Evaluate $\frac{0.8 \times 0.43 \times 0.031}{0.05 \times 0.72 \times 0.021}$. Correct to four significant figures.

To solve this expression, we will simplify the decimals by converting them into powers of 10 to make the division easier.

1. Analyze the expression

We have:

2. Convert decimals to standard form

To remove the decimals, we can express each number as a fraction or multiply both the numerator and denominator by a power of 10 that clears all decimal places.

• Numerator: $0.8 \times 0.43 \times 0.031 = \frac{8}{10} \times \frac{43}{100} \times \frac{31}{1000} = \frac{8 \times 43 \times 31}{10^6} = \frac{10664}{1,000,000}$
• Denominator: $0.05 \times 0.72 \times 0.021 = \frac{5}{100} \times \frac{72}{100} \times \frac{21}{1000} = \frac{5 \times 72 \times 21}{10^7} = \frac{7560}{10,000,000}$

3. Perform the division

Now, divide the numerator by the denominator:

When dividing powers of 10, subtract the exponents:

Now, calculate the division:

Multiply by $10^1$:

4. Round to four significant figures

Significant figures start from the first non-zero digit.

1. First: 1
2. Second: 4
3. Third: 1
4. Fourth: 0

The next digit is 5, so we round the fourth digit up from 0 to 1. Result: 14.11

5. Conclusion

Comparing our result to the options provided: A. 14.09 B. 14.1 C. 14.12 D. 14.11

The calculated value matches option D.

Exam Tip: When dealing with many decimal places in JAMB, always try to shift the decimal point to the right for both the numerator and denominator by the same number of places. This turns the problem into simple long division of whole numbers, which is much less prone to error!