This document discusses measurement units and uncertainty in measurements. It begins by introducing common SI units like meters, kilograms, and seconds. It then discusses prefixes used for units and how to convert between units. The document distinguishes between accuracy and precision, where precision refers to the closeness of repeated measurements and accuracy refers to how close measurements are to the true value. It also discusses random and systematic errors. In the end, it provides an example exercise on measurement conversions, comparisons, and calculating volume from given dimensions.

1. Measurements
slides courtesy of Dr. Gamag

2. Learning Goals
• Be familiar with the SI units.
• Be familiar with the frequently used prefixes for SI units.
• Change units.

3. Learning Goals
 Differentiate accuracy from precision
 Differentiate random errors from systematic errors

4. Units
 How many people are in this classroom?
 What’s the temperature at the moment?
 What’s your height?
 How long does it take to walk from here to the
bookstore?
 How heavy is the Physics textbook?
Measurements

5. Standard Unit (SI / MKS)
meter kilogram second
Measurement Approximate value
Size of cells in most living organisms 1 x 10-5 m
Distance of Earth to nearest star 4 x 1016 m
Electron mass 9 x 10-31 kg
Sun’s mass 2 x 1030 kg
Time between normal heartbeats 8 x 10-1 s
Measurements

6. Prefixes

7. Prefixes

8. Unit Conversion
 Choose a conversion factor that will make the units
cancel, leaving the answer in the correct units.
Convert 1.34 kg to grams:
1.34 kg
103 g
1 kg
= 1340 g
Convert 43 km/h to m/s:
43 km
1 h
103 m
1 km
1 h
60 min
1 min
60 s
= 12
m
s

9. Uncertainty in Measurements
 Scientists share their results that are reported with an
uncertainty.
 A new measurement that is within the margin of uncertainty
confirms the old measurement.
Acceleration due to gravity is g = 9.80 ± 0.02
m
s2
Acceptable measurements range from 9.78 − 9.82
m
s2

10. Uncertainty in Measurements

11. Significant Figures
Multiplication or Division : fewest significant figures
Addition or Subtraction : fewest digits to the right of
the decimal point

12. Drill: Significant Figures
Here .

13. Accuracy vs. Precision
How precise and accurate are the
measurements of the three
students?
Spring elongation measured by three students. Data averaged
over five trials.

14.  It is the degree of exactness of a measurement.
 Student 3’s measurements are the most precise, within ±0.1
cm. The measurements of the other two students are less
precise because they have larger uncertainties.
 Precision depends on the instrument and
technique used to make the measurement.
 Device with the finest division on its scale
produces the most precise measurement.
Precision: how close are the data to each other?

15.  Precision: degree of exactness of a measurement
 Least count: smallest value that can be measured by the
instrument. Measured values are good only up to this value.
Precision: Least Count

16. Accuracy
 how well the results of a measurement agree with the “real”
value
If the real length of the spring had been
14.8 cm, then student 2 would have been
most accurate and student 3 least accurate.
Student 3 may be precise in
measuring but
he is the least accurate.

17. Precision versus Accuracy
Precision: closeness of the measurements to each other
Accuracy: closeness of the measurements to the true value

18. Systematic Errors vs. Random Errors
 Systematic Errors - consistent inaccuracies in the
result of an experiment that may be incurred due to
the equipment or faulty experiment procedure
e.g. misalignment, wrong calibration, negligence of
friction
 Random Errors - errors in measurement due to the
precision of the instrument or the experimenter’s
inability to do the measurements uniformly
e.g. stop watch’s precision, response time of
experimenter

19. Chapter 1 Exercise
a) Convert the following measurements to SI units
i. 42.3 cm
ii. 214 μg
iii. 57 ns
b) Rank the following mass measurements from least to
greatest: 11.6 mg, 1021 μg, 0.000006 kg, 0.31 mg.
c) The length of a room is 16.40 m, its width is 4.5 m, and
its height is 3.26 m. What is the volume enclosed by
the room?