AN EASY METHOD TO AVOID PRODUCING MISLEADING RESULTS 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 103

How many sig figs in each #?

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