Question

Write 0.315 as a fraction in it's lowest term

Answer 1

To convert the decimal \(0.315\) to a fraction, we can express it as:

\[
0.315 = \frac{315}{1000}
\]

Next, we will simplify this fraction. We need to find the greatest common divisor (GCD) of \(315\) and \(1000\).

First, we find the prime factorization of both numbers:

- **For 315**:
- \(315 \div 3 = 105\)
- \(105 \div 3 = 35\)
- \(35 \div 5 = 7\)
- \(7\) is prime.

Thus, the prime factorization of \(315\) is:
\[
315 = 3^2 \times 5^1 \times 7^1
\]

- **For 1000**:
- \(1000 = 10^3 = (2 \times 5)^3 = 2^3 \times 5^3\)

Thus, the prime factorization of \(1000\) is:
\[
1000 = 2^3 \times 5^3
\]

Next, we identify the common prime factors:
- The common prime factor is \(5\).

Now we calculate the GCD:
\[
\text{GCD}(315, 1000) = 5^1 = 5
\]

Now, we divide both the numerator and the denominator by the GCD:

\[
\frac{315 \div 5}{1000 \div 5} = \frac{63}{200}
\]

Now, \(63\) and \(200\) have no common factors other than \(1\). Therefore, the fraction \(\frac{63}{200}\) is in its lowest terms.

Thus, the decimal \(0.315\) as a fraction in its lowest terms is:

\[
\frac{63}{200}
\]