Question
what is 0.411 as a fraction in its absolute simplest form
Answers
GPT-4o mini
To convert the decimal \(0.411\) to a fraction in its simplest form, follow these steps:
1. **Write the decimal as a fraction:**
\[
0.411 = \frac{411}{1000}
\]
2. **Simplify the fraction if possible:**
To simplify \(\frac{411}{1000}\), we need to find the greatest common divisor (GCD) of 411 and 1000.
- The prime factorization of 411 is \(3 \times 137\) (since 411 is divisible by 3).
- The prime factorization of 1000 is \(10^3 = 2^3 \times 5^3\).
Since there are no common factors between 411 (which factors into primes 3 and 137) and 1000 (which factors into primes 2 and 5), the GCD is 1.
3. **Since the GCD is 1, the fraction is already in simplest form:**
\[
\frac{411}{1000}
\]
Thus, \(0.411\) as a fraction in its simplest form is \(\frac{411}{1000}\).
1. **Write the decimal as a fraction:**
\[
0.411 = \frac{411}{1000}
\]
2. **Simplify the fraction if possible:**
To simplify \(\frac{411}{1000}\), we need to find the greatest common divisor (GCD) of 411 and 1000.
- The prime factorization of 411 is \(3 \times 137\) (since 411 is divisible by 3).
- The prime factorization of 1000 is \(10^3 = 2^3 \times 5^3\).
Since there are no common factors between 411 (which factors into primes 3 and 137) and 1000 (which factors into primes 2 and 5), the GCD is 1.
3. **Since the GCD is 1, the fraction is already in simplest form:**
\[
\frac{411}{1000}
\]
Thus, \(0.411\) as a fraction in its simplest form is \(\frac{411}{1000}\).