PHYS204 – Physics for Scientists and Engineers I
Lab Manual V2.0
Experiment 1: Graphical Analysis
, Experiment 1: Graphical Analysis
INTRODUCTION
The purpose of this lab is to investigate and understand possible sources of error when
measurements are recorded during experiments and to accurately represent these error
calculations in final results. Without this understanding, values obtained during experiments
would be meaningless. Accurately representing error calculations in reports is important because
even when taking careful measurements, there will always be some degree of error. No physical
quantity can ever be perfectly measured.
Measured Values and Uncertain Digits
When taking measurements, a measured value will first be obtained, and then the significant
digits of this value will need to be counted.
To figure out these significant digits, the “uncertain digits” need to be found in the values
recorded during the experiment. In numbers with no decimal, counting starts at the first non-
zero digit, and continues to the last non-zero digit. In numbers with a decimal, counting starts at
the first non-zero digit, but finishes at the digit after the decimal point, whether it is zero or not.
In both scenarios, these digits are called “significant figures”. Using scientific notation eliminates
confusion as to how many significant figures there are. See below:
Table 1.1 – Examples of Significant Figure Calculations
Measured Value Scientific Notation # of Significant Figures
9.7 9.7 2
9.0 9.0 2
9.70 9.70 3
970 9.7 x 102 2
970 ±𝟐 (9.70 ±𝟐) x 102 3
970.0 9.700 x 102 4
9.00770 9.00770 6
0.00970 9.70 x 10-3 3
970 x 10-8 9.70 x 10-6 3
Random and Systematic Uncertainties
There are 2 main types of uncertainties – random and systematic. Random uncertainties include
environmental factors beyond the control of the experiment, the limited capacity of the
instruments being used, and human observational errors, such as when/if there was a colour
change. Systematic errors include poor calibration of tools used for the experiment, tools that are
not working properly, or poor reading of the tools by the experimenter.
Lab Manual V2.0
Experiment 1: Graphical Analysis
, Experiment 1: Graphical Analysis
INTRODUCTION
The purpose of this lab is to investigate and understand possible sources of error when
measurements are recorded during experiments and to accurately represent these error
calculations in final results. Without this understanding, values obtained during experiments
would be meaningless. Accurately representing error calculations in reports is important because
even when taking careful measurements, there will always be some degree of error. No physical
quantity can ever be perfectly measured.
Measured Values and Uncertain Digits
When taking measurements, a measured value will first be obtained, and then the significant
digits of this value will need to be counted.
To figure out these significant digits, the “uncertain digits” need to be found in the values
recorded during the experiment. In numbers with no decimal, counting starts at the first non-
zero digit, and continues to the last non-zero digit. In numbers with a decimal, counting starts at
the first non-zero digit, but finishes at the digit after the decimal point, whether it is zero or not.
In both scenarios, these digits are called “significant figures”. Using scientific notation eliminates
confusion as to how many significant figures there are. See below:
Table 1.1 – Examples of Significant Figure Calculations
Measured Value Scientific Notation # of Significant Figures
9.7 9.7 2
9.0 9.0 2
9.70 9.70 3
970 9.7 x 102 2
970 ±𝟐 (9.70 ±𝟐) x 102 3
970.0 9.700 x 102 4
9.00770 9.00770 6
0.00970 9.70 x 10-3 3
970 x 10-8 9.70 x 10-6 3
Random and Systematic Uncertainties
There are 2 main types of uncertainties – random and systematic. Random uncertainties include
environmental factors beyond the control of the experiment, the limited capacity of the
instruments being used, and human observational errors, such as when/if there was a colour
change. Systematic errors include poor calibration of tools used for the experiment, tools that are
not working properly, or poor reading of the tools by the experimenter.
