Squaring decimals

In this chapter we will learn two methods to square decimal numbers with solved examples.

To get the basic knowledge of decimal numbers, click the red link.

How to represent square of decimal ?

The square of decimal can be represented by showing power 2 on the given decimal.

For example;
Square of decimal 2.13 is shown as;

\mathtt{\Longrightarrow \ ( 2.13)^{2}}\

How to find square of decimal number ?

In this chapter we will discuss two methods;

Method 01
By converting decimal into fraction

Follow the below steps;

(a) Convert the decimal into fraction

(b) Multiply the number by itself twice

(c) Multiply the numerator and denominator of fraction separately

(d) If possible, convert the fraction back into decimal.

The above process can be generalized as follows.

Let the given decimal is m.n

The square of above decimal is;

\mathtt{\Longrightarrow \ ( m.n)^{2}}\\\ \\ \mathtt{\Longrightarrow \ \left(\frac{mn}{10}\right)^{2}}\\\ \\ \mathtt{\Longrightarrow \ \frac{mn\times mn}{10\ \times 10}}

I hope you understood the above steps. Let us solve some problems.

Example 01
Find the square of 3.5

Solution
First convert the decimal into fraction

\mathtt{3.5\ \Longrightarrow \ \frac{35}{10}}

Now squaring the fraction.

\mathtt{\Longrightarrow \left(\frac{35}{10}\right)^{2}}\\\ \\ \mathtt{\Longrightarrow \ \frac{35\times 35}{10\times 10}}\\\ \\ \mathtt{\Longrightarrow \ \frac{1225}{100}}

Now convert the fraction back into decimal

\mathtt{\frac{1225}{100} \ \Longrightarrow \ 12.25}

Hence, 12.25 is the square of given decimal.

Example 02
Find the square of decimal 2.71

Solution
First convert the decimal into fraction.

\mathtt{2.71\ \Longrightarrow \ \frac{271}{100}}

Now squaring the fraction.

\mathtt{\Longrightarrow \left(\frac{271}{100}\right)^{2}}\\\ \\ \mathtt{\Longrightarrow \ \frac{271\times 271}{100\times 100}}\\\ \\ \mathtt{\Longrightarrow \ \frac{73441}{10000}}

Convert the fraction back into decimal.

\mathtt{\frac{73441}{10000} \ \Longrightarrow 7.3441}

Hence, 7.3441 is the solution.

I hope you understood above two examples. Let us now understand second method for squaring decimal numbers.

Method 02
Squaring using direct multiplication

Follow the below steps;

(a) Note the total decimal place value of numbers

(b) Remove the decimal point and multiply

(c) Insert the decimal point at total decimal place value.

Let us understand the above process with example.

Example 01
Square the decimal 1.5

Solution
The square of number 1.5 is represented as;

⟹ 1.5 x 1.5

Follow the below steps;

(a) Note the total decimal place value

1.5 decimal place value ⟹ 1
1.5 decimal place value ⟹ 1

Total decimal place value ⟹ 1 + 1 = 2

(b) Remove the decimal point and multiply

⟹ 15 x 15

⟹ 225

(c) Now add back the decimal point after two decimal place value.

⟹ 2.25

Hence, 2.25 is the square of decimal 1.5

Example 02
Square the decimal 1.21

Solution
The square of number 1.21 is represented as;

⟹ 1.21 x 1.21

Follow the below steps;

(a) Note the total decimal place value

1.21 decimal place value ⟹ 2
1.21 decimal place value ⟹ 2

Total decimal place value = 2 + 2 = 4

(b) Remove the decimal point & multiply

⟹ 121 x 121

⟹ 14641

(c) Now add back the decimal point after 4 decimal place value

⟹ 1.4641

Hence, 1.4641 is the square of number 1.21

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