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Measurement and Uncertainty. SPH 3U1. 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. Unit Conversions: Prefixes.

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si units
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
unit conversions prefixes
Unit Conversions: Prefixes
  • Units may be expressed with prefixes, e.g. 2.1 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
unit conversions
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)

accuracy and precision
Accuracy and Precision
  • Accuracy (or certainty)
  • Precision

How close value is to accepted value

How exact and reproducible a value is

let s try that out
Let’s try that out...

Good accuracy, poor precision

Good precision, poor accuracy

Good accuracy, good precision

accuracy significant digits
Accuracy: Significant Digits
  • All digits except leading zeros are significant
    • 0.00002010m vs. 20100000m
  • Counted numbers and defined values have an infinite number of significant digits
    • 4 cars
    • 24 hours = 1 day
rules for rounding off
Rules for Rounding Off
  • Round “down” 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 =
    • 14.543 meters =
    • 134.5 kilometers =
significant digits addition subtraction
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 + 22.11 cm =
significant digits multiplication division
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. 26.32m ÷ 2.23 s =

scientific notation
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?

scientific notation1
Scientific Notation

4.19 x 10-3 m/s

  • Power of 10 multiplier
  • Unit

Number from 1 to <10, expressed to correct significant digits

scientific notation2
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 NEGATIVE
    • IF MOVED TO THE LEFT, the exponent is POSITIVE
scientific notation examples
Scientific Notation Examples

Express 1233.45m3 to three figures.

Express 0.00000046667m/s to two figures.

precision measurement uncertainty
PrecisionMeasurement 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?
accuracy error
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