Transcript Physics Skills Review

Physics 11: Skills Review
Significant Digits
(and measuring, scientific
notation, conversions……)
• Precision: to describe
how well a group of
measurements made of
the same object or event
under the same conditions
actually do agree with one
another.
• These points on the bulls
eye are precise with one
another but not accurate.
• Accuracy:
represents the
closeness of a
measurement to the
true value.
• Ex: the bulls eye
would be the true
value, so these
points are accurate.
Let’s use a golf analogy
Accurate? No
Precise? Yes
Accurate? Yes
Precise? Yes
Precise?
No
Accurate? No
Scientific Notation
• Scientists have developed a shorter
method to express very large or very
small numbers.
• Scientific Notation is based on powers
of the base number 10.
Ex: The mass of an electron is:
0.000 000 000 000 000 000 000 000 000 000 911 kg.
This can easily be
expressed as: 9.11 X 10-31 kg
• 123,000,000,000 in s.n. is 1.23 x 1011
• The first number 1.23 is called the
coefficient. It must be between 1 - 9.99
• The second number is called the base .
The base number 10 is always written in
exponent form. In the number 1.23 x 1011
the number 11 is referred to as the
exponent or power of ten.
Using Scientific notation
in calculations:
• When using scientific notation in
calculations it is important to be able to
enter the these measurements into your
calculator.
• Use the exp or the e button on your
calculator.
Ex: divide 3.4 x 103m by 1.7s
= 2000 m/s
• When determining the # of sig figs in a
number written scientific notation in use
the same rules for sig figs. Do not include
the 10 to the power in the sig figs.
Ex.
2.350 x 106 has 4 sig figs
2.0000 x 10-5 has 5 sig figs
Practice converting to
scientific notation and back:
• A) 5934587 m
• D) 3.6 x 10-7
• B) 0.0000067 km
• E) 1.324 x 105
• C) 890000 s
• F) 5 x 104
5.934587 x 106 m
6.7 x 10-6 km
8.9 x 105 s
0.00000036
132 400
50 000
Rules on determining
significant digits:
• 1. Nonzero digits are always significant.
• 2. All final zeros after the decimal point are
significant.
• 3. Zeros between two other significant digits are
always significant.
• 4. Do not count leading zeros as significant.
• 5. Zeros at the end of a number which has no
decimal point are NOT significant.
Determine the correct number
of significant digits:
•
•
•
•
•
•
•
A)
B)
C)
D)
E)
F)
G)
1.2345 _____
4.8900 _____
22 000 _____
0.0023 _____
2567.0 _____
1999 _____
10.0001 ____
•
•
•
•
•
•
•
H) 120.0 _____
I) 555 _____
J) 0.0001 _____
K) 20 _____
L) 0.001001 ____
M) 56.0 ____
N) 230. 03 ____
ANSWERS
• A) 1.2345
(5)
• B) 4.8900
(5)
• C) 22 000
(2)
• D) 0.0023
(2)
• E) 2567.0
(5)
• F) 1999
(4)
• G) 10.0001
(6)
• H) 120.0
(4)
• I) 555
(3)
• J) 0.0001
(1)
• K) 20
(1)
• L) 0.001001
(4)
• M) 56.0
(3)
• N) 230. 03
(5)
Addition/Subtraction
using Significant Digits:
• The number of significant digits is equal
to the value having the fewest decimal
places. Ex: 2.03 mm + 3.1 mm =
5.1 mm not 5.13.
Multiplication/Division
using significant Digits:
• The number of significant digits is equal
to the value with the fewest significant
digits. Ex: 3.2 s x 2.991 =
9.6 s not 9.5712 s
Measurement: Why we
actually care about sig figs!
• When taking measurements, it is
important to note that no measurement
can be taken exactly
• Therefore, each measurement has an
estimate contained in the measurement
as the final digit
• When taking a measurement, the final
digit is an estimate and an error estimate
should be included
Significant Digits for measuring
• When using a measuring
device, use all the given
lines to measure, then
estimate the last number
• The accuracy of the sig
figs depends upon the
measuring device.
Ex: a ruler
Read the ruler
Answers
40.51 cm
42.15
Significant Figures
• Because all numbers in science are
based upon a measurement, the
estimates contained in the numbers must
be accounted for:
1+1 = 3
• While we know think this is not true, from
a science standpoint, the measurements
could have been:
1.4 + 1.4 = 2.8
Significant Figures: the
Why!
• Since the final digit in each measurement
is an estimate, we refer to it as an
uncertain digit or the least significant digit
• This means that any mathematical
operation involving this digit in introduces
uncertainty to the answer
Significant Figures: the
Why!
• 100.21
• +22.436
• 122.646
• In the result of this calculation, there are
two uncertain digits
• As this does not make sense, the second
uncertain digit would be discarded,
making the answer 122.65
SI (System International )
Units
• This system is used for scientific work
around the world
• It is based on the metric system
SI: Base Units
•
•
•
•
•
•
•
Length - meter - m
Mass - grams – (about a raisin) - g
Time - second - s
Temperature - Kelvin orºCelsius K orºC
Energy - Joules- J
Volume - Litre - L
The number of particles of a substance mole - mol
Conversions
• The metric system uses prefixes added
the base unit (SI unit).
• We often have to convert from a prefixed
unit to the base unit
• Refer to hand out for conversion chart
• Conversions are made by moving the
decimal place to the left or right the
appropriate number of times
Examples:
1. 992 mL = ? L
move the decimal 3 times left
 0.992 L
2. 28.3 kg = ? g
 move the decimal 3 times right
 28 300 g