Measurement & SF

1.Record measurements from scaled instruments to the correct number of significant figures

2.Identify the number of significant figures in a measurement.

Recording Measurements

We report a measurement to the number of digits as given by the absolute precision. For instance, if we were measuring a stick with a ruler, and the ruler could only measure to millimeters, then you can only precisely measure to the nearest millimeter. Then, when reporting a measurement, you would report an additional digit, as a guess, which would be uncertain. For example, if you measured the stick, with the ruler, to be between 3.4cm and 3.5cm (or 34mm to 35mm), you might report your measurement to be 3.45cm, with the last digit being estimated. An absolute precision of ±0.01cm (or ±0.1mm), is implied accordingly.

Significant Figure Rules

Significant Figures (SF): The digits of a number that are used to express it to a degree of precision.

Significant Figure Rules:

1. All nonzero digits are significant.
2. 0s between 2 nonzero digits are significant.
3. 0s at the beginning of a number are not significant (i.e. 0.00002 has 1 SF)
4. 0s at the end of a number are significant if and only if there is a decimal place (i.e. 100. has 3 SF, 10.0 has 3SF)
5. An exact measurement has ∞ SF (i.e. measurement of “4 people” has ∞SF)