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This is a unit conversion problem disguised with scientific notation. The trap here is getting confused between billion and trillion!

Step 1: Identify what we're converting

We need to convert 3.7 × 10^12 square inches to square miles.
Given: 1 square mile ≈ 4 billion square inches = 4 × 10^9 square inches

Step 2: Set up the conversion

Area in square miles = (Area in square inches) ÷ (square inches per square mile)
Area in square miles = (3.7 × 10^12) ÷ (4 × 10^9)

Step 3: Divide the coefficients and exponents separately

Coefficient: 3.7 ÷ 4 ≈ 0.925
Exponent: 10^12 ÷ 10^9 = 10^(12-9) = 10^3 = 1,000

Step 4: Combine

0.925 × 1,000 = 925 square miles

Looking at the answer choices, 900 square miles is the closest approximation.

Answer: B (900 square miles)

Common trap: The biggest mistake students make here is confusing 10^12 with billion. Remember: 10^9 = billion, 10^12 = trillion. Also, some students mistakenly multiply instead of divide—always ask yourself "should the answer be bigger or smaller?" Going from tiny units (square inches) to large units (square miles) means the number should get smaller.

Takeaway: For unit conversions with exponents, separate the coefficients from the powers of 10, handle each part, then recombine. And always do a sanity check—does your answer make sense in context?
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The total area of a certain city is 3.7 x 10^12 square inches. Which of the following is the closest approximation of the area of the city in square miles? (1 square mile is approximately 4 billion square inches)

A. 800 square miles
B. 900 square miles
C. 9,000 square miles
D. 10,000 square miles
E. 9 million square miles

Video explanation:

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