$\frac{0.00256 \times 0.0064}{0.025 \times 0.08}$

To solve this problem, we will convert the decimal numbers into standard form (scientific notation) to make the calculation easier and less prone to errors.

1. Analyze the expression

The expression is:

2. Convert to standard form

• $0.00256 = 256 \times 10^{-5} = 2.56 \times 10^{-3}$
• $0.0064 = 64 \times 10^{-4} = 6.4 \times 10^{-3}$
• $0.025 = 25 \times 10^{-3} = 2.5 \times 10^{-2}$
• $0.08 = 8 \times 10^{-2}$

Let's rewrite the expression using powers of 10 to simplify:

3. Simplify the numerator and denominator

Numerator: $(256 \times 64) \times (10^{-5} \times 10^{-4}) = 16384 \times 10^{-9}$

Denominator: $(25 \times 8) \times (10^{-3} \times 10^{-2}) = 200 \times 10^{-5}$

4. Perform the division

Now divide the two results:

Divide the coefficients: $16384 \div 200 = 81.92$

Divide the powers of 10: $10^{-9} \div 10^{-5} = 10^{-9 - (-5)} = 10^{-9 + 5} = 10^{-4}$

Combine them: $81.92 \times 10^{-4}$

Convert to standard form: $8.192 \times 10^1 \times 10^{-4} = 8.192 \times 10^{-3}$

Rounding to two significant figures (as seen in the options), we get $8.2 \times 10^{-3}$.

5. Conclusion

Comparing our result to the given options, we find that it matches option C.

Note: While the calculation yields 8.192, in JAMB examinations, you should look for the option that is the closest approximation if the exact value isn't listed.

Exam Tip: When dealing with decimals in JAMB, always convert them to whole numbers multiplied by powers of 10. It prevents "decimal point errors" which are the most common cause of lost marks in these types of questions.