Significant Figures

A. Significant Figures The more figures a number has, the more precise it is, right? 4 vs 4.56 What about 4 vs 000004 !? Not all digits are meaningful contributions to the precision of a number We distinguish between significant and insignificant figures of a number

Sigfigs Rules Rule 1: sigfigs are all numbers that are not zeros 22.3 has ____ 3 sigfigs 0.0004 has ____ 1 sigfig has ____ 2 sigfigs

Rule 2: A zero can be a sigfig if ….it is between non-zeros 2003 4 sigfigs ….it is after the decimal point 2.00 3 sigfigs 4.0 x 1023 2 sigfigs

Rule 3: A zero is not a sigfig if 1. It is before a number 00005 has ___ 1 sigfig 2. Is at the end of large numbers 870,000 has ___ 2 sigfigs

How many sigfigs do the following numbers have? 3.87 2,000,000 0000002 40078 4 40.00

In science, all reported figures of a result are considered significant They not only represent the outcome of an experiment but also accuracy and precision of the equipment Your worst equipment is the limiting factor for the sigfigs of the final result

Multistep experiments…. 4.6 ml → 0.8776 K →78.9665 atm = 34.999mg 2 sigfigs 4 sigfigs 6 sigfigs 5 sigfigs Result has to be rounded up to 2 sigfigs: 35 mg

Calculations in science The number with the lowest sigfigs determines the sigfigs of the result!!! Example: 10.555m x 2.3 sec= 24.2765 round to 24 m/sec 5sf 2sf 6sf 2sf

Practice 1.10 x 23.87= 0986 x 5.9 = 2.3 x 10001 = a)26.3 b) 5,800 c) 23,000