Transcript Document
SIGNIFICANT FIGURES
AN EASY METHOD TO AVOID PRODUCING MISLEADING RESULTS
IT’S EASY! IT’S FAST!
Two Rules are used:
One for Adding & Subtracting
One for Multiplying & Dividing
When adding or subtracting
Note accuracy of measurements (nearest .1? .01? .001?)
Answer can be no more accurate than the LEAST accurate number that was used to calculate it.
For Example:
5.50 grams + 8.6 grams ------- 14.1 grams
OR
52.09 ml - 49.7 ml ------------ 2.39 ml --> 2.4 ml
When multiplying or dividing
You must COUNT significant figures
The answer can have only AS MANY significant figures as the LEAST of the numbers used to get it
Here is a one sentence rule for counting sig figs: All digits ARE significant except Zeros preceding a decimal fraction and Zeros at the end of a number containing NO decimal point
For Example:
.0045
has 2 significant figures but
1.0045
has 5 significant figures
AND
45.50
has 4 signifcant figures while
45.5000
has 6 sig figs and
.0005
has only 1 sig fig
Numbers with no decimal are ambiguous...
Does 5000 ml mean exactly 5000?
Maybe.... Maybe Not!
So 5000, 500, 50, and 5 are all assumed to have 1 significant figure
If a writer means exactly 5000, he/she must write 5000. or 5.000 x 10 3
How many sig figs in each #?
2000 ml 0.2 ml 20.00 ml 20 ml 52.50 g .0900 g .0042 g 1.0000 g 4.0 cm 40 mm 40. mm .0040m
Now let’s do some math.....
(round answers to correct sig figs!) 5.0033 g + 1.55 g
answer: 6.55 g Did you need to count sig figs? NO!
Try this one....
4.80 ml - .0015 ml
answer: 4.80 ml (one might say .0015
is insignificant COMPARED TO 4.80)
Now try these...
5.0033 g / 5.0 ml
answer: 1.0 g/ml
Did you have to count sig figs?
YES!
Here’s a tougher one.....
3.0 C/s x 60. s/min x 60. min/hr =
answer: 10800 C/hr --> 11000 C/hr Note: standard conversion factors never limit significant figures- instruments and equipment do.
THAT’S ALL THERE IS TO IT!
Use least accurate measurement when adding and subtracting
Count sig figs when multiplying and dividing