NECO 2004 Mathematics · Question 10

Calculate (0.05 × 0.025) ÷ (4.25 × 3.35) and express your answer in standard form

Options

A.8.7796 × 105
B.8.7796 × 104
C.8.7796 × 103
D.8.7796 × 10-3
E.8.7796 × 10-5

Answer: E. 8.7796 × 10-5

Explanation written with AI and checked against the answer key

Analyze the question: We need to evaluate (0.05 × 0.025) ÷ (4.25 × 3.35) and write the result in standard form (a × 10ⁿ, where 1 ≤ a < 10). Step 1: Numerator 0.05 × 0.025 = 0.00125 = 1.25 × 10⁻³ Step 2: Denominator 4.25 × 3.35 = 14.2375 Step 3: Divide 0.00125 ÷ 14.2375 ≈ 8.7796 × 10⁻⁵ Check: 1.25 ÷ 14.2375 ≈ 0.087796, so 0.087796 × 10⁻³ = 8.7796 × 10⁻⁵. Let me verify 14.2375 × 0.087796: 14.2375 × 0.08 = 1.139; 14.2375 × 0.007796 = 0.11100; total ≈ 1.2500. ✓. Answer: The result is 8.7796 × 10⁻⁵, which matches option E (the exponent in the options is printed as "10-5", meaning 10⁻⁵). Tip: In standard form, first estimate the size. Numerator ≈ 10⁻³, denominator ≈ 10¹, so the answer should be around 10⁻⁴ to 10⁻⁵. Then check that the coefficient is between 1 and 10 by shifting the decimal point and adjusting the power of 10 accordingly.

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