Transcript Topic 1/MP 1 Notes CP Physics Significant Figures - kern

Topic 1/MP 1
Notes
CP Physics
I. Reading Instruments
1.
2.
3.
4.
Read the instrument to its finest division and then
estimate to within a fraction of that finest division.
The figures that you write down for the
measurement are called significant figures.
The last digit that you write down for any
measurement is the uncertain digit. The last
digit is the most likely value of that finest
division. It is still significant! Even though the
last digit is an estimate, the accuracy of the
measurement has been improved.
Significant figures are the numbers which best
represent the value of a measurement.
Ex 1:
Metal Strip
cm
.4
.7
.1
.2
.3
.5
.6
.8 .9
5
6
5.50 cm
The metal strip falls between ___________
5.60 cm
and ______________.
5.60 cm
5.50 cm and __________
The readings of _________
are at least 0.05 cm in error. It is not likely
5.55 cm
that a reading of ____________is
more than
0.01 cm in error.
II. Notation
— precision bar
U uncertain
C certain
•
decimal
III.
General Rules
1. All nonzero digits are significant.
3 sig figs
2.34 ________
2
sig
figs
23 ________
sig figs
525 3________
2. Zeros placed between (interior)
significant figures are also
significant.
6.003
4
sig
figs
________
505
3________
sig figs
5 sig figs
10,001 ________
3. Zeros at the end of a number
and to the right of a decimal
point are significant.
47.0
3 sig figs
________
15.10
4 sig figs
________
125.0020
7 sig figs
________
4. Zeros at the end of a number
and to the left of where an
implied decimal point could be
are indicated to be significant by
a precision bar (–) or an actual
decimal point (.).
1 sig fig
500
________
2 sig figs
500
________
3 sig figs
500.
_________
5. Zeros to the left of the first
nonzero digit are not significant.
1 sig fig
0.5 ________
1 sig fig
0.005 ________
sig figs
0.0500 3________
6. Show only significant digits
when writing a number in
scientific notation.
500 = 5 x 102
1 sig fig
500 = 5.0 x 102
2 sig figs
500. = 5.00 x 102 3 sig figs
7. Counting numbers and conversion
factors are considered exact.
They do not affect the number of
significant digits during
calculations.
1 electron
12 in = 1 ft
1 m = 100 cm
Ex 1:
Identify the certain and uncertain
digits. Then, write the number of
significant figures.
u
cu
c cu
100
100
100
2 sig figs
ccc u
3 sig figs
c c c cu
1 sig fig
ccu
100.
3 sig figs
100.0
4 sig figs
100.00
5 sig figs
Ex 1 continued
ccu
ccu
cu
875
508
6.7
3 sig figs
u
3 sig figs
ccu
2 sig figs
c cu
6000
0.00543
0.678
1 sig fig
cu
3 sig figs
c cu
3 sig figs
u
3800
3.20 x 102
2 sig figs
3 sig figs
0.06
1 sig fig
IV. Rounding Rules
If the digit to the right of the last
significant figure is . . .
1.
less than 5, no rounding.
2.
greater than 5, round up.
3.
equal to 5 followed by a
nonzero number, round up.
4. equal to 5 followed by a zero or
no other digits, look at the last
significant figure.
If the last significant figure is
odd, round up. If the last
significant figure is even,
do not round up.
Ex 1 Round the following numbers
to the stated number of
significant digits.
8.7645 to 3 sig figs is 8.76 (Rule 1)
8.7676 to 3 sig figs is 8.77 (Rule 2)
8.7519 to 2 sig figs is 8.8 (Rule 3)
92.350 to 3 sig figs is 92.4 (Rule 4)
92.25 to 3 sig figs is 92.2 (Rule 4)
V. Adding and Subtracting Rules
–Answer must be rounded to the same
place as the least accurate measurement.
A. Round before adding or subtracting.
Ex 1: 2.345 cm + 65.34 cm + 87.2 cm
2.3
65.3
+ 87.2
4 sig figs
154.8
B. Round after adding or subtracting.
Ex 1: 2.345 cm + 65.34 cm + 87.2 cm
2.345
65.34
+ 87.2
154.885
154.9 cm
4 sig figs
Let’s agree to round
after adding or
subtracting!
C. Addition/Subtraction Examples
Ex 1
156.9 m + 25.54 m
156.9
+ 25.54
182.44
182.4 m
4 sig figs
Ex 2
125.678 ft - 31.57 ft
125.678
– 31.57
94.108
94.11 ft
4 sig figs
Ex 3 1457.05 cm + 10 cm + 20. cm
1457.05
+
10
20.
1487.05
1490 cm
3 sig figs
VI. Rules for Multiplying and Dividing
–When measurements are
multiplied or divided, the
final answer has a number of
significant figures that equal
the smallest number of
significant figures in any of the
original factors.
Ex 1
7,864.3 m x 12.1 m
7,864.3
x 12.1
95,158.03 m2
95, 200
2
m
3 sig figs
Ex 2
266 cm/ 2.3 cm
266 cm  2.3 cm = ?
115.6521739
120
2 sig figs
Ex 3
(134/23)(120.)
699.1304348
700
2 sig figs
VII. Combination of the Rules
Round the result so that it has
the same number of significant
digits as the measurement with the
least number of significant digits.
(Use the multiplication/division rule)
Ex 1
c2 = 25.02 + 65.02 – 2(25.0)(65.0)cos 35.0o
c2 = 625 + 4225 – 2662.24414
c2 = 2187.75586
c= 46.77345251
c= 46.8
3 sig figs