Rules for counting sig figs
1. All non-zero integers are always significant.
* Leading zeros: Zeros that precede all the non-zero digits. These are not significant They are simply space fillers to indicate the position of the decimal point.
* examples: 0.0025 (2) 0.00011 (2)
* 0.000378 (3) 0.00000008 (1)
* In-between zeros: Zeros which are between two non-zero digits. These are always significant, because they are just as important as the non-zero digits.
exp: 1.008 (4) 2,037.6 (5)
10,091 (5) 900,004 (6)
* trailing zeros: Zeros at the right end of a number. These zeros are significant only if the number contains a decimal point.
exp: 100 (1) 100. (3)
340 (2) 560.0 (4)
exp: how many sig figs do each of the following numbers have?
* 3.007 (4) 0.0089 (2)
* 10,030 (4) 0.00430 (3)
calculations and sig figs:
addition and subtraction -
the answer is limited by the value with the most uncertainty
(the number with the smallest number of decimal places)
(what measurement was taken with the lousiest ruler?)
+10.3 cm <---- this measurement was taken with the lousiest ruler
147.54cm = 147.5cm
+ 6.339 g <---- least precision means greater uncertainty
1008.7999 g = 1008.800 g
multiplication and division
The number of sig figs in the result is the same as that in the measurement with the smallest number of sig figs.
* plug this into your calculator: 103.0/20.5 = 5.0243902
* did your calculator suddenly make this measurement more precise? NO!
* you must round off to the correct # of sig figs.
* if last # is >5, round up
* if last # is <5, round down
* previous problem: 103.0/20.5 = 5.02
* 3.420 x 0.0069 = .023598 = 0.024