GENERAL PHYSICS 1
Subject Description:
Mechanics of particles, rigid bodies, and
fluids; waves; and heat and
thermodynamics using the methods and
concepts of algebra, geometry,
trigonometry, graphical analysis, and basic
calculus.
UNIT CONVERSION
AND SCIENTIFIC
NOTATION
At the end of the lesson,
you are expected to:
1. Solve measurement problems
involving conversion of units,
expression of measurements
in scientific notation.
LEARNIN
G
OBJECTIV
E
What is Physical Quantity?
 A characteristic or property
of an object that can be
measured or calculated from
other measurements.
What is Unit?
 Reference standard to define
the magnitude of a physical
quantity.
Significant Figures
Determine the number of significant figures of the
values given below:
1.
2.
3.
4.
5.
0.000982 = _____
125.0010 = ____
9.81 = ____
100.90 = ____
150 = _____
Rules in determining the number of significant
figures:
1. All nonzero digits are significant.
256.78
985, 612
has 5 significant figures
has 6 significant figures
2. All zeros between nonzero digits are significant.
8006
7.01
has 4 significant figures
has 3 significant figures
3. All zeros to the left of the first nonzero digits are
NOT significant; such zeroes merely indicate the
position of the decimal point.
0.00001 has 1 significant figure
has 2 significant figures
0.015
4. Zeros to the right of a decimal point in a
number are significant.
0.900
7000
has 3 significant figures
has 1 significant figure
Rules for Mathematical Operations:
1. In adding or subtracting quantities, the least
number of decimal places in any of the numbers
being added or subtracted should also be the
number of the decimal places in the answer.
Ex:
3. 1918 m + 8.13 m + 0.156 m =
2. In multiplying or dividing quantities, the least
number of significant figures in the input number
should also be the number of significant figures in the
answer.
Ex:
(10.30 mm) (0.50 mm) (2.01)=
SCIENTIFIC NOTATION
What is Scientific Notation?
Scientific Notation, sometimes called as
powers-of-10 notation, is a convenient and
widely used method of expressing large and
small numbers. It can be expressed as,
𝒏
N x 𝟏𝟎 ,
where: N = any number between 1 and 10
n = is the appropriate power of 10
Rules in expressing standard notation to
scientific notation:
1. When the decimal point is moved from right to
left, the result is positive exponent.
Ex: 1269.4310 =
2. When the decimal point is moved left to right, the
result is negative exponent.
Ex: 0.0000003647 =
Rules converting scientific notation back to
standard notation:
1. Move the current decimal point according to the
number of places based on the exponent.
(+) positive exponent – move to the RIGHT
Ex: 3.1416 x 104 =
(-) negative exponent – move to the LEFT
−3
Ex: 5.12 x 10 =
Rules in Addition and Subtraction involving
scientific notation
1. When two or more quantities are added or
subtracted, make sure the exponents are the same. If
not, choose one to adjust the decimal and exponent.
Use LARS (Left Add, Right Subtract)
2. Add/subtract the number. Keep the exponent the
same.
Examples:
4
10
4
10
a. 3.41 x
+ 7.88 x
=
6
3
b. 19.8 x 10 + 21.23 x 10 =
2
3
5
c. 56.3 x 10 + 0.45 x 10 + 3.06 x 10 =
Rules in Multiplication and Division involving
scientific notation
1. Powers of ten are added in multiplication.
Ex: (2.4 x 102 )(10.85 x 103 ) =
1. Powers of ten are subtracted in division.
32.45×108
Ex:
2.50×105
=
Practice Exercise:
Express the following in scientific notation.
1. The amount of water surface area on the Earth is
140,000,000 miles2 .
2. The mass of a strand of hair is approximately
0.00000062 kg.
3. The length of the shortest wavelength of visible
light (violet) is 0.0000004 m.
SYSTEMS OF UNITS
1. Metric System (SI Unit)
2. English System
Metric System (SI Unit)
 mks system – meter,
kilogram and second
 cgs system –centimeter,
gram, and second
English System
 fps system – foot, pound
and second
TYPES OF PHYSICAL
QUANTITIES
 Fundamental Quantities
 Derived Quantities
Fundamental Quantities – are basic
quantities that are independent of one
another.
SI Fundamental Quantities - length,
mass, time, thermodynamic temperature,
electric current, luminous intensity and
amount of substance
Fundamental/Base Units – units
corresponding to the fundamental
quantities.
Derived Quantities – are combinations
of fundamental quantities. Examples are
speed, acceleration, density, work and
energy.
SI Fundamental Units
Quantity
Length
Mass
Time
Temperature
Electric Current
Luminous Intensity
Amount of
Substance
Unit
meter
kilogram
second
Kelvin
Ampere
Candela
mole
Symbol
m
kg
s
K
A
cd
mol
SI Prefixes
SI Prefixes
yotta
zeta
exa
peta
tera
giga
mega
kilo
hecto
deka
Symbol
Multiplier
Y
Z
E
P
T
G
M
k
h
da
1024
1021
1018
1015
1012
109
106
103
102
101
SI Prefixes
yocto
zepto
atto
femto
pico
nano
micro
milli
centi
deci
Symbol
Multiplier
y
z
a
f
p
n
µ
m
c
d
10−24
10−21
10−18
10−15
10−12
10−9
10−6
10−3
10−2
10−1
UNIT CONVERSION
CONVERSION FACTORS
Length
1 ft = 12 in
1 yd = 3 ft
1 mi = 5280 ft
= 1.609 km
1 in = 2.54 cm
1 m = 3.281 ft
= 100 cm
Volume
1 L = 1000 cm3
= 1000 ml
1 gal = 3.785 L
= 4 qt
= 231 in3
1 m3 = 1000 L
CONVERSION FACTORS
Time
1 min = 60 s
1 hr = 3600 s
= 60 min
1 day = 24 hrs
1 yr = 365 days
Force, Mass
1 lb = 4.448 N
1 slug = 14.59 kg
1 kg = 2.205 lb
1 kip= 1000 lb
UNIT CONVERSION
ILLUSTRATION:
Convert the following:
1. 115 km = ___ ft
2. 600 µg = ___ g
3. 23 Terabytes = ___ bytes
−8
4. 50 x 10 ns = ____ks
5. 0.700 nm/ms = ____ cm/min
II. Solve the following measurement problems involving
conversion of units. Express your answer in scientific
notation. Answers should include three significant figures.
1. A government owned land will be set
converted as a new wildlife refuge. Its
dimensions are 15 × 1012 𝑚𝑒𝑡𝑒𝑟𝑠 by 10 ×
106 𝑚𝑒𝑡𝑒𝑟𝑠. Find the area of the land in
ℎ𝑒𝑐𝑡𝑎𝑟𝑒𝑠.
II. Solve the following measurement problems involving
conversion of units. Express your answer in scientific
notation. Answers should include three significant figures.
2. One light-year (ly) is the distance travelled by
light in a year. Convert one light-year to meters
8
using 3 x 10 m/s for the speed of light.
3. The rest energy E of an object with rest mass m is
given by Einstein’s famous equation, E = 𝑚𝑐 2 ,
where c is the speed of light in vacuum. Find E for an
electron for which m = 9.11 × 10−31 kg. The SI unit
2 2
for E is Joule = kg-𝑚 /𝑠 . Speed of light in a vacuum is
8
2.99792458 x 10 m/s .