1. Measurement in Scientific Study and Uncertainty in Measurement
Lecture #3
Measurement in Scientific Study and Uncertainty in Measurement
Chemistry 142 B
James B. Callis, Instructor
Autumn Quarter, 2004

4. Precision and Accuracy Errors in Scientific Measurements
Precision - Refers to reproducibility or how close the
measurements are to each other.
Accuracy - Refers to how close a measurement is to the
‘true’ value.
Systematic Error - produces values that are either all higher
or all lower than the actual value.
Random Error - in the absence of systematic error, produces
some values that are higher and some that
are lower than the actual value.

6. Rules for Determining Which Digits Are Significant
All digits are significant, except zeros that are used only to
position the decimal point.
1. Make sure that the measured quantity has a decimal point.
2. Start at the left of the number and move right until you
reach the first nonzero digit.
3. Count that digit and every digit to its right as significant.
Zeros that end a number and lie either after or before the
decimal point are significant; thus mL has four
significant figures, and L has four significant figures
also. Numbers such as 5300 L have 2 sig. figs., but
5.30x103 L has 3. A terminal decimal point is often used to
clarify the situation, but scientific notation is clearer (best).

7. Examples of Significant Digits in Numbers
Number Sig digits Number Sig digits
L x 107 nm six
18.00 g four ng
kg two ,000 L two
L six ,002.3 ng six
g four g four
875,000 oz x 10–6 L
30,000 kg one oz five
m five kg six
lbs seven mL nine
g kg eight
1,470,000 L three ,000,000,000 g

8. Examples of Significant Digits in Numbers
Number Sig digits Number Sig digits
L two x 107 nm six
18.00 g four ng two
kg two ,000 L two
L five ,002.3 ng six
g four g four
875,000 oz three x 10 -6L four
30,000 kg one oz five
m five kg six
23, lbs seven mL nine
g three kg eight
1,470,000 L three ,000,000,000 g one

9. Rules for Significant Figures in answers
1. For multiplication and division. The number with the
least certainty limits the certainty of the result. therefore, the
answer contains the same number of significant figures as
there are in the measurement with the fewest significant
figures. Multiply the following numbers:
9.2 cm x 6.8 cm x cm =
2. For addition and subtraction. The answer has the same
number of decimal places as there are in the measurement
with the fewest decimal places. Example, adding two volumes
83.5 mL mL =
Example subtracting two volumes:
865.9 mL mL =

10. Rules for Significant Figures in answers
1. For multiplication and division. The number with the
least certainty limits the certainty of the result. therefore, the
answer contains the same number of significant figures as
there are in the measurement with the fewest significant
figures. Multiply the following numbers:
9.2 cm x 6.8 cm x cm = cm3 = 23 cm3
2. For addition and subtraction. The answer has the same
number of decimal places as there are in the measurement
with the fewest decimal places. Example, adding two volumes
83.5 mL mL = mL = mL
Example subtracting two volumes:
865.9 mL mL = mL = mL

11. Rules for Rounding Off Numbers
(1) In a series of calculations*, carry the extra digits through to the final result, then round off. **
(2) If the digit to be removed
is less than 5, the preceding digit stays the same. For example, 1.33 rounds to 1.3.
is equal to or greater than 5, the preceding digit is increased by one. For example, 1.36 rounds to 1.4.
(3) When rounding, use only the first number to the right of the last significant figure. Do not round off sequentially. For example, the number when rounded to two significant figures is 4.3, not 4.4.
Notes:
* Your TI-93 calculator has the round function which you can use to get the correct result. Find round by pressing the math key and moving to NUM. Its use is round(num, no of decimal places desired), e.g. round(2.746,1) =2.7.
** Your book will show intermediate results rounded off. Don’t use these rounded results to get the final answer.

12. Rounding Off Numbers – Problems
(3-1a) Round to three significant figures
Ans:
(3-1b) Round to two significant figures
We used the rule: If the digit removed is greater than or equal to 5, the preceding number increases by 1.
(3-2a) Round to three significant figures
(3-2b) Round to two significant figures
We used the rule: If the digit removed is less than 5, the preceding number is unchanged

14. Sample Problem – 3-3
Lithium (Li) is a soft, gray solid that has the lowest density
of any metal. If a slab of Li weighs 1.49 x 103 mg and has
sides that measure 20.9 mm by 11.1 mm by 12.0 mm, what
is the density of Li in g/ cm3 ?
Lengths (mm)
of sides
Mass (mg)
of Li
Lengths (cm)
of sides
Mass (g)
of Li
Volume (cm3)
Density (g/cm3) of Li

15. Sample Problem – 3-3(cont.)
Mass (g) of Li = 1.49 x 103 mg
Length (cm) of one side = 20.9 mm
Similarly, the other side lengths are:
Volume (cm3) =
Density = mass/volume
Density of Li =

17. Problem 3-4: Volume by Displacement
Problem: Calculate the density of an irregularly shaped metal
object that has a mass of g if, when it is placed into a
2.00 liter graduated cylinder containing mL of water,
the final volume of the water in the cylinder is mL ?
Plan: Calculate the volume from the different volume
readings, and calculate the density using the mass that
was given.
Solution:
Volume =
mass
Density =
volume

18. Definitions - Mass & Weight
Mass - The quantity of matter an object contains
kilogram - ( kg ) - the SI base unit of mass, is a
platinum - iridium cylinder kept in
Paris as a standard!
Weight - depends upon an object’s mass and the strength
of the gravitational field pulling on it, i.e.
w = f = ma.

19. Problem 3-5: Computer Chips
Future computers might use memory bits which require an
area of a square with 0.25 mm sides. (a) How many bits could
be put on a 1 in x 1 in computer chip? (b) If each bit required
that 25 % of its area to be coated with a gold film 10 nm thick,
what mass of gold would be needed to make one chip?
Approach:
use Achip =
(b) use r = m/V

20. Solution to Chip Problem (3-7)

21. Solution to Chip Problem (3-7)

24. Temperature Scales and Interconversions
Kelvin ( K ) - The “Absolute temperature scale” begins at
absolute zero and only has positive values.
Celsius ( oC ) - The temperature scale used by science,
formally called centigrade and most
commonly used scale around the world,
water freezes at 0oC, and boils at 100oC.
Fahrenheit ( oF ) - Commonly used scale in America for
our weather reports, water freezes at 32oF,
and boils at 212oF.
T (in K) = T (in oC)
T (in oC) = T (in K)
T (in oF) = 9/5 T (in oC) + 32
T (in oC) = [ T (in oF) - 32 ] 5/9

25. Problem 3-6:Temperature Conversions
(a) The boiling point of Liquid Nitrogen is oC, what is
the temperature in Kelvin and degrees Fahrenheit?
T (in K) = T (in oC)
T (in K) =
T (in oF) = 9/5 T (in oC) + 32
T (in oF) =
(b)The normal body temperature is 98.6oF, what is it in Kelvin
and degrees Celsius?
T (in oC) = [ T (in oF) - 32] 5/9
T (in oC) =
T (in K) = T (in oC)
T (in K) =

26. Answers to Problems in Lecture #3
(a)5.38; (b) 5.4
(a) 0.241; (b) 0.24
0.536 g/cm3
g / mL
31 mg gold
(a) 77.4 K; oF; (b) 37.0 oC; K