Topic 11

Uncertainty and Errors in measurements "Raw Data"
a) Uncertainty
 No Science can offer absolute certainty; an uncertainty range applies to any experimental value. (Measured value ± Uncertainty Unit)
 Uncertainty in a measurement depends on the precision of the measuring device:
 In graduated instruments, the uncertainty is ± of the smallest division
(Unless given a different value)
 In digital instruments the uncertainty is ± the smallest scale division

b) Significant figures
 Certain and uncertain digits are called significant figures. When making a measurement it is important to record the result to the appropriate number of significant figures. Ex: for a burette 25.00 ml and not 25 ml.
 Rules for counting significant figures

 Refer to Book page 216/423

c) Experimental Errors
 Random errors:
- Are caused by the way we read measuring instruments or by changes in surrounding conditions
- Can be reduced by repeating measurements
 Systematic errors are of 3 types:
- Instrument errors that can be corrected by calibration
Ex: Temperature measured by a thermometer that has an imperfection.
- Method errors, these are difficult to detect and control
Ex: Side reactions during a Chemical change.
- Personal errors that can be minimized by self-discipline.
Ex: Reading a burette or detecting a color change.
 Accuracy and Precision
 Precision:
- Degree of agreement among several measurements of the same quantity.
- Precise measurements have small random errors.
 Accuracy:
- Agreement of a particular value with the true value.
- Accurate measurements have small systematic errors.
 Refer to Book page 217and 218/424 and 425

Uncertainties in calculated results "Processed Data"
a) Rules for significant figures in Mathematical operations
 In a multiplication or a division; the number of significant figures in the result is the same as the number of significant figures in the least precise measurement.
 In an addition or a subtraction; the number of decimal places in the result is the same as the number of decimal places in the least precise measurement.

PS: For rounding look at the digit to be dropped; if it is ≥ 5 then round up the digit before it, if it is < 5 drop it without changing the digit before it.


Graphical Techniques
 Dependant variable and independent variable
 Best fit line (correction of random errors)
 Displaced line (As a result of systematic errors)
 Extrapolating a straight line
 Gradient of a straight line:
 Gradient of a curve at a point = Gradient of tangent at this point
 Plotting data to produce a straight line
Example: Ideal gas equation PV = nRT; Plot P (vs) 1/V
 Using Data logger to plot graphs
Example: Titration curve of an acid
 Refer to Book pages 222---225/429---432