1. (sig figs if you’re cool)
Significant Figures
(sig figs if you’re cool)

2. What are significant figures?
A process for reporting measurements using the number of digits and decimal places that tell you how EXACT the measurement is.
121 is less exact than 121.5
The difference: a more precise tool was used to measure the 121.5
Reporting tells anyone that the person was able to measure the quantity up to the tenths place.

3. So, why should I care about these?
When reporting measurements:
You need to know how to report measurements in lab correctly (both the measurement and the precision of the tool used)
Calculations with significant figures:
You need to know how to calculate values so you don’t report answers that are more exact than the numbers used to calculate that value.

4. Significant Figure Rules
#1 Non-zero digits are always significant
#2 Any zeros between two significant digits are significant (zero sandwich)
#3 A final zero or trailing zeros in the decimal portion ONLY are significant

5. How Many Sig Figs? Example Number of Sig Figs 23 203 4500 4500.2
0.0012
1.0012
51,003
43,251 8
8.0 2 3 2 5 2 5 5 5 1 2

6. Rounding Sig Figs
Sometimes you’ll need to round numbers to the correct number of sig figs
For example:
Round 90,970 to 2 sig figs  91,000
Example
Round to:
Result
678,510 miles 3 km 4
67,548 kg 2 cm
679,000 miles km
68,000 kg cm

7. Addition & Subtraction
Significant Figures in Calculations
Addition & Subtraction: The number of decimal places in the answer should be equal to the number of decimal places in the value with the fewest decimal places. Round only your FINAL answer!
Example: g g g
15.74g
(4 decimal places)
(2 decimal places)
(3 decimal places)
(4 decimal places, need to round final answer to 2)

8. Multiplication and Division
Significant Figures in Calculations
Multiplication & Division: The number of significant figures in the answer should be the same as the value with the fewest significant figures. Only round FINAL answer!
Example:
12.36 mL x g = g round to 21g mL
4 sig. fig.
2 sig. fig.
Note: Definitions and counted numbers have an unlimited number of significant figures.
Note: If your answer is being used in another equation, use the calculated answer, not the sig fig answer.

9. To change numbers to scientific notation:
Make sure number is between 1.0 and 9.9
Count the number of decimal places the decimal was moved
If moved to the left, the exponent is positive
If moved to the right, the exponent is negative
On your calculators: use EE or EXP to replace x10^
Changing numbers to scientific notation will help you count numbers of sig figs
54,970,000
5.497 x 10^7
7.86 x 10^ -4
23.001
x 10^1
2.456 x 10^ -7