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Measurement and Uncertainty

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

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  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

  3. 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

  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 How close value is to accepted value How exact and reproducible a value is

  6. Let’s try that out... Good accuracy, poor precision Good precision, poor accuracy Good accuracy, good precision

  7. 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

  8. 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 =

  9. 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 =

  10. 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 =

  11. 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?

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

  13. 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

  14. Scientific Notation Examples Express 1233.45m3 to three figures. Express 0.00000046667m/s to two figures.

  15. 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?

  16. 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

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