Math Problem Statement

You purchased 3.4 kg of apples from Wollaston. You noticed that they used a spring scale with the smallest division of 18.0 g to weigh them. What is the relative error in this weight measurement as a percentage?

Solution

To solve this problem, we need to calculate the relative error as a percentage.

Information given:

  1. Weight of apples: 3.4kg=3400g3.4 \, \text{kg} = 3400 \, \text{g}
  2. Smallest division of the scale: 18.0g18.0 \, \text{g}

Formula for Relative Error:

Relative Error (%)=(Smallest DivisionMeasured Value)×100\text{Relative Error (\%)} = \left( \frac{\text{Smallest Division}}{\text{Measured Value}} \right) \times 100

Substituting the values:

Relative Error (%)=(18.03400)×100\text{Relative Error (\%)} = \left( \frac{18.0}{3400} \right) \times 100

Calculation:

Relative Error (%)=(18.03400)×100=0.5294%\text{Relative Error (\%)} = \left( \frac{18.0}{3400} \right) \times 100 = 0.5294\%

Final Answer:

The relative error is approximately 0.53%.


Would you like further explanation or have any additional questions? 😊

Here are 5 related questions for deeper understanding:

  1. How does the relative error change with larger measured values?
  2. What is the importance of the smallest division in error calculations?
  3. How would the relative error differ if the weight was 1.7 kg instead?
  4. What is the difference between absolute and relative error?
  5. How can you reduce measurement error in practical experiments?

Tip: Always check the units in a problem to ensure consistency throughout your calculations!

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Math Problem Analysis

Mathematical Concepts

Relative Error
Percentage Calculations

Formulas

Relative Error (%) = (Smallest Division / Measured Value) × 100

Theorems

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Suitable Grade Level

Grades 9-12