1 / 17

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.

naida
Download Presentation

Measurement and Uncertainty

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related