Science Measurements Uncertainty and Error Science Measurement Uncertainty

Conversion Factor p A conversion factor is a ratio between two units: The conversion

Example p How fast is 100 km/h in m/s? Write what you have… multiply

Example p How fast is 50 mph in m/s? Write what you have… multiply

Uncertainty in Measurement and Significant Figures

The darts are all close to one another. They may or may not be

Dart is right on target. (The value is close to what it should be.

Precision and Accuracy in Measurements p Precision How reproducible are measurements? p Accuracy How

Dartboard analogy p Imagine a person throwing darts, trying to hit the bulls-eye. Not

Scientific Data Scientists always want the most precise and accurate experimental data. The precision

Dealing with Errors p Identify the errors and their magnitude. p Try to reduce

Counting Sig Fig’s – 4 Rules: 1. 2. 3. 4. Nonzero digits are always

Counting Sig Fig’s – Sci. Notation Use Scientific Notation… p Determine how many digits

How many significant figures? 1, 000. 1 5

How many significant figures? 0. 000827 3

How many significant figures? 1, 200, 000. 0 8

How do you round? p Rounding is different, depending on whether you are n

Adding/Subtracting Add/Subtract first p Round according to the fewest number of Digits After the

Multiplying/Dividing Multiply/Divide first p Round according to the fewest number of Significant Figures p

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Science, Measurements, Uncertainty and Error Science, Measurement, Uncertainty and Error 1

Conversion of Units

Conversion Factor p A conversion factor is a ratio between two units: The conversion factor can be written with either value on top, just set it up so that things cancel out!

Example p How fast is 100 km/h in m/s? Write what you have… multiply by conversion factor(s)… 27. 777. . . m/s do the math… multiply the tops, multiply the bottoms, then divide these 2 #’s

Example p How fast is 50 mph in m/s? Write what you have… multiply by conversion factor(s)… do the math… multiply the tops, multiply the bottoms, then divide these 2 #’s 22. 3472 m/s

Uncertainty in Measurement and Significant Figures

The darts are all close to one another. They may or may not be close to the intended target. http: //smedia. vermotion. com/media/12933/resources/60000. JPG http: //www. gototem. com/Webgifs/Clip. Art/Sports/Darts. GIF

Dart is right on target. (The value is close to what it should be. ) http: //smedia. vermotion. com/media/12933/resources/60000. JPG http: //www. gototem. com/Webgifs/Clip. Art/Sports/Darts. GIF

Precision and Accuracy in Measurements p Precision How reproducible are measurements? p Accuracy How close are the measurements to the true value.

Dartboard analogy p Imagine a person throwing darts, trying to hit the bulls-eye. Not accurate Not precise Accurate Not precise Not accurate Precise Accurate Precise

Scientific Data Scientists always want the most precise and accurate experimental data. The precision and accuracy are limited by the instrumentation and data gathering techniques.

Dealing with Errors p Identify the errors and their magnitude. p Try to reduce the magnitude of the error. HOW? n n n Better instruments Better experimental design Collect a lot of data

Counting Sig Fig’s – 4 Rules: 1. 2. 3. 4. Nonzero digits are always significant All final zeros after the decimal point are significant Zeros between two other significant digits are always significant Zeros used solely as placeholders are not significant

Counting Sig Fig’s – Sci. Notation Use Scientific Notation… p Determine how many digits are important when writing the number in scientific notation. p

How many significant figures? 1, 460 3

How many significant figures? 21. 76 4

How many significant figures? 421. 03 5

How many significant figures? . 002 1

How many significant figures? 1, 000. 1 5

How many significant figures? 726. 01 5

How many significant figures? 720 2

How many significant figures? 4. 801 4

How many significant figures? 0. 103 3

How many significant figures? 0. 000827 3

How many significant figures? 1. 47 3

How many significant figures? 1, 200 2