Transcript Slide 1

What is the density of a solid that has a mass
of 60.27 g and a volume of 711 mL?
D = M/V = 0.084767932 g/mL
How do we know how to express (where to
round off) this answer?
Significant (Measured) Digits in Calculatio
All nonzero digits are significant.
Evaluating Zero as a Significant Digit
A zero is significant when it is :
1. Between nonzero digits:
205 61.09
2. At the end of a number that includes a
decimal point:
0.500 25.160
3.00
20.
A zero is not significant when it is :
1. Before the first nonzero digit. (These
zeros are used to locate a decimal point.)
0.0025
0.0108
2. At the end of a number without a
1000 590
decimal point:
Practice Problem
How many significant figures are in each of
these numbers?
a)
b)
c)
d)
4.5 inches 2
3.025 feet 4
125.0 meters 4
0.001 mile 1
e) 25.0 grams
3
f) 12.20 liters 4
g) 100,000 people 1
h) 205 birds 3
Rounding Off Numbers
Look at the next digit
(after those you want to retain for the proper number of significant digits
If it is 5 or greater → round up.
If it is 4 or less → round down.
Practice Problem
Round off these numbers to the number of
significant figures indicated:
a)
b)
c)
d)
e)
f)
42.246 (four)
88.015 (three)
0.08965 (three)
0.08965 (two)
225.3 (three)
14.150 (three)
42.25
88.0
0.0897
0.090
225
14.2
Multiplication or Division
Round off your answer to be no more than th
fewest number of significant digits.
Practice Problem
a) (134 in.)(25 in.) = ?
b) 213 miles
4.20 hours = ?
c) (2.2)(273)
760
=?
3400 in2
Limited to 2 sigs
50.7 mi/hr
Limited to 3 sigs
.79
Limited to 2 sigs
Addition or Subtraction
Round off the answer to no more than the
fewest number of places to the right of the
decimal.
(i.e greatest level of shared confidence)
Practice Problem
How many significant figures should the
answer in each of these calculations contain
a) (14.0)(5.2)
2 sigs
= 73
b) (.1682)(8.2)
2 sigs
= 1.4
c) (160)(33)
4
d) 8.2 + 0.125
1 sig
= 1000
2 sigs - tenths
0.125
8.2
= 8.3
How many significant figures should the
answer in each of these calculations contain
e) 119.1 – 3.44
4 sigs - tenths= 115.7
f) 94.5
1.2
2 sigs = 79
= 1200
g) 1200 + 6.34 2 sigs - hundreds
h) 1.6 + 23 – 0.005 2 sigs - singles= 25