Question
99=26.76
converting 0.27 to a rational number in its simplest form
converting 0.27 to a rational number in its simplest form
Answers
GPT-4o mini
To convert the decimal \(0.27\) to a rational number in its simplest form, you follow these steps:
1. Recognize that \(0.27\) can be expressed as a fraction. Since \(0.27\) is read as "27 hundredths," it can be written as:
\[
0.27 = \frac{27}{100}
\]
2. Next, we check if this fraction can be simplified. We need to find the greatest common divisor (GCD) of the numerator and the denominator.
3. The prime factorization of \(27\) is \(3^3\) (since \(27 = 3 \times 3 \times 3\)), and the prime factorization of \(100\) is \(2^2 \times 5^2\).
4. The GCD of \(27\) and \(100\) is \(1\), as they have no common factors.
5. Since the GCD is \(1\), the fraction \(\frac{27}{100}\) is already in its simplest form.
Thus, the rational number representation of \(0.27\) in simplest form is:
\[
\frac{27}{100}
\]
1. Recognize that \(0.27\) can be expressed as a fraction. Since \(0.27\) is read as "27 hundredths," it can be written as:
\[
0.27 = \frac{27}{100}
\]
2. Next, we check if this fraction can be simplified. We need to find the greatest common divisor (GCD) of the numerator and the denominator.
3. The prime factorization of \(27\) is \(3^3\) (since \(27 = 3 \times 3 \times 3\)), and the prime factorization of \(100\) is \(2^2 \times 5^2\).
4. The GCD of \(27\) and \(100\) is \(1\), as they have no common factors.
5. Since the GCD is \(1\), the fraction \(\frac{27}{100}\) is already in its simplest form.
Thus, the rational number representation of \(0.27\) in simplest form is:
\[
\frac{27}{100}
\]