1. Standards for Measurement

2. Accuracy & Precision Precision:
How closely individual measurements compare with each other
The “fineness” of a measurement
Accuracy: how closely individual measurements compare with the true or accepted value

3. Precise! (but not accurate)
Accurate or Precise?
What is the temperature at which water boils?
Measurements: 95.0°C, 95.1°C, 95.3°C
True value: 100°C
Precise!
(but not accurate)

4. (it’s hard to be accurate without being precise)
Accurate or Precise?
What is the temperature at which water freezes?
Measurements: 1.0°C, 1.2°C, -5.0°C
True value: 0.0°C
Accurate!
(it’s hard to be accurate without being precise)

5. Not Accurate & Not Precise (don’t quit your day job)
Accurate or Precise?
What is the atmospheric pressure at sea level?
Measurements: atm, 0.25 atm, atm
True value: 1.00 atm
Not Accurate & Not Precise
(don’t quit your day job)

6. Accurate or Precise? Accurate & Precise (it’s time to go pro)
What is the mass of one Liter of water?
Measurements: kg, kg, kg
True value: kg
Accurate & Precise
(it’s time to go pro)

7. 2.2: Significant Figures
Every measurement has some degree of uncertainty.
Significant figures (“sig figs”): the digits in a measurement that are reliable (or precise). The greater the number of sig figs, the more precise that measurement is.
A more precise instrument will give more sig figs in its measurements.

8. Uncertainty examples:
To measure the time for a pencil to fall…compare a stopwatch and a wall clock.
To measure the volume of a liquid…compare a graduated cylinder and a beaker.
The stopwatch & graduated cylinder are more precise instruments…so the readings they produce will have more sig figs.

9. 41.2 mL (3 sig figs = very precise)
A graduated cylinder:
41.2 mL (3 sig figs = very precise)
41.0
50 mL Graduated cylinder
100 mL Beaker
A beaker:
40. mL (2 sig figs = not as precise) 50

10. When are digits “significant”?
The “Atlantic-Pacific” Rule
“PACIFIC”
Decimal point is PRESENT. Count digits from left side, starting with the first nonzero digit.
ft2
= 7 sig figs
PACIFIC
PACIFIC mL
= 4 sig figs

11. When are digits “significant”?
“ATLANTIC”
Decimal point is ABSENT. Count digits from right side, starting with the first nonzero digit.
3 sig figs =
40600 ft2
ATLANTIC
1 sig fig =
1000 mL
ATLANTIC

12. Examples
Decimal point present → “Pacific” → count digits from left, starting with first nonzero digit
= 3 sig figs
4035
Decimal point absent → “Atlantic” → count digits from right, starting with first nonzero digit
= 4 sig figs
27510

13. 2.4: Scientific Notation “Writing a number as a power of 10.”
Why? It makes very large and very small numbers more manageable to write and use.
Rule of thumb: Use when number is greater than 100 or smaller than Or, you may always use it!
The number of sig figs are clearly shown in a measurement.

14. 2.4: Scientific Notation How important is a change in the power of 10?
Diameter of Earth’s orbit around the sun
≈ 100,000,000,000 m = 1.0*1011 m
Diameter of an atom
≈ = 1.0*10-10 m

15. Writing in scientific notation
Move the decimal point in the original number so that it is located to the right of the first nonzero digit.
Multiply the new number by 10 raised to the proper power that is equal to the number of places the decimal moved.
If the decimal point moves:
To the left, the power of 10 is positive.
To the right, the power of 10 is negative.

16. Write the following measurements in scientific notation, then record the number of sig figs.
96,875 mL J
8.915 atm
0.94°C
3 sig figs
7.89*102 g
5 sig figs
9.6875*104 mL
1.33*10-5 J
3 sig figs
4 sig figs
8.915 atm
2 sig figs
9.4*10-1 °C

17. Requirements for this class:
Write answers using 3 significant figures
Use scientific notation for all numbers greater than 1000 and smaller than 0.001

18. Accuracy or Precision?
When deciding on accuracy, precision, both, or neither….it is quantitative data (numerical), not qualitative (descriptive)
The recipe calls for 25 chocolate chips per cookie. The cookies analyzed have 34, 35, and 32 respectively.
The percent NaCl is 99%, 99%, and 98%.
The number of grams of KF required is 0.04 g. The amounts used were 0.038, 0.039, 0.041, and
To win, Henry must earn 500 points. In his three trials, he earned 400, 480, and 395 points.

19. Rounding
Look at digit following specified rounding value. If it is 5 or greater, then round up. If not, truncate (cut off the rest of the numbers).
Round to the nearest tenth
6.7512
6.7777
6.7499
6.9521
6.8
6.7
7.0

20. Practice Problems
18. Round each of the following numbers to three significant figures:
8.8726
21.25
1.995 x 106
Write each of the following numbers in exponential (scientific) notation:
0.0456
4082.2
40.30
12,000,000
State the abbreviation for each of the following units:
milligram
kilogram
meter
nanometer
angstrom
microliter
State the number of significant figures in each of the following numbers:
40.0
0.081
129,042
4.090 x 10-3 mg kg m nm A
8.87
21.3
130. or 1.30 x 102
2.00 x 106 L 3 2 6 4
4.56 x 10-2
4.08 x 103
4.03 x 101
1.20 x 107