Question
Evaluate 0.05^2
Evaluate 0.05^2
The Correct Answer and Explanation is:
Answer:
0.052=0.00250.05^2 = 0.0025
Explanation
To evaluate 0.0520.05^2, we are squaring the number 0.05. This means we are multiplying 0.05 by itself: 0.05×0.050.05 \times 0.05
Now, let’s break this down in steps to make the calculation easier and better understood.
Step 1: Convert to a Fraction
We can convert 0.05 into a fraction: 0.05=5100=1200.05 = \frac{5}{100} = \frac{1}{20}
Now square the fraction: (120)2=12202=1400\left(\frac{1}{20}\right)^2 = \frac{1^2}{20^2} = \frac{1}{400}
Convert the result back to a decimal: 1400=0.0025\frac{1}{400} = 0.0025
So: 0.052=0.00250.05^2 = 0.0025
Step 2: Decimal Multiplication Method
Alternatively, we can multiply the decimals directly: 0.05×0.05=?0.05 \times 0.05 = ?
Ignore the decimals for a moment and multiply the numbers as whole numbers: 5×5=255 \times 5 = 25
Now count the total number of decimal places in the original numbers. Each 0.05 has two decimal places, so together there are 4 decimal places: 0.05×0.05=0.0025(move the decimal 4 places left)0.05 \times 0.05 = 0.0025 \quad (\text{move the decimal 4 places left})
Why This Matters:
Understanding how to square decimals is essential in many real-life applications such as finance (e.g., calculating interest), science (e.g., area of a square), and statistics (e.g., variance). The concept also strengthens your understanding of number sense and decimal place value. By squaring 0.05 and getting 0.0025, you see how small changes in input can result in significantly smaller outputs when working with values less than 1.
Final Answer:
0.0025\boxed{0.0025}
