gen chem (lecture 2) sig figs

accuracy =

how close measured values are to the actual value

precision =

how closely a series of measurements agree with one another (also related to the number of significant digits in a given measurement)

the more significant digits in a measurement…

the greater the precision and certainty

how do you know if a digit in a measurement is significant or not?

1. all nonzero digits are significant

2. interior zeros are significant 2(0.0)3

3. leading zeros (to the left of the first nonzero digit) only serve as place holders and are not significant (0).8

4. ending zeros after a decimal point are significant 45.5(00)

5. ending zeros before a decimal point are significant 26(00).728

6. ending zeros before an implied decimal point are ambiguous and scientific notion should be used instead 4(000)

exact numbers have no uncertainty and therefore…

have an unlimited number of significant digits

three categories of exact numbers…

1. numbers from accurately counting discrete objects ( 25 pennies , 230 students)

2. numbers from defined quantities (1000 mm = 1m , 1 foot = 12 in )

3. integral numbers that are part of an equation ( area of a triangle = ( b x h / 2 )

the precision and uncertainty of a measured quantity can’t be improved simply because it’s used in a calculation…

but rather the uncertainty of the individual values must be carried through the calculations and the result of a calculation can be no more precise than the least precise value.

sig figs for addition and subtraction

the precision of the final answer is dictated by the most uncertain value in the calculation. connected to the number of decimal places in a value.

sig figs in multiplication and division

the final result should have as many significant digits as the term with the fewest significant figures.

• to avoid rounding errors in multistep calculations, round only the final answer!!