Question

Convert 0.27 into a rational fraction in simplest form

Answer 1

To convert the decimal 0.27 into a rational fraction, we can follow these steps:

1. Recognize that 0.27 can be expressed as \( \frac{27}{100} \) because it is in the hundredths place.

2. Now, we need to simplify \( \frac{27}{100} \). We check for common factors between the numerator (27) and the denominator (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, the fraction \( \frac{27}{100} \) is already in its simplest form.

Thus, the rational fraction in simplest form for the decimal 0.27 is:

\[
\frac{27}{100}
\]