What is 4.65 converted to a fraction? The answer should be given in simplest form.(1 point)

Question

Responses

465
4 Start Fraction 6 over 5 End Fraction

41320
4 Start Fraction 13 over 20 End Fraction

465
Start Fraction 4 over 65 End Fraction

465100

Answer 1

To convert the decimal 4.65 to a fraction, follow these steps:

1. Write the decimal as a fraction: \[ 4.65 = \frac{465}{100} \]

2. Simplify the fraction. 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 \(2^2 \times 5^2\).

3. The GCD is \(5\).

4. Divide both the numerator and the denominator by their GCD: \[ \frac{465 \div 5}{100 \div 5} = \frac{93}{20} \]

If we separate the whole number from the fractional part, we get: \[ 4 \frac{13}{20} \]

Thus, 4.65 in simplest fraction form is: \[ 4 \frac{13}{20} \]

So the correct response is: 4 Start Fraction 13 over 20 End Fraction.