Download Give the Number of Significant Figures

SI Units
• The worldwide scientific community and most countries
currently use an adaptation of the metric system to state
measurements. The Système International d’Unités, or SI, uses
seven base quantities, which are below.
DERIVED UNITS
Defined by a combination of base units
• Volume: ml = cm3
• Density: g/ml
• Molar Mass: g/mol
PREFIXES USED WITH SI UNITS
king henry died
by drinking chocolate milk
Equivalents
For Conversions
−3
10
Kilo 10−2
−1
1000 Hecto
10
units
100 Deka
1
units
10
10
Basic
2
units
Unit Deci
3
0.1 Centi
units 0.01 Milli
units 0.001
1
10
10
units
Prefixes used with SI Units
Dimensional Analysis
(AKA Factor Label)
 Dimensional analysis is used in choosing
conversion factors. A conversion factor is a
multiplier equal to 1.
For example, because 1 kg = 1000 g, you can
construct the following conversion factors:
Conversion Factor Label
Practice!
1. Convert 12 L into milliliters:
1𝑚𝑙
12𝐿 −3 = 12000𝑚𝑙
10 𝐿
OR move the decimal 3 places to the right.
2. Convert 132 cg into kg:
10−3 𝑘𝑔
132𝑐𝑔 2 =0.00132
10 𝑐𝑔
kg
OR move the decimal 5 places to the left.
More Conversion Factor Label
Practice!
3. Convert 1201 seconds into hours:
1𝑚𝑖𝑛
1ℎ
1201𝑠
𝑥
60𝑠
60𝑚𝑖𝑛
= 0.3336h
4. Convert 17.3 g/mL to Kg/L
𝑔
10−3 𝑘𝑔 103 𝑚𝑙
17.3 𝑥
𝑥
=17.3
𝑚𝑙
1𝑔
1𝐿
kg/L
Significant Figures (Digits)
•
The numbers in measurements are
limited by the measuring tool.
•
Significant figures in a measurement
include the known digits plus one
estimated digit.
1. What is the 1st measurement?
1.42 cm
2. What is the 2nd measurement?
2.7 cm
Counting Significant Figures
•
RULE 1. All non-zero digits in a measured
number are significant. Only a zero could
indicate that rounding occurred.
Give the Number of Significant Figures
a. 38.15 cm
4
b. 5.6 ft
2
c.
65.6 lb
___
d. 122.55 m
___
Leading Zeros
RULE 2. Leading zeros in decimal numbers
are NOT significant.
Give the Number of Significant Figures
a. 0.008 mm
1
b. 0.0156 oz
3
c.
0.0042 lb
__
d. 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.)
Give the Number of Significant Figures
a. 50.8 mm
3
b. 2001 min
4
c.
0.702 lb
__
d. 0.00405 m
__
Trailing Zeros
RULE 4. Trailing zeros in numbers without
decimals are NOT significant. They are only
serving as place holders.
Give the Number of Significant Figures
a. 25,000 in.
2
b. 200. yr
3
c. 48,600 gal
__
d. 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
2) 25.300
3) 2.050 x 103
C. 534,675 rounded to 3 significant figures is
1) 535
2) 535,000
3) 5.35 x 105
Learning Check
In which set(s) do both numbers
contain the same number of
significant figures?
A. 400.0 and 40
B. 0.000015 and 150,000
C. 22.0 and 22.00
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
E. 2,080,000 bees
3
5
7
How many sig figs in the following
measurements?
1)
2)
3)
4)
5)
6)
7)
24689
1.00411
0.000062
8.01
23,000,000
2.30 x 107
2.000
Ans.1) 5 2) 6 3) 2 4) 3 5) 2 6) 3 7)4
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
B.
2) 256.8
58.925 - 18.2
1) 40.725
3) 257
=
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
2) 9.2
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
3) 9.198
3) 60
3) 0.041
Reading a Meterstick
•
. l2. . . . I . . . . I3 . . . .I . . . . I4. .
cm
First digit (known) = 2.?? cm
Second digit (known)
= 0.7
2.7? cm
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. .
What is the length of the line?
1) 9.6 cm
2) 9.62 cm
3) 9.69 cm
cm
Zero as a Measured Number
• . l3. . . . I . . . . I4 . . . . I . . . . I5. .
What is the length of the line?
First digit
Second digit
Last (estimated) digit is
cm
5.?? cm
5.0? cm
5.00 cm