1. SIGNIFICANT FIGURES

2. ACCURACY VS. PRECISION
In labs, we are concerned by how “correct” our measurements are
They can be accurate and precise
Accurate: How close a measured value is to the actual measurement
Precise: How close a series of measurements are to each other

3. EXAMPLE The true value of a measurement is 23.255 mL
Below are a 2 sets of data. Which one is precise and which is accurate?
23.300, ,
22.986, ,

4. SCIENTIFIC INSTRUMENTS
In lab, we want our measurements to be as precise and accurate as possible
For precision, we make sure we calibrate equipment and take careful measurements
For accuracy, we need a way to determine how close our instrument can get to the actual value

5. SIGNFICANT FIGURES
We need significant figures to tell us how accurate our measurements are
The more accurate, the closer to the actual value
Look at this data. Which is more accurate? Why?
25 cm
25.2 cm
25.22 cm

6. ANSWER
25.22cm
The more numbers past the decimal, the closer you get to the true value.
How do we determine how many sig. figs. we have?

7. SIGNIFICANT FIGURES
Significant figure – any digit in a measurement that is known with certainty plus one final digit, which is uncertain
Example:
4.12 cm
This number has 3 significant figures
The 4 and 1 are known for certain
The 2 is an estimate

8. SIGNIFICANT FIGURES
In general: the more significant figures you have, the more accurate the measurement
Determining significant figures with instrumentation
Find the mark for the known measurements
Estimate the last number between marks

9. SIGNIFICANT FIGURES Graduated cylinder Meter stick At your desk: Ruler
Let’s look at some examples:
Graduated cylinder
Meter stick
At your desk:
Ruler

10. RULES FOR SIGNIFICANT FIGURES
Rule 1: Nonzero digits are always significant
Rule 2: Zeros between nonzero digits are significant
40.7 (3 sig figs.)
87009 (5 sig figs.)
Rule 3: Zeros in front of nonzero digits are not significant
(4 sig figs.)
(1 sig figs.)

11. RULES FOR SIGNIFICANT FIGURES
Rule 4: Zeros at the end of a number and to the right of the decimal point are significant
85.00 (4 sig figs.)
(10 sig figs.)
Rule 5: Zeros at the end of a number are not significant if there is no decimal
40,000,000 (1 sig fig)

12. RULES FOR SIGNIFICANT FIGURES
Rule 6: When looking at numbers in scientific notation, only look at the number part (not the exponent part)
3.33 x 10-5 (3 sig fig)
4 x 108 (1 sig fig)
Rule 7: When converting from one unit to the next keep the same number of sig. figs.
3.5 km (2 sig figs.) = 3.5 x 103 m (2 sig figs.)

13. HOW MANY SIGNIFICANT FIGURES?
35.02
0.0900
20.00
3.02 X 104
4000

14. ANSWERS 4 3 1

15. ROUNDING TO THE CORRECT NUMBER OF SIG FIGS.
Many times, you need to put a number into the correct number of sig figs.
This means you will have to round the number
EXAMPLE:
You start with 998,567,000
Give this number in 3 sig figs.

16. ANSWER Step 1: Get the first 3 numbers (3 sig figs.)
998
Step 2: Check to see if you have to round up or keep the number the same
You need to look at the 4th number
9985
If the next number is 5 or higher, round up
If the next number is 4 or less, stays the same
Therefore = 999

17. ANSWER
Step 3: Look at your 3 numbers and put them in scientific notation
9.99
Step 4: Count the number of places you have to move the decimal to get the exponent
9.99 x 108

18. TRY THESE
10,000 (3 sig. figs.)
(2 sig. figs.)
347,504,221 (3 sig. figs.)
(2 sig. figs.)
89,165,987 (3 sig. figs.)