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