How many meters are equivalent to 2,300text{ centimeters}? (100text{ centimeters} = 1text{ meter})

1. TRANSLATE the problem information

• Given information:
  • We have \(\mathrm{2,300\text{ centimeters}}\)
  • Conversion factor: \(\mathrm{100\text{ centimeters} = 1\text{ meter}}\)
  • Need to find: equivalent meters

2. INFER the conversion strategy

• Since we're going from a smaller unit (cm) to a larger unit (m), we need to divide
• Set up conversion factor as a fraction: \(\mathrm{\frac{1\text{ meter}}{100\text{ centimeters}}}\)
• This fraction equals 1, so multiplying by it doesn't change the value, only the units

3. SIMPLIFY by performing the conversion

• \(\mathrm{2,300\text{ cm} \times \frac{1\text{ meter}}{100\text{ cm}}}\)
• \(\mathrm{= \frac{2,300}{100}\text{ meters}}\)
• \(\mathrm{= 23\text{ meters}}\)
• The centimeter units cancel out, leaving only meters

Answer: B. 23

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students set up the conversion factor backwards, thinking "100 cm = 1 m" means they should multiply 2,300 by 100.

They calculate: \(\mathrm{2,300 \times 100 = 230,000}\) and select Choice D (230,000).

Second Most Common Error:

Poor TRANSLATE reasoning: Students misunderstand the conversion relationship and think they need to add 100 to convert units.

They might calculate \(\mathrm{2,300 + 100 = 2,400}\) and select Choice C (2,400).

The Bottom Line:

Unit conversion problems require students to understand that conversion factors must be set up so that unwanted units cancel out. The key insight is recognizing which direction the conversion factor should point based on the units you're starting with and ending with.