How to Square 200.3 in Seconds: Easy Decimal Mental Math Trick

 

How to Square 200.3 in Seconds

A simple decimal-square mental math trick

Squaring a decimal such as 200.3 may look difficult at first, but the calculation becomes easy when you split the number into a whole-number part and a decimal part. This fast mental math strategy is based on the familiar square identity and is useful for students, teachers, and anyone who wants to calculate without reaching for a calculator.

The Key Idea

Rewrite 200.3 as 200 + 0.3. Then square the first part, double the product of the two parts, and square the last part.

The Square Formula

(a + b)² = a² + 2ab + b²

Apply It to 200.3

For this problem, choose a = 200 and b = 0.3. Substitute these values into the formula:

(200.3)² = 200² + 2(200)(0.3) + (0.3)²

Break the Calculation into Three Parts

Part 1: Square the Whole Number

First, calculate the square of 200:

200² = 40,000

Part 2: Double the Product

Multiply the two parts and then multiply by 2:

2 × 200 × 0.3 = 120

Part 3: Square the Decimal

Finally, square 0.3. Since 3 × 3 = 9 and there are two decimal places altogether, the answer is 0.09:

(0.3)² = 0.09

Add the Three Results

Now add the three parts together. Keep the decimal point aligned carefully:

40,000 + 120 + 0.09 = 40,120.09

Final Answer

(200.3)² = 40,120.09

The Integer Shortcut

There is another useful way to check the result. Move the decimal point in 200.3 one place to the right to make 2,003. Because the original number had one decimal place, its square will have two decimal places after the calculation.

Square the whole number:

2,003² = 4,012,009

Place two decimal digits in the answer:

4,012,009 ÷ 100 = 40,120.09

A General Rule for Decimals

If a number has the form A + B, its square is always made from three pieces: the square of A, twice A times B, and the square of B. This pattern works for whole numbers, decimals, and mixed numbers.

Step 1: Split the number into two convenient parts.

Step 2: Square the first part.

Step 3: Calculate twice the product of the two parts.

Step 4: Square the second part and add everything.

Practice Problems

Use the same three-part method to solve these problems mentally:

1. (100.2)² = ?

2. (50.4)² = ?

3. (300.5)² = ?

Tap to reveal the answers

1. 10,040.04   |   2. 2,540.16   |   3. 90,300.25

Final Takeaway

To square a decimal like 200.3, do not multiply it from scratch. Split it into 200 + 0.3, use (a + b)² = a² + 2ab + b², and add the three simple results. The final answer is 40,120.09.