To evaluate the expression \(\frac{0.21 \times 0.072 \times 0.00054}{0.006 \times 1.68 \times 0.063}\), we will break it down step-by-step, ensuring clarity in each part of the calculation. ### Step 1: Calculate the Numerator The numerator is \(0.21 \times 0.072 \times 0.00054\). 1. **Multiply \(0.21\) and \(0.072\)**: \[ 0.21 \times 0.072 = 0.01512 \] 2. **Now multiply the result by \(0.00054\)**: \[ 0.01512 \times 0.00054 = 0.0000081648 \] ### Step 2: Calculate the Denominator The denominator is \(0.006 \times 1.68 \times 0.063\). 1. **Multiply \(0.006\) and \(1.68\)**: \[ 0.006 \times 1.68 = 0.01008 \] 2. **Now multiply the result by \(0.063\)**: \[ 0.01008 \times 0.063 = 0.00063456 \] ### Step 3: Divide the Numerator by the Denominator Now we will divide the result from the numerator by the result from the denominator: \[ \frac{0.0000081648}{0.00063456} \] To perform this division, we can simplify it by moving the decimal point to the right in both the numerator and the denominator to eliminate the small numbers: \[ \frac{0.0000081648 \times 1000000}{0.00063456 \times 1000000} = \frac{8.1648}{634.56} \] Now, we can perform the division: \[ 8.1648 \div 634.56 \approx 0.01285 \] ### Final Answer Thus, the value of the expression \(\frac{0.21 \times 0.072 \times 0.00054}{0.006 \times 1.68 \times 0.063}\) is approximately \(0.01285\). ### Correct Option The correct option is **B. 0.01285**. ### Explanation of Other Options - **Option A (0.01286)**: This value is slightly higher than our calculated result. It may arise from rounding errors or miscalculations in the multiplication or division steps. - **Option C (0.1286)**: This value is significantly larger than our result. It seems to be a misplacement of the decimal point, possibly from misunderstanding the scale of the numbers involved. - **Option D (0.1285)**: Similar to option C, this value is also much larger than our result and likely results from a similar error in decimal placement. ### Summary of Key Points - Carefully perform multiplication and division, especially with small decimal numbers. - Always check your calculations step-by-step to avoid rounding errors. - When dealing with small numbers, consider scaling them up to simplify calculations. - Double-check the placement of decimal points to ensure accuracy in your final answer.