To convert the decimal 4.65 to a fraction, follow these steps:
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Separate the whole number and the decimal part: The whole number is 4, and the decimal part is 0.65.
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Convert the decimal to a fraction: The decimal 0.65 can be expressed as: \[ 0.65 = \frac{65}{100} \]
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Simplify the fraction: To simplify \(\frac{65}{100}\), find the greatest common divisor (GCD) of 65 and 100. The GCD is 5. Now, divide both the numerator and the denominator by 5: \[ \frac{65 \div 5}{100 \div 5} = \frac{13}{20} \]
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Combine the whole number and the fraction: The number 4.65 can be expressed as: \[ 4.65 = 4 + 0.65 = 4 + \frac{13}{20} \]
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Convert to a single fraction: To add \(4\) (which is the same as \(\frac{4 \times 20}{20} = \frac{80}{20}\)) and \(\frac{13}{20}\): \[ 4.65 = \frac{80}{20} + \frac{13}{20} = \frac{80 + 13}{20} = \frac{93}{20} \]
Thus, the simplest form of 4.65 as a fraction is: \[ \frac{93}{20} \]
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