Sure, let's convert [tex]\(0.45\%\)[/tex] to a fraction in its simplest form, step-by-step.
1. Convert the percentage to a fraction:
A percentage is just a number divided by 100. Therefore, [tex]\(0.45\%\)[/tex] can be written as:
[tex]\[
\frac{0.45}{100}
\][/tex]
2. Remove the decimal:
To remove the decimal point from 0.45, we can multiply both the numerator and the denominator by 100:
[tex]\[
\frac{0.45 \times 100}{100 \times 100} = \frac{45}{10000}
\][/tex]
3. Simplify the fraction:
We now need to simplify [tex]\(\frac{45}{10000}\)[/tex]. To do this, we find the greatest common divisor (GCD) of 45 and 10000 and then divide both the numerator and the denominator by this number.
4. Find the GCD:
The GCD of 45 and 10000 is 5.
5. Divide both the numerator and the denominator by the GCD:
[tex]\[
\frac{45 \div 5}{10000 \div 5} = \frac{9}{2000}
\][/tex]
Hence, the fraction [tex]\(\frac{45}{10000}\)[/tex] simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 5, results in:
[tex]\[
\frac{9}{2000}
\][/tex]
Therefore, [tex]\(0.45\%\)[/tex] written as a fraction in its simplest form is [tex]\(\frac{9}{2000}\)[/tex].
