Accuracy, Errors and Significant Figures

Name: Accuracy, Errors and Significant Figures
Author: StemPy Lab

Measure the same pencil ten times, and you may get ten slightly different numbers. In this course we find why, we learn to say how accurate and how precise a result is, we read a vernier callipers and a screw gauge, we find the error in a result that comes from several measurements, and we write an answer with the right number of significant figures.

4 lessons, about 1 h 40 min4 simulations14 problems8 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (4 lessons)

Lesson 1about 25 min
Accuracy, precision and kinds of error
No measurement is exact. Accuracy is how close a result is to the true value; precision is how close repeated readings are to each other. A systematic error shifts every reading the same way and is not cured by more readings; a random error scatters them and averages out. A result is the mean $\pm$ the mean absolute error; the relative and percentage errors compare errors of different sizes.
1 simulation2 practice questions1 Python program4 problems1 Python lab1 question set
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Lesson 2about 25 min
Least count: vernier callipers and screw gauge
The least count is the smallest step an instrument can read. A vernier callipers whose $n$ vernier divisions fill $n - 1$ main scale divisions has a least count of one main division $\div n$ ( $0.1\ \text{mm}$ for $n = 10$ ). A screw gauge has a least count of pitch $\div$ circular divisions ( $0.01\ \text{mm}$ for $0.5\ \text{mm}$ and $50$ ). Reading $=$ main reading $+$ coinciding division $\times$ least count, corrected by subtracting the zero error.
1 simulation2 practice questions1 Python program3 problems1 Python lab
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Lesson 3about 25 min
Combining errors in calculations
A result worked out from measured quantities carries their errors. For a sum or a difference the absolute errors add. For a product or a quotient the relative errors add. For a power, the relative error is multiplied by the power: if $Z = A^p B^q / C^r$ , then $\frac{\Delta Z}{Z} = p\frac{\Delta A}{A} + q\frac{\Delta B}{B} + r\frac{\Delta C}{C}$ . Errors never cancel.
1 simulation2 practice questions1 Python program4 problems
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Lesson 4about 25 min
Significant figures and rounding
The significant figures of a measurement are the digits we are sure of plus the first uncertain one. Non-zero digits count; zeros between them count; leading zeros do not; trailing zeros after a decimal point do. A product or quotient keeps as many significant figures as its least precise factor; a sum or difference keeps as many decimal places as its least precise term. Round only at the end.
1 simulation2 practice questions1 Python program3 problems1 note
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Errors and Measurement: Practice Paper

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Accuracy, Errors and Significant Figures

Course outline (4 lessons)

Accuracy, precision and kinds of error

Least count: vernier callipers and screw gauge

Combining errors in calculations

Significant figures and rounding

Test Your Learning

Your teacher

Discussion (0)