Question

practice: squaring fractions and decimals
multiplying a number by itself is called \squaring.\ for example, \5 squared\ means 5 × 5. you can use an exponent—a raised number—to write the same thing.
( 5^2 = 5 \times 5 = 25 )
square these fractions or decimals:

1. ( left( \frac{1}{2}

ight)^2 = )

1. ( .05^2 = )
2. ( left( 9 \frac{1}{3}

ight)^2 = )

1. ( (2.5)^2 = )
2. ( (.2)^2 = )
3. ( (.02)^2 = )
4. ( (5.8)^2 = )
5. ( left( \frac{5}{6}

ight)^2 = )
complete the following sentences:

1. when you square a number less than 1, the result is always

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1. when you square a number greater than 1, the result is always

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1. what other patterns do you notice?

Explanation:

1. $(\frac{1}{2})^2$

Step1: Recall squaring a fraction rule

To square a fraction $\frac{a}{b}$, we square the numerator and the denominator, i.e., $(\frac{a}{b})^2=\frac{a^2}{b^2}$.

Step2: Apply the rule

For $(\frac{1}{2})^2$, $a = 1$, $b = 2$. So $(\frac{1}{2})^2=\frac{1^2}{2^2}=\frac{1}{4}$.

Step1: Recall squaring a decimal rule

To square a decimal, multiply the decimal by itself.

Step2: Calculate the square

$.05\times.05 = 0.0025$.

Step1: Convert mixed number to improper fraction

$9\frac{1}{3}=\frac{9\times3 + 1}{3}=\frac{28}{3}$.

Step2: Square the improper fraction

$(\frac{28}{3})^2=\frac{28^2}{3^2}=\frac{784}{9}=87\frac{1}{9}$.

Answer:

$\frac{1}{4}$

2. $.05^2$