1. Chapter 2. Measurement
Chemistry is a physical science, one that depends heavily on measurement to obtain quantitative data.
Measurement is the determination of dimensions, capacity, quantity, or extent of something.

2. Precision, Accuracy, Error

3. Precision, Accuracy, Error
Precision refers to the reproducibility of a given measurement.
Accuracy refers to the agreement between a measurement (or average several measure-ments) to the true or accepted value.
Errors are deviations (differences) between the true value and a measurement. They can be random or systematic.

4. Uncertainty in Measurement
All measurements contain some error, or uncertainty.
Heisenberg's Uncertainty Principle is a natural law that states that the act of observing something changes it. In its mathematical form, it states the limits of accuracy in a measurement.

5. Uncertainty in Measurement
Generally, uncertainty is minimized (accuracy is maximized) by using equipment that is better designed, more expensive, and more demanding to use.
Beaker  1 milliliter $3.00
Cylinder  0.1 milliliter $6.00
Buret  0.01 milliliter $90.00

6. Uncertainty in Measurement

7. Uncertainty in Measurement
Numbers express uncertainty.
Exact numbers contain no uncertainty. They are obtained by counting objects (integers) or are defined, as in some conversion factors.
Inexact numbers contain uncertainty. They are obtained from measurements. The un-certainty in a measurement is shown by the number of digits recorded.

8. Uncertainty in Measurement
Significant figures are the digits in a measure-ment that are known with certainty, plus one digit that is uncertain. Last digit is uncertain.
14.3 gallons  0.1 gal (13 oz)
gallons  gal (¾ tsp)

9. Uncertainty in Measurement
Significant figures allow us to estimate the uncertainty of a value:
10 +/– x 100% = 10% 10
10.0 +/– x 100% = 1%
10.0
/– x 100% = 0.1%
10.00

10. Uncertainty in Measurement
Significant figures and measurements:
With digital instruments (reading is numbers) record all digits from the instrument. The last digit is uncertain and may fluctuate.
With analog instruments (reading is a scale) "read between the lines" for last digit. That digit is an estimate, and contains uncertainty.

11. Working with "Sig Figs"
How many significant figures are there in each of these numbers?
14.3 gallons
gallons
14.0 gallons
0.025 gallons

12. Working with "Sig Figs" In a number from a measurement:
All nonzero digits are significant.
Internal zeroes are significant.
Leading zeroes are not significant.
Trailing zeroes are significant if there
is a decimal point in the number.

13. Working with "Sig Figs" How many significant figures in each number?
1800
1800.

14. Working with "Sig Figs"
Why does this matter? Because we usually do calculations on measurements.
I ride my bike to school. The distance is 4.1 miles. The other day it took minutes. What was my average speed, in miles per minute, and in miles per hour?
4.1 mi = mi
25.7 min min
4.1 mi = mi = 9.6 mi
25.7 min min hr

15. Working with "Sig Figs" Why did I convert 0.1595440793 mi/min to
0.16 mi/min and not something else?
Rules for working with significant figures:
Rounding
Sig figs in calculations

16. Working with "Sig Figs"
Rounding numbers is disposing of nonsig-nificant digits
Only do this in calculations!
Do not round off measurements!

17. Working with "Sig Figs" Rules for rounding:
1. Decide how many digits are significant.
2. Underline them (till you catch on)
3. Look at digit to right of last underlined digit
a. If it's 1  4, drop it.
b. If it's 5  9, add 1 to last sig. fig.

18. Working with "Sig Figs" Examples:
Round the following values to 3 sig. figs.
27.428
39.572

19. Calculating with "Sig Figs"
Rules for Calculations:
1. Multiplication and division:
The result has the same number of sig figs as the value with the fewest sig figs.
4.1 mi = mi
25.7 min min
4.1 mi = mi = 9.6 mi
25.7 min min hr

20. Calculating with "Sig Figs"
Rules for Calculations:
2. Addition and Subtraction:
The result has the same uncertainty as the value with the greatest uncertainty.
Keep digits as far to the right as all values have sig figs. ~

21. Calculating with "Sig Figs"
Examples:
Calculate the quantities, and round to the correct number of significant figures:
15.86 x 2.34  =
– 15.5 =
( – ) =

22. Calculating with "Sig Figs"
Rules for Calculations:
4. Working with exact and inexact numbers:
Exact numbers don't have sig figs because they don’t introduce uncertainty.
Just use sig figs in inexact numbers
0.16 mi x 60 min = 9.6 mi
min hr hr
60 min/hour is an exact conversion

23. Calculating with "Sig Figs"
Rules for Calculations:
5. If your calculator gives you fewer sig figs
than the value should have, add zeroes
0.465 x =
4.389 – =

24. Calculating with "Sig Figs"
Rules for Calculations:
6. If your calculator gives you more digits to
the left of the decimal than are significant,
use scientific notation.
75.3 x 24.8 x 675 =
= 1.26 x 106

25. Scientific Notation
Scientific notation is a numerical system in which a decimal number is expressed as the product of a number between 1 and 10, and 10 raised to a power.
= x 1,000,000
= x 106
= x 106
1.26 is the coefficient
106 is the exponential term

26. Scientific Notation
Scientific notation is useful for expressing very large or very small numbers.
93,000,000 miles from earth to sun
9.3 x 107 miles
grams
3.0 x grams is mass of 1 water molecule

27. Scientific Notation When should scientific notation be used?
1. It MUST be used if you have more digits
than significant digits to the left of the
decimal point.
2. It CAN be used whenever it's convenient.
Often, this involves very small numbers.

28. Summary
It’s easy to keep track of significant figures if you remember WHY you’re doing it.
WHY are you doing it?
Significant figures reflect the accuracy of measured quantities and of results calculated from measured quantities.