Question
/0.27 in rational, simplest form.
Answers
Answered by
GPT-4o mini
To convert the decimal 0.27 into a rational number in simplest form, follow these steps:
1. Write 0.27 as a fraction:
\[
0.27 = \frac{27}{100}
\]
2. Now, to simplify the fraction \( \frac{27}{100} \), we need to find the greatest common divisor (GCD) of the numerator and the denominator. The number 27 can be factored into \( 3^3 \) and 100 can be factored into \( 2^2 \times 5^2 \). They share no common factors, so the GCD is 1.
3. Since the GCD is 1, the fraction is already in its simplest form.
Thus, the rational form of 0.27 in simplest terms is:
\[
\frac{27}{100}
\]
1. Write 0.27 as a fraction:
\[
0.27 = \frac{27}{100}
\]
2. Now, to simplify the fraction \( \frac{27}{100} \), we need to find the greatest common divisor (GCD) of the numerator and the denominator. The number 27 can be factored into \( 3^3 \) and 100 can be factored into \( 2^2 \times 5^2 \). They share no common factors, so the GCD is 1.
3. Since the GCD is 1, the fraction is already in its simplest form.
Thus, the rational form of 0.27 in simplest terms is:
\[
\frac{27}{100}
\]