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How do you evaluate the power $ - {\left( {1.2} \right)^2}$?

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Last updated date: 14th Jun 2024
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Answer
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Hint: Here, we need to square the decimal number. For this we will first convert it into the fraction form so that it will be easy for us to do its square. Also it is important to consider that the negative sign is out of the bracket, so when we square the number, the negative sign will remain as it is.

Complete step-by-step solution:
We need to evaluate the power $ - {\left( {1.2} \right)^2}$.
First we will convert $1.2$ into fraction form.
As there is one digit after the decimal, we will divide the number with 10 after removing the decimal sign to convert it into fraction form.
$ \Rightarrow 1.2 = \dfrac{{12}}{{10}}$
We will not simplify the fraction here as it is easy to convert the fraction into decimal after squaring if it has the denominator in multiplication with 10.
Therefore, we can write
$ \Rightarrow - {\left( {1.2} \right)^2} = - {\left( {\dfrac{{12}}{{10}}} \right)^2} = - \dfrac{{144}}{{100}}$
Now, we will again convert the decimal number into fraction form.
As the denominator is 100, we will put a decimal sign after two digits from the left side.
$ - \dfrac{{144}}{{100}} = - 1.44$
Thus, by evaluating the power $ - {\left( {1.2} \right)^2}$, we get $ - 1.44$.

Note: While solving this type of question, be careful when we convert decimals into fraction and fraction into decimals. We can also solve this problem by directly multiplying the number twice.
\[ - {\left( {1.2} \right)^2} = - \left( {1.2 \times 1.2} \right) = - 1.44\].

When we multiply two decimals, the number of digits after decimal sign in the product will be the total number of digits after decimal sign in the number. For example, here $1.2$ has one digit after decimal and when it is multiplied two times. The final answer $1.44$ has two digits after the decimal sign.