The value of z is 1.13 * 100. The value of z is what percent greater than 100?

1. TRANSLATE the problem information

• Given information:
  • z is 1.13 times 100
  • Need to find: what percent greater z is than 100
• What this tells us: \(\mathrm{z = 1.13 × 100}\)

2. INFER the approach

• To find "what percent greater," we need to:
  • First find the actual value of z
  • Then calculate how much larger z is than 100
  • Finally express this difference as a percentage of 100

3. SIMPLIFY to find the value of z

• \(\mathrm{z = 1.13 × 100 = 113}\)

4. INFER and SIMPLIFY the percent increase calculation

• Difference between z and 100: \(\mathrm{113 - 100 = 13}\)
• Percent increase formula: \(\mathrm{(difference/original) × 100\%}\)
• Percent greater than 100: \(\mathrm{(13/100) × 100\% = 13\%}\)

Answer: B. 13

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE reasoning: Students confuse "percent greater than" with "what percent of" or misunderstand what the question is asking.

Some students might calculate \(\mathrm{z = 113}\) correctly but then think the answer is 113% (since 113 is 113% of 100). They fail to recognize that "percent greater than" means the additional amount above the original value. This leads to confusion and guessing among the larger answer choices.

Second Most Common Error:

Poor INFER skill: Students don't recognize that they need to find the difference first before calculating the percentage.

They might think that since \(\mathrm{z = 1.13 × 100}\), the answer is simply 1.13 or 1.13%. This stems from not understanding that "1.13 times" means the whole value is 1.13 times the original, not that there's a 1.13% increase. This may lead them to select Choice A (11.3) after making calculation errors with decimals.

The Bottom Line:

The key challenge is understanding that "percent greater than" asks for the additional amount as a percentage of the original value, not the total value as a percentage. Students must distinguish between "what percent of" versus "what percent greater than."