Question

write each decimal as a fraction in lowest terms.
9.06, what is this as a fraction in lowest terms?

Answer 1

To convert the decimal \(9.06\) into a fraction, we can follow these steps:

1. **Express as a fraction**: Write \(9.06\) as \(\frac{906}{100}\) because there are two decimal places.

2. **Simplify the fraction**: We need to find the greatest common divisor (GCD) of 906 and 100.

The prime factorization of \(906\) is:
- \(906\) is divisible by \(2\) (it is even), giving \(906 \div 2 = 453\).
- \(453\) is divisible by \(3\) (the sum of the digits is \(12\), which is divisible by \(3\)), giving \(453 \div 3 = 151\).
- \(151\) is a prime number.

Thus, the prime factorization of \(906\) is:
\[
906 = 2 \times 3 \times 151
\]

The prime factorization of \(100\) is:
\[
100 = 2^2 \times 5^2
\]

The only common factor between \(906\) and \(100\) is \(2\).

3. **Divide both the numerator and denominator by their GCD**, which is \(2\):
\[
\frac{906 \div 2}{100 \div 2} = \frac{453}{50}
\]

4. **Final fraction**: Since \(453\) and \(50\) have no common factors (as \(453\) is only divisible by \(3\) and \(151\), while \(50\) is divisible by \(2\) and \(5\)), the fraction \(\frac{453}{50}\) is in lowest terms.

Thus, the decimal \(9.06\) as a fraction in lowest terms is:
\[
\frac{453}{50}
\]