1. SIGNIFICANT DIGITS AN EASY METHOD TO AVOID PRODUCING MISLEADING RESULTS

2. Determining the number of sig digs in a measurement
The number of SD expressed reflects the accuracy and precision of the measuring device and the measurement.

3. Here are some rules for counting significant digits in measurements:
All digits ARE significant except
Zeros preceding a decimal
and
Zeros at the end of a number containing NO decimal point – may or may not be significant

4. For Example: 0.0045 has 2 significant digits but

5. AND
has 4 sd while
has 6 sd and
has only 1 sd

6. Numbers with no decimal point in them are ambiguous...
Does 5000 mL mean exactly 5000? Maybe.... Maybe Not!
So 5000, 500, 50, and 5 are all assumed to have 1 significant digit for certain
If a writer means exactly 5000, he/she should write or x 103

7. How many sig digits in each #?
200 mL 0.2 mL mL mL
52.50 g g g g
4.0 cm 40 mm 40. mm m

8. IT’S EASY! IT’S FAST! Two Rules are used: One for Adding & Subtracting
One for Multiplying & Dividing

9. For Example:
5.50 grams grams grams

10. OR
mL mL mL --> 2.4 mL

11. Now let’s do some math..... (round answers to correct sig digs!)
g g
answer: 6.55 g
Did you need to count sig digs? NO!

12. Try this one.... 4.80 mL - 0.0015 mL answer: 4.80 mL
(one might say is insignificant COMPARED TO 4.80)

13. When multiplying or dividing
You must COUNT significant digits
The answer can have only AS MANY significant digits as the LEAST of the numbers used to get it

14. Now try these... 5.0033 g / 5.0 mL answer: 1.0 g/mL
Did you have to count sig figs?
YES!

15. Here’s a tougher one.....
3.0 C/s x 60 s/min x 60 min/hr = answer: C/hr --> C/hr
Note:
Standard conversion factors and numerical constants never limit significant digits—only instruments and equipment do.

16. THAT’S ALL THERE IS TO IT!
Use the least accurate measurement when adding and subtracting
Count the number of significant digits when multiplying and dividing