Simplify and express in standard form $\frac{0.00275 \times 0.00640}{0.025 \times 0.08}$

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

1. Analyze the question

We need to simplify the expression:

2. Explain the concept

Standard form is written as $a \times 10^n$, where $1 \le a < 10$.

• $0.00275 = 2.75 \times 10^{-3}$
• $0.00640 = 6.4 \times 10^{-3}$
• $0.025 = 2.5 \times 10^{-2}$
• $0.08 = 8.0 \times 10^{-2}$

3. Show the solution

Substitute these values into the expression:

Step A: Multiply the numerators and denominators separately Numerator: $(2.75 \times 6.4) \times (10^{-3} \times 10^{-3}) = 17.6 \times 10^{-6}$ Denominator: $(2.5 \times 8.0) \times (10^{-2} \times 10^{-2}) = 20 \times 10^{-4}$

Step B: Divide the results

Divide the coefficients: $17.6 \div 20 = 0.88$ Divide the powers of 10: $10^{-6} \div 10^{-4} = 10^{-6 - (-4)} = 10^{-2}$

So, we have: $0.88 \times 10^{-2}$

Step C: Convert to standard form To make $0.88$ a number between 1 and 10, we move the decimal point one place to the right: $0.88 = 8.8 \times 10^{-1}$

Now, multiply this by the $10^{-2}$ we already had: $(8.8 \times 10^{-1}) \times 10^{-2} = 8.8 \times 10^{-1 + (-2)} = 8.8 \times 10^{-3}$

4. Identify the answer

Comparing our result to the given options, the correct choice is C.

5. Exam Tip

When dealing with many decimal places in JAMB, always convert to powers of 10 first. It prevents "decimal point errors" which are the most common cause of mistakes in these types of questions. Also, remember the law of indices: $10^a \div 10^b = 10^{a-b}$. Be very careful with the signs when subtracting negative exponents!