Transcript Rules For Significant Figures

What are Significant Figures?
The significant figures
in a measurement
Consist of all the digits
known with certainty
plus one final digit,
which is uncertain or is
estimated.
Your reading might be
76 ml. But, how sure
are you that it is really
76 ml? Is it possible
that it’s also 75.99 or
76.01?
CERTAIN VALUE: 75
UNCERTAIN VALUE:
0.99~1.1
• All measurements are approximations—
no measuring device can give perfect
measurements without experimental
uncertainty. By convention, a mass
measured to 13.2 g is said to have an
absolute uncertainty of plus or minus 0.1
g and is said to have been measured to
the nearest 0.1 g. In other words, we are
somewhat uncertain about that last
digit—it could be a "2"; then again, it
could be a "1" or a "3". A mass of 13.20 g
indicates an absolute uncertainty of plus
or minus 0.01 g.
Measurements are always all measured values plus one
approximated value. The pencil is 3.6 cm long.
1
2
3
4
5
6
7
With more calibration a more
precise measurement is possible
The pencil is 3.64 cm long!
3
4
3.6
The calibration of the instrument
determines measurement precision
3.7
Now 3.640 cm !
What is Accuracy?
• Accuracy - a measure of how close
a measurement is to the true value
of the quantity being measured.
►Who is more accurate when measuring a
book that has a true length of 17.0cm?
• Andrea:
• 17.0cm, 16.0cm, 18.0cm, 15.0cm
• Amy:
• 15.5cm, 15.0cm, 15.2cm, 15.3cm
What is Precision?
• Precision – a measure of how close a
series of measurements are to one
another. A measure of how exact a
measurement is.
• ►Who is more precise when measuring the
same 17.0cm book?
• Andrea:
• 17.0cm, 16.0cm, 18.0cm, 15.0cm
• Amy:
• 15.5cm, 15.0cm, 15.2cm, 15.3cm
Rules For Significant Figures
1. Significant figures are used for measured
numbers and for numbers derived from
measurements; does not include
definitions (ex. 1000ml=1L) or
counting numbers (ex. 1,2,3 etc)
10 mm = 1cm = (2 significant figures)
100cm = 1m = (3 significant figures)
1000g = 1kg= (4 significant digits)
2. Digits from 1-9 are always
significant.
Ex. 2342 = 4 significant figures
25 = 2 significant figures
23.42 = 4 significant figures
3. Zeros between two other
significant digits are always
significant.
Ex. 5 055 g = 4 significant figures
207 ml = 3 significant figures
4. One or more additional zeros
to the right of both the decimal
place and another significant
digit are significant.
• Ex. 5.00 = 3 significant figures
50.05 = 4 significant figures
50.50 = 4 significant figures
5. Zeros used solely for spacing the decimal
point (placeholders) are not significant.
Ex. 0.007 (1 significant figure)
1000 ( 1 significant figure)
0.015 ( 2 significant figures)
6. Exact numbers have an infinite
number of significant digits but
they are generally not reported.
All non zero digits are significant.
Ex. 2 ( 1 significant figure)
453 (3 significant figures)
Exact equivalences have an unlimited number of
significant figures
There are exactly 3 feet in exactly 1 yard.
Therefore the 3 can be 3 or 3.0 or 3.00 or 3.000 etc.
and the 1can be 1 or 1.0 or 1.00 or 1.000 etc. !
The same is true for:
SUMMARY
EXAMPLES
# OF SIG.
FIG
453 kg
3
5057 L
4
5.00 g
3
0.007 ml
1
0.02300 ml
4
Rules
All non-zero digits are always
significant.
Zeros between 2 sig. dig. are
significant.
Additional zeros to the right of
decimal and a sig. digits are
significant.
Placeholders are not sig.
Zeros to the right of the decimal
and to the right of non zeros are
significant.
It’s Your Turn To Try!
•How many
significant figures
do the following
numbers have?
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
1234 _____
0.023 _____
890 _____
91010 _____
9010.0 _____
1090.0010 _____
0.00120 _____
0.00030 _____
1020010 _____
72 _____
1000 _____
918.010 _____
0.0001 _____
0.00390 _____
8120 _____
1.) 4
2.) 2
3.) 2
4.) 4
5.) 5
6.) 8
7.) 3
8.) 2
9.) 6
10.)2
11.) 1
12.) 6
13.) 1
14.) 3
15.) 3
ASSIGNMENT:
Determine the number of significant digits in
the following numbers.
1) 5600 _____
2) 45.00_____
3) 105.0_____
4) 0.00565_____
5) 0.005400_____
6) 89.543_____
7) 5, 056, 300_____
8) 95.0540_____
9) 93, 000, 000_____
10) 21.35_____