1. Significant Figures

2. Accuracy versus Precision
When taking scientific measurements, the goals are to measure accurately and with precision.
Accuracy refers to how close a measured value is to the actual or real value
Precision refers to how close the measurements are to one another

3. Accuracy versus Precision
Accuracy refers to how close a measured value is to the actual or real value
Precision refers to how close the measurements are to one another
Examine the diagrams on the right. Which displays accuracy? Precision? Assume the bull’s-eye represents the true value
Neither
Precision
Accuracy
Accuracy and Precision

4. Measuring Tools
In order to take measurements, scientists must use a measuring tool
Ruler
Scale
Spectrometer
Barometer
Etc.
Each device has a maximum level of precision that it can measure.

5. Measuring Tools
Eg. Which of the following best describes the length of the red rectangle?
A. 2 cm B cm C cm D cm

6. Measuring Tools
The smallest division this ruler shows is millimeters (0.1 cm), however, we are able to estimate up to a tenth of a millimeter (0.01cm).
In general, a measurement includes:
The smallest marked interval on the tool
Eg. Millimeters on a ruler
One more estimated decimal place
Eg. Tenths of a millimeter on a ruler
The number of digits or decimal places in a measurement represents our certainty, or to what degree we are confident that our measurement represents the true value.

7. Measurements
The number of digits and decimal places in a measurement represents our certainty, or to what degree we are confident that our measurement represents the true value.
This is referred to as the number of significant figures
Significant figures (sig figs): the digits that contribute meaning to a measurement

8. Significant Figures include:
All non-zero digits
Eg. 3.4 has 2 significant figures
All zeros between non-zero digits
Eg has 3 significant figures
All zeros trailing non-zero digits after a decimal place
Eg has 5 significant figures

9. Significant Figures Do Not Include:
Any leading zeros
Eg has 1 significant figure
Any trailing zeros necessary to denote scale UNLESS they are followed by a decimal point
Eg. 10,000 has 1 significant figure
10,000. has 5 significant figures

10. Significant Figures
In general: ask yourself “is this zero necessary or did we go out of our way to include it?”
If it is necessary, it is not significant
If we went out of our way to include it, it is significant
How many significant figures? x x x
NOTE: With proper scientific notation, all the digits at the front are significant

11. Operations with Significant Figures
Significant figures must also be tracked when performing operations on measurements. We can’t be more confident of an output than we were of the input.
Adding and subtracting: the sum or difference should be rounded to the same number of decimal places as the input with the fewest number of decimal places
Eg =  Our answer needs to be rounded to 58.1 (one decimal place)
Multiplying and dividing: the product or quotient should be rounded to the same number of sig figs as the input with the fewest number of sig figs
Eg * 47 =  Our answer needs to be rounded to 95 (two sig figs)