Uncertainty & Significant Digits
Uncertainty and Significant Digits
Uncertainty in Measurement
- Depends on the precision of the measuring device
- For example a measurement of 1.682956 grams is more precise measurement than 1.7 grams
- Reliability in Measurements
- Accuracy: the closeness to the actual scientific value
- Precision: getting repeated measurements in repeated trials
- Type of Errors
- Random: error in measurement has equal probability of being high or low
- Systematic: errors all occur in the same direction
General Rules for Determining if a Number is Significant
- Draw a box around all nonzero digits beginning with the leftmost nonzero digit and ending with the rightmost nonzero digit in the number.
- If a decimal is present, draw a box around and trailing zeros
- Consider any all boxed digits significant
- Example 1:
20406 = 5 significant digit
- Example 2:
0.0045 = 2 significant digit
- Example 3:
4000 = 1 significant digit
- Example 4:
4000. = 4 significant digit
- Example 5:
0.002500 = 4 significant digit
- Example 6:
3.00 = 3 significant digit
- The answer can only be as precise as your least precise measurement
Add / Subtract Example:
| 2.87 (precise 2 places to the right of the decimal)
3.5673 (precise 4 places to the right of the decimal)
+ 301.2 (precise 1 place to the right of the decimal)
------------
307.6373 (rounds off to 307.6 because answer can only have 1 significant digit after the decimal)
|
- The answer can have no more significant figures than there are in the measurement with the fewest number of significant figures.
Multiply / Divide Example
| 12.257 (5 total significant digits)
X 1.162 (4 total significant digits)
------------
14.2426 (rounds off to 14.25 because answer can only have 4 significant digits)
|
RULE of THUMB
As a rule, when performing a series of calculation, wait until the very end to round off to the proper number of significant figures instead of rounding off each intermediate result.