Measurements and Sig Figs
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Transcript Measurements and Sig Figs
What is the Length?
1
2
3
We can see the markings between 1.6-1.7cm
We can’t see the markings between the .6-.7
We must guess between .6 & .7
We record 1.67 cm as our measurement
The last digit an 7 was our guess...stop there
1
4 cm
Learning Check
What is the length of the wooden stick?
1) 4.5 cm
2) 4.58 cm
3) 4.584 cm
Measurement and Significant Figures
Every experimental measurement
has a degree of uncertainty.
The volume, V, at right is certain in
the 10’s place, 10mL<V<20mL
The 1’s digit is also certain,
17mL<V<18mL
A best guess is needed for the
tenths place.
Chapter Two
3
Scientific Notation
Find your Notecard Partner.
Why would we use scientific
notation?
SCIENTIFIC NOTATION
A QUICK WAY TO
WRITE
REALLY, REALLY
OR
REALLY, REALLY SMALL
BIG
NUMBERS.
Scientific Notation
# from 1 to 9.999 x 10exponent
800 = 8 x 10 x 10
= 8 x 102
2531 = 2.531 x 10 x 10 x 10
= 2.531 x 103
0.0014 = 1.4 ÷ 10 ÷ 10 ÷ 10
= 1.4 x 10-3
Rules for Scientific Notation
To be in proper scientific
notation the number must be
written with
* a number between 1 and 10
* and multiplied by a power of
ten
23 X 105 is not in proper
scientific notation. Why?
Change to standard form.
1.87 x 10–5 = 0.0000187
3.7 x 108 = 370,000,000
7.88 x 101 =
78.8
2.164 x 10–2 = 0.02164
Change to scientific notation.
12,340 = 1.234 x 104
0.369 = 3.69 x 10–1
0.008 = 8 x 10–3
3
1.000
x
10
1,000. =
The International System of Units
Quantity
Name
Length
Mass
Time
Amount of substance
Temperature
Electric current
Luminous intensity
meter
kilogram
second
mole
Kelvin
amperes
candela
Dorin, Demmin, Gabel, Chemistry The Study of Matter , 3rd Edition, 1990, page 16
Symbol
m
kg
s
mol
K
amps
cd
SI
The International System of Units
Derived Units Commonly Used in Chemistry
System
Map of the world where red represents countries
which do not use the metric system
NEED TO KNOW Prefixes in the SI System
Power of 10 for
Prefix
Symbol
Meaning
Scientific Notation
_________________________________________________________
1,000,000
106
k
1,000
103
deci-
d
0.1
10-1
centi-
c
0.01
10-2
milli-
m
0.001
10-3
micro-
m
0.000001
10-6
nano-
n
0.000000001
10-9
pico-
p
0.000000000001 10-12
mega-
M
kilo-
Significant figures
Method used to express accuracy and
precision.
You can’t report numbers better than
the method used to measure them.
67.20 cm = four
??? significant figures
Certain
Digits
Uncertain
Digit
Significant figures
The number of significant
digits is independent of
the decimal point.
255
31.7
These numbers
All have three
5.60
significant figures!
0.934
0.0150
Rules for Counting Significant figures
Every non-zero digit is
ALWAYS significant!
Zeros are what will give
you a headache!
They are used/misused all
of the time.
SEE p.24 in your book!
Rules for zeros
Leading zeros are not significant.
0.421 - ???
three significant figures
Leading zero
Captive zeros are always significant!
Captive zeros
4,008 -???
four significant figures
Trailing zeros are significant …
IF there’s a decimal point in the number!
114.20 -???
five significant figures
Trailing zero
Examples
250 mg
\__ 2 significant figures
120. miles
\__ 3 significant figures
0.00230 kg
\__ 3 significant figures
23,600.01 s
\__ 7 significant figures
Significant figures:
Rules for zeros
Scientific notation - can be used to clearly
express significant figures.
A properly written number in scientific
notation always has the proper number of
significant figures.
0.00321
=
3.21 x 10-3
Three Significant
Figures
Significant figures and calculations
An answer can’t have more
significant figures than the
quantities used to produce it.
Example
How fast did you run if you
went 1.0 km in 3.0 minutes?
speed
= 1.0 km
3.0 min
= 0.33 km
min
0.333333
cos tan
CE
ln
7 8 9
/
log
4 5 6
x
1/x
1 2 3
-
.
+
x2 EE
0
Significant figures and calculations
Multiplication and division.
Your answer should have the same
number of sig figs as the original
number with the smallest number of
significant figures.
ONLY 3 SIG FIGS!
21.4 cm x 3.095768 cm = 66.2 cm2
135 km ÷ 2.0 hr = 68 km/hr
ONLY 2 SIG FIGS!
Significant figures and calculations
Addition and subtraction
Your answer should have the same
number of digits to the right of the
decimal point as the number having
the fewest to start with.
123.45987 g
+ 234.11 g
357.57 g
805.4 g
- 721.67912 g
83.7 g
Rounding off numbers
After calculations, you may need to
round off.
If the first insignificant digit is 5 or
more, you round up
If the first insignificant digit is 4 or
less, you round down.
Examples of rounding off
If a set of calculations gave you the
following numbers and you knew
each was supposed to have four
significant figures then 2.5795035 becomes 2.580
1st insignificant digit
34.204221 becomes 34.20
Examples of Rounding
For example you want a 4 Sig Fig number
0 is dropped, it is <5
4965.03
4965
780,582
780,600 8 is dropped, it is >5; Note you
must include the 0’s
1999.5
2000.
5 is dropped it is = 5; note you
need a 4 Sig Fig
Multiplication and division
32.27 1.54 = 49.6958
49.7
3.68 .07925 = 46.4353312
46.4
1.750 .0342000 = 0.05985
.05985
3.2650106 4.858 = 1.586137 107 1.586 107
6.0221023 1.66110-24 = 1.000000 1.000