Bio/Chem
Chemistry
Chapter 2
Scientific Measurements & Calculations
I
Importance of Measurement
A. Qualitative – give results in a descriptive nonnumeric form
B. Quantitative – give results in a definite form, usually numeric
II
Accuracy & Precision
A. Accuracy – how close a single measurement comes to a true value (correct) (depends on
the quality of the tool)
B. Precision – how close several measurements are to the same value (reproducible) (depends
on the skill of the person using the tool)
III
Measurement
A. Scientific Notation - a number is written as the product of two numbers: a coefficient and a
power of 10
1. Form C x 10n
a. C is a number between 1 & 10
b. n is a positive or negative #
2. To write numbers in scientific notation:
a. determine “C” by moving the decimal
b. count the number of places that you move the decimal, this is “n”
c. if the decimal moves to the left, then n is positive
d. if the decimal moves to the right, then “n” is negative
Ex. 15,000,000.00  1.5 x 107
IV
Significant figures in a measurement include all the digits that are known and one
last one that is estimated
A. Rules:
1. all nonzero (1-9) are significant
2. zeros between nonzero digits are significant
3. zeros in front of nonzero digits are not significant
4. zeros at the end of a number and to the right of a decimal point are significant
** 5. zeros at the end of a measurement and to the left of the decimal are not significant
if they are just place markers. IF they are measured values, then they are
significant.
Ex.
25.5
467
202
202.00
0.0202
500
500.
3 sig. fig
3 sig. fig
3 sig. fig.
5 sig.fig.
3 sig. fig.
1 sig.fig
3 sig.fig.
rule 1
rule 1
rule 2
rule 2 &4
rule 3
rule 5
rule 5
*** To avoid problems, write the measurements in scientific notation.
*** Direct counting & Defined measurements have unlimited sig. fig.
V
Significant Figures in Calculations
A. An answer cannot be more precise than the lease precise measurement from which
it was calculated.
*** Calculators do not use Significant Figures or round correctly.***
B. Addition & Subtraction – the answer should be rounded to have the same number of
decimal places as the measurement with the least number of decimal places.
Ex.
1.
12.52m + 349.0 m + 8.24m =
12.52 m
349.0
+
8.24
369.76 m  369.8m 3.698 x 102m
2.
4.626m - 28.34m =
74.626m
- 28.34
__________________
46.286 m  46.29m  4.629 x 102m
C. Multiplication & Division - the answer is rounded to the number of significant figures in
the least precise term used in the calculation.
Ex.
1.
2.
7.55m x 0.34m = 2.567m2
3 sf
2 sf
 2.6m2
2.456m
4sf
/
 2.6 x 100m2
8.4 = .2919761905
2sf  .29
*** The position of the decimal is important when rounding the answer of an addition or
substraction problem. It has nothing to do with rounding in multiplication or
division.
VI
International Units – 1960 revision of metrics
VII
Units of Length – meter (m)
VIII Unit of Volume –
A. Solid – cm3 = cubic meter
B. Liquid – L = liter
IX
Units of Mass
A. Kilogram (kg) was originally defined as the mass of 1L of H2O @ 4° C
B. Gram (g) is more commonly used
*** Metric Prefixes
Kilo
(k)
1000
Hecto
(h)
100
Deca
(da)
10
Basic
Units
Deci
(d)
.1
Centi
(c)
.01
m
l
g
Measuring Density – the ratio of a substances mass to its volume
X
A. Formula:
d = m/d
d = density (g/cm3)
m = mass (g )
v = volume (cm3 or ml)
B. Density usually decreases with an increase in temperature.
H2O is an important exception.
XI
Specific Gravity – the comparison of a substances density to a reference
substance. ( Usually H2O )
Specific Gravity = d of substance g/cm3
d of H2O
g/cm3
Density of H2O = 1.0 g/cm3
Milli
(m)
.001
XII
Measuring Temperature
A. Temperature is the measure of the average kinetic energy (E) of the molecules of an
object ( degree hot/cold)
1. Most substances expand with an increase of temperature
2. H2O is an important exception
B. Scales:
1. Celsius – uses the freezing and boiling point of H2O as reference points
2. Kelvin – SI unit of temperature; the zero value is given to the lowest possible
Temperature theoretically achievable called absolute zero.
C. Formulas:
1. To convert °F  °C use:
°C = (°F – 32) / 1.8
2. To convert °C  °F use :
°F = (°C) (1.8) +32
3. To convert °C  K use:
K = °C + 273
Ex. °C =
XIII
Evaluating Measurements:
A. Accepted Value – true/correct
- based on reliable references
B. Experimental Value – measured value obtained in the lab
C. Error – the difference between the accepted and the experimental
Error = Accepted – Experimental
D. Percent Error
% Error = error
accepted
value
x 100
*** Error can be positive (+) or negative (-)
*** % Error the absolute value is used
(% Error will always be POSITIVE !!!)
XIV
Dimensional Analysis (Chapter 3)
(Factor-Label Method)
Steps:
1. Write the given measurement as a fraction over 1.
2. Set up the conversion factor (s)
a.
b.
c.
d.
Place the given unit as the denominator.
Place the desired unit as the numerator.
Cancel the units.
Solve the problem.
Ex. How many minutes has a 16.5 yr. old been alive?
(16.5 yrs) (365 days) (24 hrs) (60 min)
(1)
(1)
(1)
(1)
= 8,672,400 min