Transcript sigdigs

Using a Calculator
Do the following calculations by pressing
your calculator as few times as possible.
4528
25616
1.105
3.16 10
8.714 10 
6
9.54 10
2
5
1.203 10
4
The physics in this course is
challenging but 90% of the difficulties
arising in solving physics problems
come from small math mistakes (what I
call little math). When difficulties arise
the first thing to do is look over every
step of your calculation or have
someone else look it over.
SIGNIFICANT DIGITS
Two types of quantities are used in science:
exact values and measurements. Exact
values include defined quantities (1 kg is
1000 g) and counted values ( 12 donuts).
Measurements are not exact because they
always include some degree of uncertainty.
A measurement is made up of numbers that
are certain and one digit, the last one that is
estimated or uncertain.
Digits that are part of the measurement are
significant while digits that are not part of
the measurement are insignificant. A few
rules will help distinguish this statement.
•all non-zero digits and in-between zeroes
are significant
•zeroes in front of all of the non-zero digits
are insignificant
•zeroes behind all of the non-zero digits and
behind the decimal point are significant
•zeroes behind all of the non-zero digits but
before the decimal may be significant or
insignificant (assume insignificant unless
you know where the estimated value of the
measurement actually is)
-use scientific notation to show how
many significant digits are present
40025
4.0025 x 104
5
360.20
3.6020 x 102
5
0.00450
4.50 x 10-3
3
2600
2.6 x 103
2
2600.0
2.6000 x 103
5
850000
8.5 x 105
2
12401
1.2401 x 104
5
0.00007
7 x 10-5
1
Calculations and Significant Figures
Performing the actual calculation and
tracking significant figures is the only real
way to ascertain the number of significant
figures that make up the correct answer.
Whenever an estimated value is part of a
calculation the number it produces is
estimated.
Simplified rules have been developed to
make these calculations easier.
Adding and Subtracting
When adding and subtracting, the answer
should be precise to the same number
column as the most imprecise number in
the calculation.
Multiplying and Dividing
When multiplying and dividing, the answer
should have the same number of significant
digits as the number in the calculation which
has the fewest significant digits.
105.7
 86.84
18.86
18.9
23.45
1147
 571.5
1741.95
1742
56.3
 2 .9
163.27
160
The rules and procedures you have seen
apply to measured values. They will be
utilized in lab write-ups or in other lab based
evaluations where indicated.
On tests, quizzes or assignments you are
expected to use 4 significant figures and
only 4 significant figures. You may use less
if the calculation yields an answer with less
than four.
examples
2.39 on calculator could be written 2.39 or
2.390 on test
5.9 on calculator could be written 5.9, 5.90
or 5.900 on test
6.00042 on calculator must be written 6.000
on test
homework: complete significant figures
worksheet
UNIT CONVERSION
The metric system will be used in this unit so
conversions with prefixes will be performed.
The units of time also often need to be
converted.
km 20km 20 1000m
20


?
hr
1hr
3600s
9
nm 50nm 50 110 m
50 2 


?
2
3
2
ms
1ms
(110 s)
Convert the following measurements to the units
stated.
-express answer in scientific notation
-express answer to 4 significant digits (round
properly)
a) 6.42 km to m
c) 52.3 km/hr to m/s
e) 45.9 nm to km
g) 45.6 km/hr2 to m/s2
b) 1478 s to hr
d) 34.5 Mm to mm
f) 79 m/s to km/hr
h) 0.239 m/s2 to km/hr2
homework: p.349 6, 8, 9 and worksheets
Answers
a) 6.420 x 103 m
b) 4.106 x 10-1 hr
c) 1.453 x 101 m/s
d) 3.450 x 1013 mm
e) 4.59 x 10-11 km
f) 2.844 x 102 km/hr
g) 3.519 x 10-3 m/s2
h) 3.097 x 103 km/hr2
REARRANGING EQUATIONS
Rearrange the following equations so that
the letter indicated is isolated on the left
hand side of the equals symbol.
v2  v1  at
v2  v1  at
v2  v1
 t
a
t
v2  v1
 t 
a
7 homework p.349 7
n
a) A  LW W
g) V  V 
n
1
2
t
b) P  2L  2W W
n
h) V  V 
t
1
2
2 r
c) A  r
t
Gm
m
1
2 d
d) y  mx  b x
i) F 
2

d
e) E  I 2 RT R
v

v
1
2
j) d  (
)t
f) C  A(r  2r ) r2
2
1
2
v2