1. Measurement and Uncertainty
SPH 3U1

2. SI Units
“SI” stands for “Systeme International d’Unites”. It is a system of units used in measurement.
All physical quantities can be expressed as some combination of fundamental units, called base units
Quantity
Quantity Symbol
Unit
Unit Symbol
Length
Metre
Mass
Kilogram
Time
Second
Electric Charge
Coulomb

3. Unit Conversions: Prefixes
Units may be expressed with prefixes, e.g gigabytes or 2.1GB
Each prefix is associated with a power of 10 factor
To convert a measurement to base units, look up the correct factor and multiply
E.g. Convert 2.1 GB to B

4. Unit Conversions
The most common method used to convert units is to multiply by conversion factors.
E.g. Convert 12km into miles
(1 mile = 1.61km)

5. Accuracy and Precision
Accuracy (or certainty)
Precision

7. Let’s try that out...

8. Accuracy: Significant Digits
All digits except leading zeros are significant
m vs m
Counted numbers and defined values have an infinite number of significant digits
4 cars
24 hours = 1 day

9. Rules for Rounding Off Round “down” when... Round “up” when...
The digit dropped is less than 5, 50, 500 etc., the remaining digit is left unchanged.
Round “up” when...
Digit dropped is greater than or equal to 5, 50, 500 etc., the remaining digit is increased.
E.g. Round to three significant figures:
2.146 seconds =
meters =
134.5 kilometers =

10. Significant Digits: Addition& Subtraction
State final answer with the same number of decimal places as the number with the least number of decimal places.
E.g. 251 cm cm =

11. Significant Digits: Multiplication & Division
State final answer with the same number of significant digits as the number with the least number of significant digits.
E.g m ÷ 2.23 s =

12. Scientific Notation Calculate: 50 m x 121 m = 2.10 cm ÷ 501.00 s =
How can we express each of the above to
the correct number of significant digits?

13. Scientific Notation 4.19 x 10-3 m/s
Number from 1 to <10, expressed to correct significant digits
Power of 10 multiplier
Unit

14. Scientific Notation
Move the decimal left or right to express the number as a value between 1 and <10.
Round the number to the correct number of significant digits.
Count the number of spaces the decimal place has been moved. This indicates the value of the exponent.
IF MOVED TO THE RIGHT, the exponent is
IF MOVED TO THE LEFT, the exponent is

15. Scientific Notation Examples
Express m3 to three figures.
Express m/s to two figures.

16. Precision Measurement Uncertainty
Every measurement has some degree of uncertainty in the last (right most) digit.
What is the length of the rod using Ruler A?
Which digits are you certain of? Which are you uncertain of?
How could you express this uncertainty in your measurement?
What about Ruler B?

17. Accuracy: Error
Error in measurements may also be expressed as a percentage
Percent error or relative error:
Percent difference
Indicates difference between two or more measurements