Evaluate. Write your answer as a decimal or whole number.
$(0.04)^2=$
The problem asks us to evaluate the square of the decimal number \(0.04\). This is represented by the expression \((0.04)^2\). Squaring a number means multiplying that number by itself. So, \((0.04)^2 = 0.04 \times 0.04\).
To simplify the multiplication, we can express the decimal \(0.04\) as a fraction. Since the 4 is in the hundredths place, we can write \(0.04 = \frac{4}{100}\). Alternatively, we can use the property of decimals that states \(0.04 \times 0.04 = 4 \times 10^{-2} \times 4 \times 10^{-2}\). Using the fraction approach, \(\left(\frac{4}{100}\right)^2 = \frac{4^2}{100^2}\).
Now, we compute the square of the numerator and the denominator separately. The square of the numerator is \(4^2 = 16\). The square of the denominator is \(100^2 = 100 \times 100 = 10000\). Therefore, \(\left(\frac{4}{100}\right)^2 = \frac{16}{10000}\).
Finally, we convert the fraction \(\frac{16}{10000}\) back into decimal notation. Since dividing by \(10000\) moves the decimal point four places to the left, we start with \(16.0\) and move the decimal point four positions to the left: \(0.0016\). Thus, \((0.04)^2 = 0.0016\). The result is \(\boxed{0.0016}\).
Understanding how to square decimals is vital in many real-world scenarios, such as calculating the area of a small square patch. If you are designing a tiny square circuit component with a side length of \(0.04\) cm, the area is \((0.04 \text{ cm}) \times (0.04 \text{ cm}) = 0.0016 \text{ cm}^2\). Mastering these decimal operations helps in precision-based tasks in engineering, finance, and science.