Math Problem Statement

If the uncertainty of a balance is plus or minus .005grams, which of the following would be used to report the scale reading. 8.00grams or 8.000grams

Solution

When reporting a measurement, the number of decimal places should reflect the precision of the instrument, which in this case is determined by the uncertainty. The uncertainty is ±0.005\pm 0.005 grams, which suggests that the measurement is precise to the nearest thousandth of a gram (three decimal places).

Therefore, the correct way to report the scale reading is 8.000 grams. This shows that the measurement is precise to the thousandth of a gram, consistent with the uncertainty provided.

Would you like to know more details about how uncertainty affects measurements?

Here are some related questions:

  1. How do you calculate uncertainty in multiple measurements?
  2. What is the difference between accuracy and precision in measurements?
  3. How do you determine significant figures in a measurement?
  4. What role does uncertainty play in scientific experiments?
  5. How do you propagate uncertainty in a series of calculations?

Tip: Always ensure that the number of significant figures in your measurement matches the precision indicated by the uncertainty.

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Math Problem Analysis

Mathematical Concepts

Measurement Uncertainty
Significant Figures

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12