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Measurement and Uncertainty

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# Measurement and Uncertainty - PowerPoint PPT Presentation

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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### 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
• 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
• 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 (or certainty)
• Precision

How close value is to accepted value

How exact and reproducible a value is

Let’s try that out...

Good accuracy, poor precision

Good precision, poor accuracy

Good accuracy, good precision

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
• 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
• 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

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

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 Notation

4.19 x 10-3 m/s

• Power of 10 multiplier
• Unit

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

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

Express 1233.45m3 to three figures.

Express 0.00000046667m/s to two figures.

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