Evaluate: $\frac{0.42 \div 2.5}{0.5 \times 2.05}$, leaving the answer in the standard form.

Step 1: Analyze the question We need to evaluate a fraction involving decimals and write the result in standard form (A × 10ⁿ, where 1 ≤ A < 10).

Step 2: Solve the numerator 0.42 ÷ 2.5 = 0.168

Check: 2.5 × 0.168 = 0.42 ✓

Step 3: Solve the denominator 0.5 × 2.05 = 1.025

Step 4: Divide 0.168 ÷ 1.025 = ?

Estimate: 1.025 × 0.1639 = 0.16800 (approximately)

• 1.025 × 0.16 = 0.164
• 1.025 × 0.0039 = 0.003998
• Total = 0.167998 ≈ 0.168 ✓

So the value is ≈ 0.1639

Step 5: Write in standard form 0.1639 = 1.639 × 10⁻¹

Tip: In standard form, count how many places the decimal point must move. Moving it right by 1 place (0.1639 → 1.639) gives a negative power: 10⁻¹. Small numbers (less than 1) always have negative powers. You can also quickly rule out options A and B, since the answer is clearly less than 1.