Which of these measurements do you
consider to be most precise?
a) 21.5 inches
b) 21.501 inches
c) 21.50 inches
d) 21 inches
Scientific Measurement
Chapter 3
I. Significant Figures
A. Which figures “count” in a
calculated answer?
B. The rules are different
for “multiplication and
division” than for “addition
and subtraction”
C. These are the textbook
rules to determine which
figures are significant:
(these apply to multiplication
and division problems)
1. Every nonzero digit in a measurement
is considered significant
2. Zeroes between nonzero digits are
significant
3. Leftmost zeroes appearing in front
of nonzero digits are NOT significant
4. Zeroes at the end of numbers and to
the right of a decimal point are
always significant
5. Zeroes at the rightmost end of a
number that lie to the left of an
understood decimal are NOT
significant
6. Quantities that have been counted
have unlimited significant figures
D. Simplified significant digit rules:
1) Numbers with decimal points:
a) Zeroes in the front of any
number DON’T count
b) Once you start counting, don’t
stop
2) Numbers without decimal points:
- Every digit counts except ending
zeroes
Ex: How many
sig figs in these
numbers:
a)
b)
c)
d)
e)
0.00251
1.0025
2300
0.10000
23.10
1) Numbers with decimal points:
a) Zeroes in the front of any
number DON’T count
b) Once you start counting, don’t
stop
2) Numbers without decimal points:
- Every digit counts except ending
zeroes
How many sig
figs in these
numbers:
a)
b)
c)
d)
e)
2105.0
0.00500
0.008
57.200
59,810
1) Numbers with decimal points:
a) Zeroes in the front of any
number DON’T count
b) Once you start counting, don’t
stop
2) Numbers without decimal points:
- Every digit counts except ending
zeroes
II. Multiplication and Division
A. Calculated answers cannot
have more sig figs than the number
used with the fewest
Ex: 3.22 3 sig figs
x .15
2 sig figs
0.483 = 0.48
0.0025
x 2.12
0.0053
0.0025
x 0.0101
0.000025
1250
x 0.110
138
10.0 = 5.0
2.0
III. Scientific Notation
A. Very large and very small
numbers are more conveniently
written in scientific notation:
Ex:
2,785,000
= 2.785 x 106
0.0000125
= 1.25 x 10-5
Ex: Convert these numbers into
scientific notation:
4
=
9.452
x
10
94,520
0.002000 = 2.000 x 10-3
Ex: Convert these numbers into
regular numbers:
1.25 x 10-2
3.50 x 105
= 0.0125
= 350,000
9
10
6.52 x
4
X 5.2 x 10
3.4 x
14
10
-3
10
2.10 x
-4
9.9 x 10
= 2.1
III. Rules for Addition and Subtraction
A. The number of decimal places in a
calculated answer is limited by the
number used with the fewest
Ex:
3.221
+ .15
3.371
= 3.37
0.0025
+ 2.12
2.12
25.19
- 24.9
0.3
5
6.45 x 10
2
- 6.45 x 10
6.44 x
5
10
IV. The Metric System
A. Specific units are assigned for
various scientific measurements:
1) length = meter
2) volume = liter
3) mass = gram
B. Fractions and multiples of these
units use a prefix to indicate the
amount
C. These prefixes are written
before the liter, meter, gram
words:
Kilo hecta deka
1000
100
10
meter
liter
gram
deci centi milli
0.1
0.01
0.001
Examples using abbreviations:
ml = milliliter
cm = centimeter
kg = kilogram
m = meter