div 2} = \frac{21}{50} \]
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Combine the whole number and the fractional part: Rewrite 6 as a fraction: \[ 6 = \frac{6 \cdot 50}{50} = \frac{300}{50} \] Now add \(\frac{300}{50}\) and \(\frac{21}{50}\): \[ \frac{300}{50} + \frac{21}{50} = \frac{300 + 21}{50} = \frac{321}{50} \]
Thus, the decimal 6.42 as a fraction in lowest terms is: \[ \frac{321}{50} \]
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