Answer :

To write [tex]\( 97.5\% \)[/tex] as a fraction in simplest form, follow these steps:

1. Understand Percentages: The term "percent" means per hundred. So, [tex]\( 97.5\% \)[/tex] can be written as:
[tex]\[
97.5\% = \frac{97.5}{100}
\][/tex]

2. Convert the Decimal to a Fraction: Next, express the decimal as a fraction. Since 97.5 is not a whole number, convert it to a fraction. We can write 97.5 as:
[tex]\[
97.5 = 97.5 = 97 \frac{5}{10} = 97 \frac{1}{2}
\][/tex]
Which is the same as:
[tex]\[
97.5 = \frac{975}{10}
\][/tex]

3. Simplify the Fraction: We have the fraction [tex]\(\frac{975}{1000}\)[/tex] because moving the decimal one place to the right in 97.5 means we must multiply by 10, and then finally divide both the numerator and the denominator by the greatest common divisor (GCD) of 975 and 1000. The GCD of 975 and 1000 is 25.
[tex]\[
\frac{975 \div 25}{1000 \div 25} = \frac{39}{40}
\][/tex]

Thus, [tex]\( 97.5\% \)[/tex] as a fraction in its simplest form is:
[tex]\[
\boxed{\frac{39}{40}}
\][/tex]

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