Question

Convert 0.27 to a rational number in simplest form. (1 point)

Answer 1

To convert the decimal 0.27 to a rational number in simplest form, we can express it as a fraction.

1. The decimal 0.27 can be written as \(\frac{27}{100}\) because there are two digits after the decimal point.
2. Next, we check if the fraction \(\frac{27}{100}\) can be simplified. To do this, we find the greatest common divisor (GCD) of 27 and 100.
- The prime factorization of 27 is \(3^3\).
- The prime factorization of 100 is \(2^2 \times 5^2\).

Since 27 and 100 have no common factors, their GCD is 1.

3. Therefore, \(\frac{27}{100}\) is already in its simplest form.

Thus, the rational number in simplest form is \(\frac{27}{100}\).