Post on 02-Feb-2021
DIFFERENTIATE:
ACCURACY AND
PRECISION
Three targets with three arrows each to shoot.
Can you hit the bull's-eye?
Both accurate and precise
Precise but not accurate
Neither accurate nor precise
How do they compare?
Can you define accuracy and precision?What would a bullseye with accuracy and no precision look like?
Significant Figures
What is a significant figure?• There are 2 kinds of numbers:
APPROXIMATE (OR MEASURED): weight, height, mass, distance—anything MEASURED needs significance attached.
No measurement is perfect.
EXACT (counted items and conversion factors have unlimited significant digits): the amount of money in your account, jelly beans in a jar, etc. And #m in a km or in in a ft
Reading a Meterstick
. l2. . . . I . . . . I3 . . . .I . . . . I4. . cm
First digit (known) = 2 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
When to use Significant figures
To a mathematician 21.70, or 21.700 is the same.
But, to a scientist
21.7cm and 21.70cm
is NOT the same
When to use Significant figures
•When a measurement is recorded only those digits that are dependable are written down.
Always estimate ONE place past the smallest mark!
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
Enter question text...
1 2 3
0% 0%0%
. 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?
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 4
5.6 m 2
65.6 kg ___
122.55 m ___
How many sig figs in 65.8 kg
1 2 3 4 5
0% 0% 0%0%0%
1. 1
2. 2
3. 3
4. 4
5. 5
How many sig figs in 122.55 m
1 2 3 4 5
0% 0% 0%0%0%
1. 1
2. 2
3. 3
4. 4
5. 5
Leading Zeros
RULE 2. Leading zeros in decimal numbers are
NOT significant.
Number of Significant Figures
0.008 mm 1
0.0156 mg 3
0.0042 kg ____
0.000262 mL ____
How many sig figs in 0.0042 kg
1 2 3 4 5
0% 0% 0%0%0%
1. 1
2. 2
3. 3
4. 4
5. 5
How many sig figs in 0.000262 mL
1 2 3 4 5
0% 0% 0%0%0%
1. 1
2. 2
3. 3
4. 4
5. 5
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 kg ____
0.00405 m ____
How many sig figs in 0.702 kg
1 2 3 4 5
0% 0% 0%0%0%
1. 1
2. 2
3. 3
4. 4
5. 5
How many sig figs in 0.00405 m
1 2 3 4 5
0% 0% 0%0%0%
1. 1
2. 2
3. 3
4. 4
5. 5
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 cm 2
200. yr 3
48,600 L ____
25,005,000 g ____
How many sig figs in 48,600 L
1 2 3 4 5
0% 0% 0%0%0%
1. 1
2. 2
3. 3
4. 4
5. 5
How many sig figs in 48,600. L
1 2 3 4 5
0% 0% 0%0%0%
1. 1
2. 2
3. 3
4. 4
5. 5
How many sig figs in 25,005,000 g
1 2 3 4 5
0% 0% 0%0%0%
1. 1
2. 2
3. 3
4. 4
5. 5
Which answers contain 3
significant figures?
) 0
.476
0
) 0
.004
706
) 4
760
0% 0%0%
1. ) 0.4760
2. ) 0.004706
3. ) 4760
All the zeros are significant in
.003
7
2530
0
2.
050
x 10.
..
0% 0%0%
1. .00370
2. 25,300
3. 2.050 x 103
534,675 rounded to 3 significant figures is
535
5350
00
5.3
5 x 1
05
0% 0%0%
1. 535
2. 535,000
3. 5.35 x 105
In which set(s) do both numbers contain the same number of
significant figures?
22.
0 an
d 22
.0...
400
.0 a
nd 4
0
0.0
0001
5 and
1...
0% 0%0%
1. 22.0 and 22.00
2. 400.0 and 40
3. 0.000015 and 150,000
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 2) 9.2 3) 9.198
B. 4.311 ÷ 0.07 =1) 61.58 2) 62 3) 60
C. 2.54 X 0.0028 =
0.0105 X 0.060
1) 11.3 2) 11 3) 0.041
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
Learning Check
How many sig figs?
•7
•40
•0.5
•0.00003
•7 x 105
•7,000,000
•1
•1
•1
•1
•1
•1
How many sig figs here?
• 1.2
• 2100
• 56.76
• 4.00
• 0.0792
• 7,083,000,000
• 2
• 2
• 4
• 3
• 3
• 4
How many sig figs here?
• 3401
• 2100
• 2100.0
• 5.00
• 0.00412
• 8,000,050,000
• 4
• 2
• 5
• 3
• 3
• 6
Sig Figs?? 640
1 2 3 4 5 6
0% 0% 0%0%0%0%
a) 1
b) 2
c) 3
d) 4
e) 5
f) 6
Sig Figs?? 200.0
1 2 3 4 5 6
0% 0% 0%0%0%0%
a) 1
b) 2
c) 3
d) 4
e) 5
f) 6
Sig Figs?? 0.5200
1 2 3 4 5 6
0% 0% 0%0%0%0%
a) 1
b) 2
c) 3
d) 4
e) 5
f) 6
Sig Figs?? 1.005
1 2 3 4 5 6
0% 0% 0%0%0%0%
a) 1
b) 2
c) 3
d) 4
e) 5
f) 6
Sig Figs?? 10,000
1 2 3 4 5 6
0% 0% 0%0%0%0%
a) 1
b) 2
c) 3
d) 4
e) 5
f) 6
How many sig figs?
700
700.
700.00
.007
.00700
•1
•3
•5
•1
•3
How many sig figs here?
• 1.02 x 2.3
• 210 x 200
• 210. x 210
• .070 x .910
• 0.0791 x 33.1
• 2.3x105 x 200
• 2
• 1
• 2
• 2
• 3
• 1
How many sig figs here?
• 23 x 2 x 231
• 455 x 21 x 25.2
• 2100.0 x .0005
• 5.00 x 311.22
• 0.00412 x 9.1
• 1
• 2
• 1
• 3
• 2
Metric Prefixes