To solve for [tex]\((1.2)^{-2}\)[/tex] and convert it to a fraction, let’s break it down into clear steps:
1. Understanding the Expression: We need to evaluate [tex]\((1.2)^{-2}\)[/tex].
2. Evaluating the Power:
[tex]\[
(1.2)^{-2} = \frac{1}{(1.2)^2}
\][/tex]
When raising a number to the power of -2, it is the same as taking the reciprocal of the number raised to the positive 2.
3. Square the Base:
[tex]\[
(1.2)^2 = 1.2 \times 1.2 = 1.44
\][/tex]
4. Take the Reciprocal:
[tex]\[
\frac{1}{1.44}
\][/tex]
5. Convert to Fraction:
To find a more simplified form, we recognize that:
[tex]\[
\frac{1}{1.44} \approx 0.6944444444444445
\][/tex]
Which can be exactly expressed in fractional form as:
[tex]\[
\frac{25}{36}
\][/tex]
This is derived from identifying the exact decimal representation and simplifying or equivalent fraction calculations.
6. Verification:
By back-calculating, you can confirm:
[tex]\[
\frac{25}{36} \approx 0.6944444444444444
\][/tex]
Thus matching the correctly simplified fraction.
Therefore, [tex]\((1.2)^{-2}\)[/tex] expressed as a fraction is:
[tex]\[
\boxed{\frac{25}{36}}
\][/tex]
