Significant Figures
Uncertainty



We do not know infinite digits of a measurement
Exact numbers are known for sure
Inexact – have some question (estimates)
Precision and Accuracy
Accuracy refers to the agreement of a
particular value with the true value.
Precision refers to the degree of agreement
among several measurements made in the same
manner.
Neither
accurate nor
precise
Precise but not
accurate
Precise AND
accurate
Reporting Numbers




In recorded numbers, all the digits are
considered exact up until the last digit which
may be off by one
2.2405 ± .0001
All digits including the uncertain one are called
significant figures
We are fairly confident of these digits
Further uncertainty can be eliminated by
repeating the experiment
Which Digits Are Significant?




Any non-zero number is significant
Any number to the left of a decimal is
significant
Zeros to the right of a decimal and behind
other numbers are significant
Zeros to the right of a decimal but in front
of other numbers are not significant
How many Significant Figures in
each below?
1)
2)
3)
4)
5)
6)
7)
8)
28.6
910
0.0076000
0.0144030
400
700.0
0.4004
1.30
3440.
10) 0.04604
11) 804.05
12) 1002
13) 400.
14) 0.000625000
15) 6000
16) 0.00067
9)
Round each to 3 Significant
Figures
1)
2)
3)
4)
5)
31.068
2.613
81.436
0.001567
1.1353
149.51
7) 6.561
8) 13.1252
9) 143.81
10) 0.000355
6)
Multiplying and Dividing

Multiply or divide the number out as
normal but round the answer to the least
number of significant figures in the
problem
Solve each with correct Sig Figs
1)
2)
3)
4)
5)
6)
2.4 x 15.82 =
94.20  3.16722 =
0.8102 x 3.44 =
25.75  0.00045 =
(5.682 x 105) x (2.87 x 104) =
(2.145 x 10-5)  (6.75 x 104) =
Addition and Subtraction

Add or subtract as normal but round the
answer with the same number of decimal
places as the quantity in the calculation
having the least
Solve each with correct Sig Figs
1)
2)
3)
4)
5)
6)
7)
5.44 – 2.6103
2.099 + 0.05681
87.3 – 1.655
6.078 + 0.3329
8.2 – 7.11
4.6521 + 183.2 + 240
0.004375 – 0.0036
Conversions


Often the units must be changed in order
to do a problem
Conversion factor method Is utilized
Examples

How many inches in 3.5 km?

A chemical reaction produces 3.5 x 1025
atoms of product every second. How
many will be produced in 2.5 hours?

How many square cm in a square inch?