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 Quantity Quantity Symbol Unit Unit Symbol Length Metre Mass Kilogram Time Second Electric Charge Coulomb

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

Let’s try that out...

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... 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 = 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 Number from 1 to <10, expressed to correct significant digits Power of 10 multiplier Unit

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

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

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?

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