To express 0.36 as a fraction in simplest form, follow these steps:
1. Write 0.36 as a fraction:
We start by writing 0.36 as a fraction over 1. This gives us:
[tex]\[
\frac{0.36}{1}
\][/tex]
2. Remove the decimal by multiplying both the numerator and denominator by 100:
Since 0.36 has two decimal places, we can eliminate the decimal by multiplying both the numerator and the denominator by 100:
[tex]\[
\frac{0.36 \times 100}{1 \times 100} = \frac{36}{100}
\][/tex]
3. Simplify the fraction:
To simplify [tex]\(\frac{36}{100}\)[/tex], we need to find the greatest common divisor (GCD) of 36 and 100.
- The prime factorization of 36 is [tex]\(2^2 \times 3^2\)[/tex].
- The prime factorization of 100 is [tex]\(2^2 \times 5^2\)[/tex].
The common factors are [tex]\(2^2 = 4\)[/tex].
- Divide both the numerator and denominator by their GCD:
[tex]\[
\frac{36 \div 4}{100 \div 4} = \frac{9}{25}
\][/tex]
Therefore, 0.36 expressed as a fraction in simplest form is:
[tex]\[
\frac{9}{25}
\][/tex]
