Express the product of 0.21 and 0.34 in standard form

Analyze the question: We need to multiply 0.21 by 0.34, then write the result in standard form (scientific notation), which means the form A × 10ⁿ where 1 ≤ A < 10.

Concept: To multiply decimals, multiply them as whole numbers, then place the decimal point by counting the total decimal places in both numbers.

Solution:

Step 1: Multiply as whole numbers. 21 × 34 = 714

Step 2: Count decimal places.

• 0.21 has 2 decimal places
• 0.34 has 2 decimal places
• Total = 4 decimal places

So 0.21 × 0.34 = 0.0714

Step 3: Convert to standard form. Move the decimal point to get a number between 1 and 10: 0.0714 → 7.14, which means moving the decimal point 2 places to the right.

So 0.0714 = 7.14 × 10⁻²

Check: 7.14 × 10⁻² = 7.14 ÷ 100 = 0.0714 ✓

Answer: Option B (7.14 × 10⁻²).

Tip: When converting a small decimal to standard form, the power of 10 is negative, and its size equals the number of places you move the decimal point to the right. Here, 0.0714 → 7.14 needs 2 moves, so the power is −2. Always verify by converting back.