1. CH. 2 - MEASUREMENT
I. Using Measurements

2. A. 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

3. Accuracy vs. Precision
Even the most carefully taken measurements are always inexact. This can be a consequence of inaccurately calibrated instruments (rulers, graduated cylinder, human error, or any number of other factors.
Two terms are used to describe the quality of measurements: and
PRECISION
ACCURACY

4. What is ? PRECISION ACCURACY
Precision is a measure of how closely individual measurements agree with one another.
Accuracy refers to how closely individually measured numbers agree with the correct or "true" value.

5. Precision: these measurements agree with one another.
Accuracy: these numbers agree with the correct or "true" value.

6. What is the uncertain digit?
The number 83.4 has three digits. All three digits are significant. The and the are “ digits" while the 4 is the “ digit." As written, this number implies uncertainty of plus or minus 0.1, or error of 1 part in 834. 8 3
certain
estimated

7. 79.85 Most certain number Least certain number
Which number is least certain and an estimate?
Which number is most certain and accurate?
Most certain number
Least certain number

8. B. Percent Error your value accepted value
Indicates accuracy of a measurement
your value
accepted value

9. B. Percent Error % error = 2.9 %
A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL.
% error = 2.9 %

10. C. Significant Figures Indicate precision of a measurement.
Recording Sig Figs
Sig figs in a measurement include the known digits plus a final estimated digit
2.35 cm

11. C. Significant Figures Counting Sig Figs Count all numbers EXCEPT:
Leading zeros
Trailing zeros without a decimal point -- 2,500

12. All non zero numbers are significant
Ex: 96, , 3.21X108
Zeros between non zero digits are significant
101, , X108
Zeros at the end of a number that include a decimal are significant
, , , 3.0X108

13. The Atlantic Pacific Rule
Simplified Sig Figs
The Atlantic Pacific Rule
The “A” in Atlantic represents the absence of a decimal in a number.
The “P” in Pacific represent the presence of a decimal in a number.
Pacific Ocean
Decimal Present
Atlantic Ocean
Decimal Absent

14. Atlantic Pacific Rule
To use this rule we must 1st understand what a “non-zero” digit is.
Digits are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
These digits are used in many combinations to create what we call numbers.
A “non zero” digit is any digit other than 0.
1, 2, 3, 4, 5, 6, 7, 8, 9, these are all “non zero” digits.

15. In the number 12.01 is the decimal present or absent?
So we start from the Pacific side of the U.S.
Then we travel from the Pacific to the Atlantic counting digits along the way. We begin counting digits at the 1st “non-zero” digit, and count it and every digit (even zeros) that follows.
So we count this number and every digit that follows toward the Atlantic.
Is this digit a “non-zero” digit?
yes 1 2. 1
Therefore, the number has 4 significant digits.

16. In the number 1,200 is the decimal present or absent?
So we start from the Atlantic side of the number.
Yes, we count this digit and every digit that follows toward the Pacific.
Is this a “non-zero” digit?
Then we travel from the Atlantic to the Pacific counting digits along the way. We begin counting digits at the 1st “non-zero” digit, and count it and every digit (even zeros) that follows.
Do we count this digit? no
yes 1 2
Therefore, the number 1,200 has only 2 significant digits.

17. Counting Sig Fig Examples
C. Significant Figures
Counting Sig Fig Examples
3. 5,280
3. 5,280

18. C. Significant Figures (13.91g/cm3)(23.3cm3) =
Calculating with Sig Figs
Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer.
(13.91g/cm3)(23.3cm3) =
4 SF
3 SF

19. C. Significant Figures 3.75 mL + 4.1 mL 3.75 mL + 4.1 mL 224 g + 130 g
Calculating with Sig Figs (con’t)
Add/Subtract - The # with the lowest precision (decimal place) determines the place of the last sig fig in the answer.
3.75 mL mL
3.75 mL mL
224 g
+ 130 g
224 g
+ 130 g  

20. C. Significant Figures Calculating with Sig Figs (con’t)
Exact Numbers do not limit the # of sig figs in the answer.
Counting numbers: 12 students
Exact conversions: 1 m = 100 cm
“1” in any conversion: 1 in = 2.54 cm

21. C. Significant Figures Practice Problems 5. (15.30 g) ÷ (6.4 mL) = 
4 SF
2 SF = 
2 SF g g 