Transcript sig figs - MrKanesSciencePage

What are significant figures?
(aka sig figs)
When experimental numbers are
added, subtracted, multiplied and
divided, your answer can have too
few or too many sig figs, depending
on how you round the final answer.
How Rounding Influences Sig Figs


1.024 x 1.2 = 1.2288
Too many numerals
(sig figs)
Too precise
1.024 x 1.2 = 1
Too few numerals
(sig figs)
Not precise enough
Why This Concept is Important




We will be adding, subtracting,
multiplying and dividing numbers
throughout this course.
You MUST learn how many sig figs to
report each answer in or the answer is
meaningless.
Lab Reports: Correct number of sig figs
needed or lose 1 point.
Tests/Quizzes: Correct number of sig figs
+/- 1 needed or lose 1 point.
How Do We Find the Correct Number
of Sig Figs In an Answer?


First, we will learn to count number
of sig figs in a number. You must
learn 4 rules and how to apply
them.
Second, we will learn the process
for rounding when we add/subtract
or multiply/divide. We will then
apply this process in calculations.
Rules for Counting Sig Figs

Rule #1: Read the
number from left
to right and count
all digits, starting
with the first digit
that is not zero.
Do NOT count final
zero’s unless there
is a decimal point
in the number!
3 sig
figs
4 sig
figs
5 sig figs
23.4
234
0.234
2340
203
345.6
3.456
0.03456
34560
3405
678.90
6789.0
0.0067890
67008
60708
Rules for Counting Sig Figs

Rule #2: A final
zero or zero’s can
be designated as
significant if a
decimal point is
added after the
final zero.
3 sig
figs
4 sig
figs
2340
2340.
23400
2000.
234000
2340000
5 sig figs
20000.
23400.
Rules for Counting Sig Figs

Rule #3: If a
number is
expressed in
standard scientific
(exponential)
notation, assume
all the digits in the
scientific notation
are significant.
2 sig
figs
3 sig figs 4 sig
figs
2.3 x 102
2.30 x 102
2.300 x 102
2.0 x 103
2.00 x 103
2.000 x 103
Rules for Counting Sig Figs


Rule #4: Any number which
represents a numerical count or is
an exact definition has an infinite
number of sig figs and is NOT
counted in the calculations.
Examples:



12 inches = 1 foot (exact definition)
1000 mm = 1 m (exact definition)
24 students = 1 class (count)
Practice Counting Sig Figs

How many sig figs in each of the
following?







1.2304 mm
1.23400 cm
1.200 x 105 mL
0.0230 m
0.02 cm
8 ounces = 1 cup
30 cars in the parking lot
Answers to Practice

How many sig figs in each of the
following?
 1.2304 mm (5)
 1.23400 cm (6)
 1.200 x 105 mL (4)
 0.0230 m (3)
 0.02 cm (1)
 8 ounces = 1 cup (infinite, exact def.)
 30 cars in the parking lot (infinite,
count)
General Rounding Rule

When a number is rounded off, the last
digit to be retained is increased by one
only if the following digit is 5 or greater.
EXAMPLE: 5.3546 rounds to
5 (ones place)
5.35 (hundredths place)
5.355 (thousandths place)
5.4 (tenths place)
You will lose points for rounding incorrectly!
Process for Addition/Subtraction


Step #1: Determine the number of
decimal places in each number to
be added/subtracted.
Step #2: Calculate the answer, and
then round the final number to the
least number of decimal places
from Step #1.
Addition/Subtraction Examples
Example #1:
Round to
tenths place.
23.456
+
1.2
+
0.05
-------------24.706
Rounds to:
24.7
Example #2:
Round to
hundredths
place.
3.56
- 0.14
- 1.3501
--------------2.0699
Rounds to:
2.07
Example #3:
Round to ones
place.
14
+
0.735
+ 12.0
-------------26.735
Rounds to:
27
Process for Multiplication/Division


Step #1: Determine the number of
sig figs in each number to be
multiplied/divided.
Step #2: Calculate the answer, and
then round the final number to the
least number of sig figs from
Step #1.
Multiplication/Division Examples
Example #1:
Round to
1 sig fig.
23.456
x
1.2
x
0.05
-------------1.40736
Rounds to:
1
Example #2:
Round to
2 sig figs.
3.56
x 0.14
x 1.3501
--------------0.67288984
Rounds to:
0.67
Example #3:
Round to
3 sig figs.
14.0/
11.73
-------------1.193520887
Rounds to:
1.19
Practice
Example #1:
Example #2:
Example #3:
.
17/
22.73
23.456
x
4.20
x
0.010
-------------Rounds to:
?
0.001
+
1.1
+
0.350
--------------- -------------Rounds to:
Rounds to:
?
?
Answers to Practice
Example #1:
Example #2:
Example #3:
.
17/
22.73
23.456
x
4.20
x
0.010
-------------0.985152
Rounds to:
0.99 (2 sf)
0.001
+
1.1
+
0.350
--------------- -------------1.451
0.747910251
Rounds to:
Rounds to:
1.5 (tenths)
0.75 (2 sf)
Other Rules


If you are using constants which are
not exact, try to select one which
has at least one or more sig figs
that the smallest number of sig figs
in your original data. That way, the
constant will not impact the number
of sig figs in your final answer.
Example: pi = 3.14 (3 sig figs)
= 3.142 (4 sig figs)
= 3.1459 (5 sig figs)
Important Rounding Rule

When you are doing several
calculations, carry out all the
calculations to at LEAST one more
sig fig than you need (I carry all
digits in my calculator memory) and
only round off in the FINAL result.