Transcript Significant Figures

Significant
Figures
Chemistry I
Significant Figures
The numbers reported in a
measurement are limited by the
measuring tool
Significant figures in a measurement
include the known digits plus one
estimated digit
Counting Significant Figures
RULE 1. All non-zero digits in a measured
number are significant. Only a zero could
indicate that rounding occurred.
Number of Significant Figures
38.15 cm
5.6 ft
65.6 lb
122.55 m
4
2
___
___
Leading Zeros
RULE 2. Leading zeros in decimal numbers
are NOT significant.
Number of Significant Figures
0.008 mm
1
0.0156 oz
3
0.0042 lb
____
0.000262 mL
____
Sandwiched Zeros
RULE 3. Zeros between nonzero numbers are
significant. (They can not be rounded unless
they are on an end of a number.)
Number of Significant Figures
50.8 mm
3
2001 min
4
0.702 lb
0.00405 m
____
____
Trailing Zeros
RULE 4. Trailing zeros in numbers without
decimals are NOT significant. They are
only serving as place holders.
Number of Significant Figures
25,000 in.
2
200. yr
3
48,600 gal
____
25,005,000 g
____
Learning Check
A. Which answers contain 3 significant
figures?
1)
0.4760
2) 0.00476
3) 4760
B. All the zeros are significant in
1) 0.00307
103
2) 25.300
3) 2.050 x
C. 534,675 rounded to 3 significant figures is
1) 535
105
2) 535,000
3) 5.35 x
Learning Check
In which set(s) do both numbers
contain the same number of
significant figures?
1) 22.0 and 22.00
2) 400.0 and 40
3) 0.000015 and 150,000
Learning Check
State the number of significant figures in
each of the following:
A. 0.030 m
1
2
3
B. 4.050 L
2
3
4
C. 0.0008 g
1
2
4
D. 3.00 m
1
2
3
3
5
E. 2,080,000 bees
7
Significant Numbers in Calculations



A calculated answer cannot be more
precise than the measuring tool.
A calculated answer must match the least
precise measurement.
Significant figures are needed for final
answers from
1) adding or subtracting
2) multiplying or dividing
Adding and Subtracting
The answer has the same number of
decimal places as the measurement with
the fewest decimal places.
25.2
one decimal place
+ 1.34
two decimal places
26.54
answer 26.5 one decimal place
Learning Check
In each calculation, round the answer to
the correct number of significant figures.
A. 235.05 + 19.6 + 2.1 =
1) 256.75
2) 256.8
3) 257
B.
58.925 - 18.2 =
1) 40.725
2) 40.73
3) 40.7
Multiplying and Dividing
Round (or add zeros) to the
calculated answer until you have the
same number of significant figures
as the measurement with the fewest
significant figures.
Learning Check
A.
2.19 X 4.2 =
1) 9
3) 9.198
B.
4.311 ÷ 0.07 =
1) 61.58
2) 62
C.
2.54 X 0.0028
0.0105 X 0.060
1) 11.3
2) 11
2) 9.2
3)
60
=
3) 0.041
Reading a Meterstick
. l2. . . . I . . . . I3 . . . .I . . . . I4. .
First digit (known)
=2
Second digit (known)
cm
cm
2.?? cm
= 0.7
2.7?
Third digit (estimated) between 0.05- 0.07
Length reported
=
2.75 cm
or
2.74 cm
or
2.76 cm
Known + Estimated Digits
In 2.76 cm…
• Known digits 2 and 7 are 100%
certain
• The third digit 6 is estimated
(uncertain)
• In the reported length, all three digits
(2.76 cm) are significant including the
estimated one
Learning Check
. l8. . . . I . . . . I9. . . .I . . . . I10. .
cm
What is the length of the line?
1)
9.6 cm
2)
9.62 cm
3)
9.63 cm
How does your answer compare with your
neighbor’s answer? Why or why not?
Zero as a Measured Number
. l3. . . . I . . . . I4 . . . . I . . . . I5. .
cm
What is the length of the line?
First digit
5.?? cm
Second digit
5.0? cm
Last (estimated) digit is
5.00 cm
What is a significant figure?
There
are 2 kinds of
numbers:
Exact: the amount of
money in your
account. Known with
certainty.
What is a significant figure?
Approximate:
weight,
height—anything
MEASURED. No
measurement is
perfect.
When to use Significant figures
When
a
measurement is
recorded only those
digits that are
dependable are
written down.
When to use Significant figures
When
a
measurement is
recorded only those
digits that are
dependable are
written down.
When to use Significant figures
If
you measured the
width of a paper with
your ruler you might
record 21.7cm.
To a mathematician
21.70, or 21.700 is
the same.
But, to a scientist 21.7cm and
21.70cm is NOT the same
21.700cm
to a
scientist means the
measurement is
accurate to within
one thousandth of a
cm.
But, to a scientist 21.7cm and
21.70cm is NOT the same
If
you used an
ordinary ruler, the
smallest marking is
the mm, so your
measurement has to
be recorded as
21.7cm.
How do I know how many Sig Figs?
 Rule:
All digits are
significant starting with the
first non-zero digit on the
left.
 Ex:
7.5 or 0.5
 Ex:
0.05 OR 00.05 OR 000.05
 You
can have as many
decimals as you want on
the left of the decimal
How do I know how many Sig Figs?
Exception
to rule: In
whole numbers that
end in zero, the
zeros at the end are
not significant.
How many sig figs?
7
1
40
1
0.5
1
0.00003
1
7
5
10
x
7,000,000
1
1
How do I know how many Sig Figs?
nd
2
Exception to
rule: If zeros are
sandwiched between
non-zero digits, the
zeros become
significant.
How do I know how many Sig Figs?
3rd
Exception to
rule: If zeros are at
the end of a number
that has a decimal,
the zeros are
significant.
How do I know how many Sig Figs?
3rd
Exception to
rule: These zeros are
showing how
accurate the
measurement or
calculation are.
How many sig figs here?
 1.2
2
 2100
2
 56.76
4
 4.00
3
 0.0792
3
 7,083,000,00
4
0
How many sig figs here?
 3401
4
 2100
2
 2100.0
5
 5.00
3
 0.00412
3
 8,000,050,00
6
0
What about calculations with
sig figs?
Rule:
When adding or
subtracting measured
numbers, the answer
can have no more places
after the decimal than
the LEAST of the
measured numbers.
Add/Subtract examples
 2.45cm
+ 1.2cm = 3.65cm,
 Round off to
= 3.7cm
 7.432cm
+ 2cm = 9.432
round to
 9cm
Multiplication and Division
Rule: When
multiplying or
dividing, the result
can have no more
significant figures
than the least
reliable
measurement.
A couple of examples
56.78
cm x 2.45cm =
139.111 cm2
Round to

139cm2
75.8cm
x 9.6cm = ?
The End
Have Fun Measuring
and Happy
Calculating!