LECTURE NOTE 2
Measurement is defined as a number with an attached unit. For example, the mass
of a coin, weighed on a balance, as 5g while its diameter is 2cm. A balance is an
instrument used in measuring mass.
Physical Quantity
Units in Metric Unit
Length
Mass
Volume
Centimeter(cm)
Gram(g)
Milliliter(mL)
Units in English
Unit
Inches(in)
Pound(lb)
Quart(qt)
LENGTH MEASUREMENT
Uncertainty is the degree of inexactness in an instrument. Scientists use the term
uncertainty in unit measurement, it is always better to use instrument with the most exact
measurement, least uncertainty. When you have uncertainty ( plus and minus signs on
each other) written after a reading, this tells you that the reading falls within a certain
range of reading. This has to do with the calibration on the object. The lower the
uncertainty is, the better the result, while the higher the uncertainty the less well the
result. The candy example in the textbook illustrates better.
MASS MEASUREMENT
Mass of an object is a measure of the amount of matter it possesses. Mass is
measured with a balance and is constant, it is not affected by gravity because the gravity
on the object cancels out with the gravity on the pans of the balance. Weight and mass are
used interchangeably but they do not mean the same thing.
Weight is the force exerted by gravity on an object. Knowing that the earth is
heavier than the moon, earth’s gravity is greater than the moon; objects weigh more on
earth than on the moon. Similarly, the same object weighs more on the huge planet
Jupiter than on earth.
VOLUME MEASUREMENT
Volume is the amount of space occupied by a solid, gas or liquid. Example of
instruments used to measure volume are Graduated cylinder, syringe, pipet and buret.
The most common sizes of graduated cylinder are 10 mL, 50 mL and 100ml. The
uncertainty of graduated cylinder ranges from (0.1 to 0.5). Pipet are mostly used to
deliver mixed volumes of liquids. The volume delievered varies, but the uncertainty
ranges from (0.1 to 0.001).
A buret is a long, narrow piece of calibrated glass tubing with a valve called
“stopclock” at the bottom. Flow of liquid is regulated by closing the stopclock. The initial
and final liquid levels in the buret are observed and recorded. Burets usually have
uncertainty ranging from (0.1 to 0.001).
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SIGNIFICANT FIGURES
Significant figures are figures you get from a properly recorded measurement.
They are also known as significant digits. In every measurement, significant figures
express the uncertainty of the instrument in use.
Rules of Significant Figures.
1) A number is a significant figure if it is:
a) a non-zero digit. Example,
4.5g
2s.f
122.35m
5s.f
b) a zero between non-zero digits
205
5.082
5.0
25.0
16.00
3s.f
4s.f
2s.f
3s.f
4s.f
4.0x105
5.70x10-3
2s.f
3s.f
0.0004 cm
0.075m
8500g
125000g
1s.f
2s.f
2s.f
3s.f
c) a zero at the end of a decimal number
d) any digit in the coefficient of a
number written in scientific notation.
2) A number is non-significant if it is:
a) a zero at the beginning of a decimal
number
b) a zero used as a placeholder in a large
number without a decimal point
Rounding off Non-significant digits:
1) If the first non-significant digit is less than 5, drop all non-significant figures.
Example, 505.05 rounds to 505 (3s.f)
2) If the first non-significant is 5 or greater, add 1 to the last significant digit.
Example, 505.50 rounds to 506 (3s.f)
ADDING AND SUBTRACTING MEASUREMENTS
The answer is limited by the least certain measurement in a set of data( least
decimal place in the measurement). Example, 106.7g+0.25g+0.195g=107.145g
The answer is 107.1g since 106.7 has the least uncertainty(least d.p).
35.45m – 30.5m=4.95m
The answer is 5.0m since 30.5 has the least uncertainty(least d.p)
MULTIPLYING AND DIVIDING MEASUREMENTS
The answer is limited by the least number of significant digits in the given data.
Example, 359 x 0.20 =71.8
The answer is 72 since 0.20 is in 2s.f with the least significant figure.
73.950g/25.5mL = 2.9g/mL
the answer is 2.90g/mL since 25.5 has the least significant figures.
EXPONENTIAL NUMBERS
Numbers greater than 1 have a positive exponent, example
1,000,000 = 1 x 106
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Numbers less than 1 have negative exponent, example
0.000001= 1 x 10-6
SCIENTIFIC NOTATION
Place the decimal point after the first non-zero digit. Using an exponent, indicate
how many places the decimal is moved. Example
55,500g = 5.55 x 104g
0.000555g = 5.55 x 10-4
EXACT NUMBER
Counted Numbers
8 doughnuts
2 baseballs
5 capsules
U.S system
1ft=12 in
1qt=4 cups
1lb=16 ounces
Metric system
1L=1000mL
1m=100cm
1kg=1000g
Exact numbers (counted numbers) do not have significant figures that require
rounding off answers while measured numbers have significant figures that require
rounding off answers.
What Is An Equivalent Relationship?
An equivalent relationship is a relationship between two quantities that are equal.
Unit equation is a statement of two equivalent values. For example,
1$=10 dimes
Unit factor is a ratio of two quantities that are equivalent and can be applied to
convert from one unit to another, for example,
1$ =
10dimes
10 dime
1$
Application of unit equation and unit Factor:
Given a unit equation of 1 year = 365 days
Therefore, the unit factors are
I year = 365 days
365 days
1 year
You then apply a unit factor to convert the given unit to the answer.
UNIT ANALYSIS PROBLEM SOLVING
This is a method used to systematically solve problems.
(2)
(3)
(1)
Given value x
Unit factor
=
Unit of answer
PERCENTAGE
Percentage (%) expresses the amount of a single quantity compared to an entire
sample. For example, 1 dime is 10% of 1$, while 25cent is 25% of 1$. If a 14-karat ring
contains 20.0g gold and 14.3g silver, what is the percentage of gold?
20.0 g x
100%= 58.3%
(20.0+14.3)g
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