1. Significant
Figures

2. Laboratory measurements are made by reading all digits on the instrument, and estimating one digit.

3. Significant Figures
All the digits of a measurement that you are sure of (markings on the instrument) plus one estimated digit.

4. Rules for significant digits.
Nonzero digits are always significant.
Example: 5.67
All final zeros used after the decimal point are significant.
Example: 5.60
Zeros between two other significant digits are always significant.
Example: 5006, 5.006
Zeros used solely for spacing the decimal point are not significant.
Example: 56,000 , , 0.560

5. Significant zeros If a zero is used only to place the decimal, it is NOT significant.
Examples:
Desk measures cm
What is the last marking on the instrument?
How many significant figures in this number.
Counting numbers
are exact whole numbers.
30 people in the room
$20.05 dollars in my pocket

6. You try it!
405
3.208
3000
0.0045 3 4 1 6 2

7. Rules for calculating with significant figures.
Addition or subtraction
Your final answer may contain no more places after the decimal than your least known quantity.
(Round the answer so that it has the same number of decimal places as the measurement having the fewest decimal places.)

8. Example: mL mL mL mL
*Answer can only have as many places to the right of the decimal as that of the known quantity with the least: = mL

9. Example: 62 cm x 33.03 cm = 2047.86 cm2 *only good to 2 figs
Multiplication and division Your final answer may have no more total Significant digits than your known quantity with the least number of significant figures.
Example:
62 cm x cm = cm2
*only good to 2 figs
2.0 x 10 3 cm2

10. Rules for rounding off
Look at digit to the right of digit to be rounded. IF:
Greater than or equal to 5 round up, less than 5 leave.

11. Examples: Round to three significant figures.
8.73
126
3.44
3.42
3.43 = = = = =

12. = 4.385 g Example: 4.383 g 0.0023 g 4.3853 g If 4.383 g of oxygen
combine with g of carbon,
what’s the mass of the resulting compound? g g g
= g

13. = 8.8105727 = 8.81 oz Example: 250.0 g 1.00 lb 16 oz 454 g 1.00 lb
What is the mass in ounces
of g of bromine?
250.0 g lb oz
454 g lb =
= oz

14. Example: = 2.54 x 10-7 = 2.5 x 10-7 mm/molecule
If a line of 1.0 x 108 water molecules is 1.00 inches long, what is the average diameter, in millimeters of a water molecule?
1.00 inch cm 1 m mm
1.0 x 108 molecules 1 inch cm 1 m
= x 10-7
= 2.5 x 10-7 mm/molecule

15. You try it!
A student places g of iron,
oz of aluminum, and lb of
copper in a beaker that weighs 138 g.
What is the total mass in grams of the
beaker and its contents?
oz 1.0 lb 454 g
16 oz 1.0 lb
28.70 g
10.8 g
1.77 g
138 g
= 179 g
= 10.8 gAl
lb 454 g
1.00 lb
= 1.77 gCu

16. You try it!
A girl needs to reflux a mixture
for 9.85 hours. How long must
the mixture reflux in minutes?
9.85 h 60 min
1 h
= 591 min

17. You try it!
A group of chemistry students are instructed to measure a m length of magnesium ribbon. How long will each ribbon be in mm?
0.75 m mm
1 m
= 750 mm

18. Accuracy & Precision Accuracy:
how close a measurement is to the true value of the quantity that was measured.
Precision:
how closely two or more measurements of the same quantity agree with one another
Can NOT have accuracy without precision.
Can have precision without accuracy