Question

Convert the decimal below to a fraction in simplest form.
0.913

Answer 1

To convert the decimal \(0.913\) to a fraction, follow these steps:

1. Write the decimal as a fraction:
\[
0.913 = \frac{913}{1000}
\]

2. Simplify the fraction \( \frac{913}{1000} \) if possible. First, we need to find the greatest common divisor (GCD) of 913 and 1000.

3. Check if 913 is a prime number. The prime factors are only 1 and 913. The prime factors of 1000 are:
\[
1000 = 10^3 = (2 \times 5)^3 = 2^3 \times 5^3
\]

4. Since 913 does not share any factors with 1000 (the only prime factor of 913 is itself), the GCD is 1.

5. Since the GCD of 913 and 1000 is 1, the fraction cannot be simplified further.

Thus, the fraction in simplest form is:
\[
\frac{913}{1000}
\]