Evaluate $\frac{12.02 \times 20.06}{26.04 \times 60.06}$, correct to three significant figures.

1. Analyze the question

We are asked to evaluate the expression $\frac{12.02 \times 20.06}{26.04 \times 60.06}$ and round the final result to three significant figures.

2. Explain the concept

To solve this, we perform the multiplication in the numerator and the denominator separately, then divide the results. Finally, we apply the rule of significant figures: counting from the first non-zero digit, we keep three digits and round the third digit based on the fourth.

3. Show the solution

Step 1: Multiply the numerator $12.02 \times 20.06 = 241.1212$

Step 2: Multiply the denominator $26.04 \times 60.06 = 1563.9624$

Step 3: Divide the numerator by the denominator $\frac{241.1212}{1563.9624} \approx 0.154173...$

Step 4: Round to three significant figures

• The first significant figure is 1.
• The second significant figure is 5.
• The third significant figure is 4.
• The next digit is 1 (which is less than 5), so we keep the 4 as it is.

Rounding $0.154173...$ to three significant figures gives 0.154.

4. Identify the answer

Comparing our result to the given options: A. 0.157 B. 0.154 C. 0.155 D. 0.158

The correct option is B.

5. Tip

When dealing with decimals in JAMB, don't rush to round the numbers before you perform the calculation. Rounding too early (e.g., rounding to 12, 20, 26, and 60) can introduce "rounding errors" that lead you to the wrong option. Always perform the full calculation first, then round only at the very final step.