Math Problem Statement
Solution
The question asks to calculate the maximum possible percentage error in the amount of cream due to Emma's assumption that the measurement is exact.
Step 1: Understand the rounding range
- The cream's quantity is given as 150 ml to the nearest milliliter.
- Since it's rounded to the nearest milliliter, the actual quantity of cream could be anywhere between 149.5 ml and 150.5 ml.
Step 2: Calculate the possible error
The error is the difference between the assumed value (150 ml) and the extreme actual values:
- Maximum error = 0.5 ml (this is the difference between 150 ml and either 150.5 ml or 149.5 ml).
Step 3: Calculate the percentage error
The percentage error is calculated as:
Substitute the values:
Now, let's compute that.The maximum possible percentage error is approximately 0.33% due to Emma's assumption that the measurement is exact.
Would you like further details or clarification? Here are 5 questions related to this topic:
- How is rounding related to percentage error?
- What happens if the measurement precision changes (e.g., rounding to the nearest 0.1 ml)?
- How can Emma minimize the percentage error in future measurements?
- Why is understanding percentage error important in practical measurements?
- Can percentage error increase if more assumptions are made?
Tip: Always consider both the upper and lower bounds when calculating potential errors in measurements.
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Math Problem Analysis
Mathematical Concepts
Percentage Error
Rounding
Measurement Error
Formulas
Percentage error = (Maximum error / Measured value) * 100
Theorems
-
Suitable Grade Level
Grades 9-11
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