1.3: Uncertainty

UNCERTAINTY IN MEASUREMENTS

Uncertainty - Inexact measurements (Everything we agree on + 1 estimated)

________

|_______|

_____________________________

| ---------|---------|

1cm 2cm 3cm

How much does the rod measure?

It measures 2.3 (We know for sure it measures 2cm, and we estimate the 0.3cm)

 SIGNIFICANT FIGURES

Significant Figures - Number of values in a measurement.

Always report measurements to correct number of significant figures based on precision of instrument,

by determining number of significant figures in a given measurement.!!!

a) Precision: How close your measurements are to each other.

b) Accuracy: How close your actual value.

IDENTIFYING SIGNIFICANT FIGURES

                                                                                  Is your number DECIMAL?...

(YES?)----(NO?)

1. If YES!

a) Zeros at the beginning do not count as significant, all other-zeros count as significant.

2. If NO!

b) Zeros at the end of measurements do not count, all other zeros do count as significant.

Exercise:
Determine the number of significant figures in each of the following:

* 0.0004201050 cm = 7 significant figures 

* 0.050600 g = 5 significant figures

* 63.0002 m = 6 significant figures

* 5.9 x 10⁵ m = 2 significant figures

* 25 students = Rules don't apply since there's not uncertainty of measurement.

* 5020600 cm = 5 significant figures

* 602.00 g = 5 significant figures

* 340. g = 3 significant figures

* 340 m = 2 significant figures

RULES OF SIGNIFICAN FIGURES IN MATHEMATICAL OPERATIONS

1. Multiplication / Division

The result of calculation must have the same number of significant figures as the measurements with the least significant figure. (Note: If we don't have the correct amount of significant figures we round off.)

Example:

0.06 cm (1 significant figure)   x
1.0 cm   (2 significant figure )
500 cm (1  significant figure )
________________________
30 mL (1 significant figure)

2. Addition / Subtraction

The result of the calculation must have the same number of significant figures to the right of the decimal as the measurement with the least number of significant figures to the right of the decimal.

Example:

5.02 cm (2 decimal places)    +
0.1 cm   (1 decimal place)
10 cm    (No decimal places)
______________________
15 cm (No decimal places)

(Number with the least amount of decimal places has zero, so answer has 0 decimal places as well)