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Measurements, Accuracy, & Precision
Accuracy Vs. Precision
Accuracy
• How correct you are
• How close your answer is to the expected or actual value
• How accurate is determined by the person making the measurement
• Calculated with the percent error formula
% 𝑒𝑟𝑟𝑜𝑟 = 𝑎𝑐𝑡𝑢𝑎𝑙−𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑𝑎𝑐𝑡𝑢𝑎𝑙
𝑥 100
Precision
• How close your measurements are to one another
• How precise is determined by the smallest increment (division) on the measuring tool
• Determined (shown) by the number of significant digits used to record measurement.
Important Terminology
• Precision of Instrument: what is the smallest unit that can be read on the tool (instrument) – Example: on a meter stick, you can read millimeters or
thousandths of a meter (0.001 m)
• Precision of Measurement (Uncertainty): half of the smallest value that can be read on the tool (instrument) – Example: on a meter stick, you can read millimeters or
thousandths of a meter so the uncertainty is half a millimeter or 0.0005 meters.
• Uncertain Digit: the final digit in any measurement when recorded to the correct precision; it is usually an estimated or approximated value.
• Remember: All measurements MUST include the uncertain digit, the uncertainty and the units
Ruler
Millimeter Scale
Precision of Instrument: 1mm
Uncertainty: 0.5mm
Sample Reading: 14.5mm +/- 0.5mm
Ruler
Centimeter Scale
Precision of Instrument: 0.1cm
Uncertainty: 0.05cm
Sample Reading: 1.45cm +/- 0.05cm
Meter stick 1
Centimeter Scale (up to 100.00cm)
Precision of Instrument:
0.1cm
Uncertainty:
0.05cm
Sample Reading:
5.00cm +/- 0.05mm
Meter stick 2
Centimeter Scale (up to 100.00cm)
Precision of Instrument:
0.5cm
Uncertainty:
0.25cm
Sample Reading:
23.3cm +/- 0.25mm
Showdown 1
Ruler
Measurement Reading:
20.0mm +/- 0.05mm
Showdown 2
Ruler
Measurement Reading:
49.5mm +/- 0.5mm
Showdown 3
Ruler
Measurement Reading:
36.0mm +/- 0.05mm
Showdown 4
Ruler
Measurement Reading:
4.00cm +/- 0.05cm
Showdown 5
Ruler
Measurement Reading:
2.55cm +/- 0.05cm
Showdown 6
Ruler
Measurement Reading:
3.05cm +/- 0.05cm
Showdown 7
Ruler
Measurement Reading:
4.55cm +/- 0.05cm
Showdown 8
Ruler
Measurement Reading:
2.05cm +/- 0.05cm
Showdown 9
Ruler
Measurement Reading:
3.10cm +/- 0.05cm
Showdown 10
Ruler
Measurement Reading:
6.50cm +/- 0.25cm
Showdown 11
Ruler
Measurement Reading:
11.00cm +/- 0.25cm
Showdown 12
Ruler
Measurement Reading:
15.25cm +/- 0.25cm
Showdown 13
Ruler
Measurement Reading:
20.75cm +/- 0.25cm
Showdown 14
Ruler
Measurement Reading:
4.50cm +/- 0.25cm
Showdown 15
Ruler
Measurement Reading:
12.50cm +/- 0.25cm