1. Measurements
Scientists use two word to describe how good the measurements are
Accuracy- how close the measurement is to the actual value (how right you are)
Precision- how well can the measurement be repeated (how close the measurements are to each other, right or wrong)

2. Accuracy vs. Precision Good accuracy Good precision Poor accuracy
Scientists repeat experiments many times to increase their accuracy.
Good accuracy
Good precision
Poor accuracy
Good precision
Poor accuracy
Poor precision

3. Differences
Accuracy can be true of an individual measurement or the average of several
Precision requires several measurements before anything can be said about it

4. Let’s use a golf anaolgy

5. Accurate? No
Precise?
Yes 10

6. Accurate?
Yes
Precise?
Yes 12

7. Accurate? No
Precise? No 13

8. Accurate?
Yes
Precise?
We cant say! 18

9. PRECISE = CONSISTENT(Reproducible)
Accuracy vs. Precision
Accuracy - how close a measurement is to the accepted value
Precision - how close a series of measurements are to each other
ACCURATE = CORRECT
PRECISE = CONSISTENT(Reproducible)

10. In terms of measurement
Three students measure the width of the classroom to be m, 10.3 m and 10.4 m across.
Were they precise?
Were they accurate?

11. In Chemistry…. 7.0 does not equal 7.00
If your lab partner has 5.50 cm as an answer and you have 5.5 cm, one of you will not earn credit!!!
Because in science 5.50 cm does not equal 5.5 cm
How are these measurements different?

12. Significant Digit Rules
All non-zero digits are significant
145 has three significant digits
1,376 has four significant digits
Courtesy Christy Johannesson

13. 2. Zeros Leading Zeros – NEVER significant
Middle Zeros – ALWAYS significant
Trailing Zeros – SOMETIMES significant
(Depends on the presence of a decimal point)
i. If decimal point is present:
IS significant
ii. If decimal point is not present:
IS NOT significant

14. Examples
4 sig figs
3 sig figs
3. 5,280
3. 5,280
3 sig figs
2 sig figs

15. Let’s Practice!!!
Take 2 minutes to answer the practice problems at the bottom of the page.
Put your pencil down when you are finished and we can check our answers together.

16. Significant Digits and Calculators
Many calculators display several additional, meaningless digits.  Be sure to record your answer with the correct number of significant digits.  Calculator answers are not rounded to significant digits. You will have to round-off the answer to the correct number of digits.

17. (13.91g/cm3)(23.3cm3) = 324.103g 324 g Significant Digits
Calculating with Significant Digits
Multiply/Divide - The number of significant digits in the answer should be equal to the number of significant digits in the least accurate factor.
(13.91g/cm3)(23.3cm3) = g
4 SF
3 SF
3 SF
324 g

18. Significant Digits
Calculating with Significant Digits (con’t)
Addition and Subtraction - The number of decimal places in the answer should be equal to the number of decimal places in the number with the fewest decimal places
224 g
+ 130 g
354 g
224 g
+ 130 g
354 g
3.75 mL mL
7.85 mL
3.75 mL mL
7.85 mL
 350 g
 7.9 mL

19. 6. 18.9 g - 0.84 g 18.06 g Practice Problems 5. (15.30 g) ÷ (6.4 mL)
Significant Digits
Practice Problems
5. (15.30 g) ÷ (6.4 mL)
4 SF
2 SF
= g/mL
 2.4 g/mL
2 SF g g
 18.1 g
18.06 g

20. Reporting Measurements
Using significant figures
Report what is known with certainty
Add ONE digit of uncertainty (estimation)
By adding additional numbers to a measurement – you do not make it more precise. The instrument determines how precise it can make a measurement. Remember, you can only add ONE digit of uncertainty to a measurement.

21. Significant Digits
The purpose of significant digits is to indicate the precision of a measurement.
Recording Significant Digits
Significant digits in a measurement include the known digits plus a final estimated digit
1.19 cm
Centimeters 1 2 3 4 5

22. Practice Measuring cm 1 2 3 4 5 4.5 cm cm 1 2 3 4 5 4.54 cm cm 1 2 3 41 2 3 4 5
4.5 cm cm 1 2 3 4 5
4.54 cm
PRACTICE MEASURING
Estimate one digit of uncertainty.
a) 4.5 cm
b) * 4.55 cm
c) 3.0 cm
*4.550 cm is INCORRECT while 4.52 cm or 4.58 cm are CORRECT (although the estimate is poor)
The better marks the better we can estimate.
Scientist always understand that the last number measured is actually an estimate cm 1 2 3 4 5
3.0 cm