To convert the decimal 4.65 to a fraction, follow these steps:
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Write the decimal as a fraction: \[ 4.65 = \frac{465}{100} \]
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Simplify the fraction: To simplify \(\frac{465}{100}\), we need to find the greatest common divisor (GCD) of 465 and 100.
- The prime factorization of 465 is \(3 \times 5 \times 31\).
- The prime factorization of 100 is \(2^2 \times 5^2\).
The only common factor is 5.
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Divide both the numerator and the denominator by 5: \[ \frac{465 \div 5}{100 \div 5} = \frac{93}{20} \]
So, the decimal 4.65 converted to a fraction in simplest form is:
\[ \frac{93}{20} \]