How many square meters are equivalent to 18,000 square centimeters? (1text{ meter} = 100text{ centimeters})1.8181801,800

1. TRANSLATE the problem information

• Given information:
  • 18,000 square centimeters to convert
  • \(\mathrm{1\ meter = 100\ centimeters}\)
• Find: equivalent square meters

2. INFER the conversion approach

• Key insight: Area conversions require squaring the linear conversion factor
• Since we're converting square units (not linear units), we can't simply use 100 as our conversion factor
• We need to find: How many square centimeters equal 1 square meter?

3. INFER the area conversion factor

• If \(\mathrm{1\ meter = 100\ centimeters}\), then:
• \(\mathrm{1\ square\ meter = (1\ meter)^2 = (100\ centimeters)^2 = 10{,}000\ square\ centimeters}\)

4. SIMPLIFY the conversion calculation

\(\mathrm{18{,}000\ square\ centimeters \div 10{,}000\ square\ centimeters\ per\ square\ meter = 1.8\ square\ meters}\)

Answer: A. 1.8

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Not recognizing that area conversions require squaring the linear factor

Students often think: "1 meter = 100 centimeters, so I'll just divide 18,000 by 100."

This gives them \(\mathrm{18{,}000 \div 100 = 180}\), leading them to select Choice C (180)

Second Most Common Error:

Conceptual confusion about area units: Not understanding why area units need different conversion factors than linear units

Some students might divide by 1,000 (perhaps mixing up area and volume conversions), getting \(\mathrm{18{,}000 \div 1{,}000 = 18}\), leading them to select Choice B (18)

The Bottom Line:

The key challenge is recognizing that when converting area units, you must square the linear conversion factor. This isn't just memorization—it comes from understanding that area measures two-dimensional space, so both length and width get converted.