Chapter 2- Learning Outcome 1_Mathematics for Technologists

Chapter 2- Learning Outcome 1_Mathematics for Technologists

1. 21
st
Century Mathematics for
the Industrial Technology
Learners: Automotive
Technology
BABY 'RLENE I. BAYOC

2. Measurements and
Scientific Notation
Chapter II
21
st
Century Mathematics for the Industrial Technology Learners: Automotive Technology

3. CHAPTER
 II: Measurements and Scientific Notations
Learning Outcome 1:
Explain the concept of
measurement and scientific
notation.

4. Measurement is the assignment of a number to a
characteristic of an object or event, which can be compared with other
objects or events using measuring devices or tools.
There are two acceptable systems of measure that are used
internationally, the Metric (SI) and the English system. The basic units of
measurements in the metric system are Meter (m) for linear, Gram (g) for
weight and Liter (L) for volume. The English system uses inch, foot, and
the yard in measuring length.
CHAPTER
 II: Measurements and Scientific Notations

5. THE METRIC SYSTEM OF MEASUREMENTS
LENGTH
millimeter (mm)
1 centimeter =10mm
1 decimeter =100mm =10cm
1 meter =1000mm =100cm =10dm
1 dekameter =10000mm =1000cm =100dm = 10m
1 hectometer =100000mm =10000cm =1000dm = 100m =10dkm
1 kilometer =1000000mm =100000cm =10000dm =1000m =100dkm =10hm
WEIGHT VOLUME TIME
milligram milliliter seconds
centigram centiliter 1 minute = 60 seconds
decigram deciliter 1 hour = 60 minutes
gram liter 1 day = 24 hours
dekagram dekaliter 1 week = 7 days
hectogram hectoliter 1 month = 30 days
kilogram kiloliter 1 year = 365 days
CHAPTER
 II: Measurements and Scientific Notations

6. THE METRIC SYSTEM OF MEASUREMENTS
MEASURABLE QUANTITIES UNIT ABREVIATION
Acceleration meter per second squared m/s
2
Amount of substance Mole mol
Angle Radian R
Angular Acceleration radian per second squared r/s
2

Angular Velocity radian per second r/s
Area square meter m
2
Density kilogram per cubic meter kg/m
3
Electrical Current Ampere A
Energy Joule J or N-m
Force Newton N or kg-m/s
2
Frequency Hertz Hz or 1/s
Impulse Newton-second kg-m/s
CHAPTER
 II: Measurements and Scientific Notations

7. THE METRIC SYSTEM OF MEASUREMENTS
MEASURABLE
QUANTITIES
UNIT ABREVIATION
Length Meter M
Luminous intensity Candela cd
Mass Kilogram kg
Moment of a Force Newton-meter N-m
Power Watt W or J/s
Pressure Pascal Pa or N/m
2
Stress Pascal Pa or N/m
2
Temperature Kelvin K
Time Second S
Velocity meter per second m/s
Volume 
(solids)
cubic meter m
3
Volume (liquids) Liter L or 10
-3
 
m
3
Work Joule J or N-m
CHAPTER
 II: Measurements and Scientific Notations

8. E
N
G
L
IS
H
S
Y
S
T
E
M
O
F

M
E
A
S
U
R
E
M
E
N
T
S
Length Capacity (Dry)
12 inches = 1 foot 16 fluid ounces = 1 pint
3 feet = 1 yard 2 pints = 1 quart
220 yards = 1 furlong 8 quarts = 1 peck
8 furlongs = 1 mile 4 pecks = 1 bushel
5,280 feet = 1 mile Capacity (Liquid)
1,760 yards = 1 mile 4 gills = 1 pint
Mass 2 pints = 1 quart
437.5 grains = 1 ounce 4 quarts = 1 gallon
16 ounces = 1 pound Troy Weights
14 pounds = 1 stone 24 grains = 1 pennyweight
100 pounds = 1 hundredweight20 pennyweights = 1 ounce
Area Apothecaries' Measures
144 square inches= 1 square foot60 minims = 1 fluid dram
9 square feet = 1 square yard8 fluid drams = 1 fluid ounce
4,840square yards= 1 acre 16 fluid ounces = 1 pint
640 acres = 1 square mile Apothecaries' Weights
1 square mile = 1 section 20 grains = 1 scruple
36 sections = 1 township 3 scruples = 1 dram
Volume 8 drams = 1 ounce
1,728 cubic inches= 1 cubic foot
  
27 cubic feet = 1 cubic yard  
CHAPTER
 II: Measurements and Scientific Notations

9. SCIENTIFIC NOTATION
A real number x is said to be expressed in scientific notation if it is written
in the form x = ± a.b × 10n, where n is an integer and 1 ≤ a ≤ 9 and b is a
decimal number or zero. The integer n is called the characteristic of x, the
number a.b is called the mantissa of x, and the factor 10n is called the order
of magnitude of x.
To change a number from ordinary decimal form to scientific notation,
move the decimal point to obtain a number between 1 ≤ x < 10 and multiply
by 10n or by 10–n , where n is the number of times the point moved to the
left or to the right.
CHAPTER
 II: Measurements and Scientific Notations

10. NAMES AND SCIENTIFIC PREFIXES FOR SOME
INTEGER POWERS OF 10
Let us consider the number of electrons passing by a point in a circuit every second with a steady
electric current of 1 amp: 1 amp = 6,250,000,000,000,000,000 electrons per second. This can be
change to scientific notation by moving the decimal point 18 places to the left to obtain
6.250,000,000,000,000,000 and multiply it by 1018, so that 6,250,000,000,000,000,000 =6.25×1018
electron per second. Another example is the Proton mass = 0.000 000 000 000 000 000 000 00167
grams. To change it to scientific notation, we move the decimal point 25 places to the right to obtain
1.67 then multiply it by 10–25, so that we have 1.67×10–25 grams.
CHAPTER
 II: Measurements and Scientific Notations

11. NAMES AND
SCIENTIFIC
PREFIXES
FOR SOME
INTEGER
POWERS OF
10
Power of
 10
Names Numeral Prefix Abbreviation
10
18
Quintillion 1,000,000,000,000,000,000Exa E
10
15
Quadrillion 1,000,000,000,000,000 Peta P
10
12
Trillion 1,000,000,000,000 Tera T
10
9
Billion 1,000,000,000 Giga G
10
6
Million 1,000,000 Mega M
10
3
Thousand 1,000 Kilo k
10
2
Hundred 100 Hecto h
10
1
Ten 10 Deka da
10
0
Unit 1  
10
–1
Tenth 0.1 Deci d
10
–2
Hundredth 0.01 Centi c
10
–3
Thousandth 0.001 Milli m
10
–6
Millionth 0.000 001 Micro µ
10
–9
Billionth 0.000 000 001 Nano n
10
–12
Trillionth 0.000 000 000 001 Pico p
10
–15
Quadrillionth 0.000 000 000 000 001 Femto f
10
–18
Quintillionth 0.000 000 000 000 000 001Atto A
CHAPTER
 II: Measurements and Scientific Notations

12. References
https://en.wikipedia.org/wiki/Measurementhttps://www.allaboutcircuits.com/
textbook/direct-
current/chpt-4/scientific-notation
https://www.emathzone.com/tutorials/algebra/introduction-to-scientific-
notation.html#ixzz6K8JlkdXW
https://www.khanacademy.org/math/arithmetic-home/arith-review-decimals/
arithmetic-significant-
figures-tutorial/v/significant-figures
https://www.mathsisfun.com/measure/metric-units-details.html
https://www.nde-ed.org/GeneralResources/Units/USCustomarySystem.htm
CHAPTER
 II: Measurements and Scientific Notations

13. CHAPTER
 II: Measurements and Scientific Notations
Thank you