Simplify (0.09)2 and give your answer correct to 4 significant figures

Analysis

The question asks us to calculate the square of the decimal $0.09$ and express the result to 4 significant figures.

Concept

To square a decimal, you multiply the number by itself. When multiplying decimals:

1. Ignore the decimal points and multiply the numbers as whole numbers.
2. Count the total number of decimal places in the original numbers.
3. Place the decimal point in your result so that it has the same total number of decimal places.

Solution

Step 1: Perform the multiplication We are calculating $(0.09)^2$, which is $0.09 \times 0.09$.

Ignore the decimals: $9 \times 9 = 81$.

Step 2: Determine decimal places $0.09$ has 2 decimal places. Since we are multiplying $0.09$ by $0.09$, the total number of decimal places in the result must be $2 + 2 = 4$.

Step 3: Place the decimal point We need 4 decimal places for the number $81$. We add leading zeros to achieve this: $0.0081$

Step 4: Check significant figures Significant figures are counted starting from the first non-zero digit. In $0.0081$:

• The zeros before the '8' are not significant.
• The '8' is the 1st significant figure.
• The '1' is the 2nd significant figure. Since the value is exactly $0.0081$, it is already expressed to 2 significant figures. To express it to 4 significant figures, we would add trailing zeros ($0.008100$), but looking at the options provided, $0.0081$ is the intended value.

Conclusion

Comparing our result to the options: A. 0.81 B. 0.081 C. 0.0081 D. 8.0001

The calculated value matches option C.

Exam Tip

When squaring decimals, a quick way to check your work is to count the decimal places. If you have $n$ decimal places in the base, your square will always have $2n$ decimal places. Here, $2$ decimal places $\times 2 = 4$ decimal places. $0.0081$ has exactly 4 decimal places, confirming the calculation is correct.