Simplify $\frac{0.026 \times 0.36}{0.69}$. Leave your answer in standard form

To solve this problem, we will break it down into simple arithmetic steps and then convert the final result into standard form.

1. Analyze the question

We are asked to simplify the expression $\frac{0.026 \times 0.36}{0.69}$ and express the result in standard form (scientific notation).

2. Explain the concept

• Standard Form: A number in standard form is written as $a \times 10^n$, where $1 \le a < 10$ and $n$ is an integer.
• Decimal Multiplication/Division: It is often easier to convert decimals into fractions or whole numbers by multiplying by powers of 10 to remove the decimal points.

3. Show the solution

Step 1: Simplify the expression by removing decimals. To make the calculation easier, let's multiply the numerator and denominator by a power of 10 that clears the decimals:

Step 2: Simplify the powers of 10. The $10^{-2}$ in the numerator and denominator cancel each other out:

Step 3: Perform the multiplication and division. First, multiply $26 \times 36$: $26 \times 36 = 936$

Now, divide by $69$: $936 \div 69 \approx 13.565...$

Wait, let's re-examine the calculation. If we calculate $0.026 \times 0.36 = 0.00936$. Now, divide $0.00936$ by $0.69$: $0.00936 \div 0.69 \approx 0.013565...$

Rounding this to two decimal places for the coefficient (as suggested by the options): $0.013565 \approx 0.0136$

Step 4: Convert to standard form. To write $0.0136$ in standard form, we move the decimal point two places to the right: $0.0136 = 1.36 \times 10^{-2}$

4. Identify the answer

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

5. Tip

When dealing with decimals in JAMB, if the numbers look messy, convert them to whole numbers using powers of 10 (e.g., $0.026 = 26 \times 10^{-3}$). This prevents errors caused by misplacing the decimal point during long division.