Sig Figs
The Saga
• In a galaxy far, far away, a bunch of
students were arguing whether there was
a difference between two measurements.
20.4 cm and 20.40 cm
Reading measuring instruments to
their limit
• You can only be as precise as your measuring
instrument allows you to be.
• Ex.
Other examples:
• How much fluid is in this
graduated cylinder?
(73.0 ml)
What is the temperature?
(38.45 oC)
What are Significant Figures?
(as opposed to significant figurines...)
• Sig figs help us understand how precise
measurements are.
• Using sig figs increases accuracy and
precision.
• Sig figs cut down on error caused by
improper rounding.
HOORAY
FOR
SIG FIGS!!!
So… which digits are significant?
• Rule #1:
– All non-zero digits are significant.
• 24 has two sig figs, 24.1 has 3 sig figs
• Rule #2:
– All zeros bounded by non-zero integers are
significant
• 2004 has four sig figs
• 20.04 also has 4 sig figs
So… which digits are significant?
• Rule #3:
– Zeros placed before other digits (leading zeros)
are not significant
• 0.024 has 2 sig figs
• Rule #4:
– Zeros at the end of a number are significant
ONLY if they come after a decimal point
• 2.40 has three sig figs
• 240 only has 2 sig figs
Practice:
• How many sig figs?
»
»
»
»
»
»
»
»
»
409.25
83
98.207
0.001
4.3 x 102
0.003050
4200
0.9106
0.200
o
o
o
o
o
o
o
o
o
0.050
300 900
5.5 x 102
45.030
35 000
0.00400
16.8090
460 090
150 000 000
Rules for Addition and Subtraction
• In an addition or subtractions,
– answers must be rounded to the same
decimal place (not sig figs) as the least
number of decimal places in any of the
numbers being added or subtracted
– Ex. 2.42 + 14.2 + 0.6642
– Ex. 2.42 + 14.2 + 0.6642
• Step 1 line them up
2.42
14.2
+0.6642
17.2842
• Step 2: round to 3.3, because 0.2 only has
one decimal place
The answer is 17.3
Ex 16.25 + 4.350 + 15.809 = 26.409
becomes
26.41
WHY
Ex 214.4 + 12.0 - 5 = 21.4
becomes
21 WHY
Ex 3-
589.090 + 0.04 + 78.890 = 668.02
becomes
668.02
WHY
Ex 433.2306 + 5.050 + 0.00604 = 38.28664
becomes
38.287
WHY
Rules for Multiplication and Division
• The number of sig figs in the answer should
be the same as in the number with the least
sig figs being multiplied or divided.
– Ex. 7.3 x 1264 = 9227.2
» The answer must only contain 2 sig figs, so we
use scientific notation
»The answer becomes 9.2 x 103
»This answer contains 2 sig figs
Ex 115.0 x 4.515 x 1376 = 931 896
becomes
9.32 x 105 WHY
Ex 2-
0.003 x 0.050 x 0.04 = 0.000006
becomes
0.000006 = 6 x 10-6 WHY
Ex 345.56 x 134.04 x 0.340 = 2076.333216
becomes
2.08 x103
WHY
Ex 434.56 x 14 x 134.020 = 64844.2368
becomes
6.5 x 104
WHY
Adding and multiplying numbers in a
word problem
1- Set up numbers according to the word
problem
2- Solve using order of operations
3- At each step give the answer in sig figs
4- Convert final answer to sig figs
Ex 1.
4.67 + 8.953 + 0.652
765.32 x 8.9
- 4.67 + 8.953 + 0.652 = 14.275
becomes 14.28
- 765.32 x 8.9 = 6811.348
becomes 6.8 x 103
- 14.28/6.8 x 103 = 0.0021
becomes 0.0021 = 2.1x10-3
Ex 2
6.8 + 5.80 x 8.0 x 0.06 - 7.870
0.0800
- 6.8 +(5.80 x 8.0 x 0.06) - 7.870
0.0800
- 6.8 + (2.784) - 7.870 which becomes
0.0800
- 6.8 + 3 – 7.870
0.0800
1.93
which becomes
0.0800
2
0.0800 = 25
becomes
30
why
Exceptions and special
circumstances
• Adding and scientific notation
(5.8 x 102) + 368
4.87 x 105
When adding in using SN, the exponents
must be the same.
You have 2 options to solve the problem.
1- Convert 5.8 x102 to 580 and get rid of
the exponent
580 + 368
2- Convert 368 to the same exponent so it
• Rounding off and keeping a zero as
a significant digit
8253.0569 = 649.847
12.7
In this example you must keep 3 sig figs in
your answer.
When rounding off 649.847 should become
650.
Problem, 650 only has 2 sig figs
Solution: put a – above the zero, this makes
• Having many insignificant zero’s and
addition
When adding the following:136.2 + 2 500
000 + 14.01
We get 2 500 150.21 which should become
2 500 150.
EXCEPT, we have to use sig figs, and the
addition rule says that
we must round to the least precise decimal
place.
Therefore, because 2 500 000 is only
• Converting units
When converting units, sig figs need to be
maintained.
Ex 1- 4.0 cm to m becomes 0.040 not 0.04
Ex 2- 1250 mL becomes 1.25 L not 1.250
Solve the following:
5.3 x 4.2 + 1.50
2.5 + 8.163 x 5.67
(5.3 x 4.2) + 1.50 =
(22.26) + 1.50
=
2.5 + (8.163 x 5.67) 2.5 + (46.28421)
22 + 1.50 = 23.50 becomes
2.5 + 46.3 48.8
24 = 0.4918032 which becomes
48.8
0.49
(6.42 x 105) x (0.45 x 10-3) + 56.5 +
150.03
(6.42 x 105) x (0.45 x 10-3) + 56.5 + 150.03
=
(288.9) + 56.5 + 150.03 =
(2.8 x 102 ) + 56.5 + 150.03 =
280 + 56.5 + 150.03 =
486.53 which becomes
487 which becomes
490
Holy cow, zero’s have become the enemy!!
Your next assignment is hand
in a
2000word essay on the history
and
importance of significant
figures and how
they positively affect our
everyday lives.
PsychWhy would I want to correct
96 essays
on significant figures?????