What length, in centimeters, is equivalent to a length of 51text{ meters}? (1text{ meter} = 100text{ centimeters})

1. TRANSLATE the problem information

• Given information:
  • Length to convert: 51 meters
  • Conversion factor: \(\mathrm{1\ meter = 100\ centimeters}\)
  • Need to find: equivalent length in centimeters

2. INFER the conversion approach

• Since we're converting from meters (larger unit) to centimeters (smaller unit), we need to multiply by the conversion factor
• The numerical value should get larger when going from a larger unit to a smaller unit
• Set up: \(\mathrm{51\ meters \times \frac{100\ centimeters}{1\ meter}}\)

3. SIMPLIFY the calculation

• \(\mathrm{51 \times 100 = 5{,}100\ centimeters}\)
• The units cancel properly: \(\mathrm{meters \times \frac{centimeters}{meters} = centimeters}\)

Answer: C. 5,100

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students confuse which operation to use for unit conversion. They think "there are 100 centimeters in 1 meter, so 51 meters must be smaller when expressed in centimeters" and divide 51 by 100 instead of multiplying.

This faulty reasoning gives them \(\mathrm{51 \div 100 = 0.51}\), leading them to select Choice B (0.51).

Second Most Common Error:

Conceptual confusion about metric units: Students correctly multiply by 100 but then second-guess themselves, thinking they might need to multiply by 1,000 instead (confusing the centimeter conversion with the millimeter conversion).

This leads them to calculate \(\mathrm{51 \times 1{,}000 = 51{,}000}\) and select Choice D (51,000), which would actually be the correct answer if the question asked for millimeters.

The Bottom Line:

Success requires clearly understanding the direction of unit conversion - when going from larger units to smaller units, the numerical value increases, so you multiply by the conversion factor.