Significant Figures and Uncertainty
Significant Figures
Review of significant figures
Significant Figures refer to the digits that make up a measurement made with a relatively large level of certainty.
Our instruments are what determine how many significant digits we might have. Yet if we are working on operations, we must assume that the numbers given to us were taken from measurements that have the precision necessary to give us the provided number of significant digits.
Examples:
Our ruler can measure somewhere between 2- 3 significant digits of precision
The balances in the Chemistry Department are able to read a precision of about 5-6 significant digits
We can apply operations to measured values with their respective significant digits but we must be conscious of how to round
There are rules that allow us to carry on these operations
Examples:
22.568 + 21.8 = 44.3 [smallest number of significant digit in decimal places]
12.45 * 2.0 = 25 [smallest number of significant digits in general]
It is possible to perform operations on measured values and increase the number of significant digits
Significant figures can increase due to statistical significance - repetition in measurement
Example:
5 measurements of the same thing - the diameter of a planet as recorded by a telescope pictures:
0.87 0.85 0.86 0.87 0.88 [ All with 2 significant figures ]
We can take the average of these values. In order to take the average, we first add
0.87 + 0.85 + 0.86 + 0.87 + 0.88 = 4.33 [We keep 2 significant figures after the decimal Now we have 3 significant figures]
Next, to take the average we divide by the exact number of data points we had. Since this is an exact number we keep the significant figures of the value we had before thus we get: 4.33/5 = 0.866 [Now 3 significant digits]
how to do unit conversions
We use conversion factors as rations (Multiplying by 1)
Example:
We have 34 yards of ribbon. Can we cover 28 meters with it?
1 m= 3.28 yrd -----> 1m/3.28 yrd = 1 --------> 3.28 yrd/1m = 1
Then:
34 yrd (1m /3.28 yrd) = 10 m. Thus I cannot cover 28 meters
Conversion can become a bit tricky with larger dimensions
4.23 m^3 to ml where 1ml = 1 cm^3
Knowing that 1m = 100 cm will help us. Here is how this would be set up
4.23 m^3 ( 100cm/ 1m) ^3 = 4230000 cm ^3 = 4230000 ml
