Base and derived quantities

There two types:

•Base quantities

•Derived quantities

A base quantity is physical quantity which cannot be defined in term of other physical quantity

A derived quantity is a physical quantity. produced from combination of base quantities.

• Physical quantities are related to one another by mathematical equations, for example:

• velocity = displacement / time.

• Some physical quantities are chosen as base quantities. Other physical quantities are obtained from the base quantities using the appropriate algebraic relationships and these are called derived quantities .

Physical QuantitySymbol for the Quantity

length l

mass m

time t

electric current I

thermodynamic temperature

T

luminous intensity Iv

amount of substance n

Base Quantity

BASE UNITS

Physical Quantity Name of Unit Symbol

length metre m

mass kilogram kg

time second s

electric current ampere A

temperature kelvin K

luminous intensity

candela cd

amount of substance

mole mol

SOME EXAMPLES OF DERIVED SI UNITS

Physical Quantity SI Unit Symbol

area square metre m2

volume cubic metre m3

densitykilogram per cubic metre

kg.m-3

speedmetre per second

m.s-1

accelerationmetre per second squared

m.s-2

concentrationmole per cubic metre

mol.m-3

SOME DERIVED SI UNITS WITH SPECIAL NAMES

Physical Quantity Name of Unit Symbol

energy joule J

force newton N

pressure pascal Pa

power watt W

electric charge coulomb C

electric potential difference

volt V

electric resistance ohm W

frequency hertz Hz

PREFIXES

• Prefixes are used to represent physical quantities which are very big or very small in SI units.

• Prefixes correspond to powers of 10

• Each prefix has a specific name

• The table show list of prefixes with its multiplication factor.

• Students are required to memorize all prefixes start from pico until the tera.

Prefixes

Prefixes SI PrefixesPrefixes Symbol Multiple

PicoNanoMicroMilliCentiDeciKiloMegaGigaTera

pnµmcdkMGT

x10-12

x10-9

x10-6

x10-3

x10-2

x10-1

x103

x106

x109

x1012

• The prefixes can be used with any base units

• They are multipliers of the base unit

• Examples:

– 1 mm = 10-3 m

– 1 mg = 10-3 gMemorise all this Prefixes !!!!

Convert single number to standard form

STEP

1.Copy the digit but not digit of zero

2.Place the decimal point after first digit

3.Multiply with a power of ten4.Find the exponent of ten

Given:4,750,000

4.75 (moved 6 decimal places)

answer: 4.75 X 106

The original number was greater than 1 so the exponent is positive.

Given:0.000789

7.89 (moved 4 decimal places)

answer:7.89 x 10-4

The original number was less than 1 so the exponent is

negative.

Examples:

• The height of Mount Everest = 8848 m. Convert the height of Mount Everest into standard form.

Answer : 8.848 X 103

Answer

a. 0.0093

b. 0.000002

c. 3,013,000,000

d. 12,000,000,000

e. 130,000,000,000,000

Convert single number to standard form

Single numberStandard Form

a. 0.0093 9.3x10-3

b. 0.000002 2.0x10-6

c. 3,013,000,000 3.013x109

d. 12,000,000,000 1.2x1010

e. 130,000,000,000,000 1.3x1014

• Move decimal point to right for positive exponent of 10.

• Move decimal point to left for negative exponent of 10.

To Change from Standard Form to

Single Number:

Examples:

Given: 5.024 x 103

answer: 5,024 (3 places to right)

Positive exponent move decimal to the right.

Given:1.015 x 10-8

(8 places to left)answer: 0.00000001015

Negative exponent move decimal to the left.

Answer

Standard form

a. 1.3x10-5

b. 9.43 x10-4

c. 3.423 x107

d. 3.23 x106

e. 6.003 x109

to Single number

Answer

Standard Form Single number

1.3 x10-5 0.000013

9.43 x10-4 0.000943

3.423 x107 34,230,000

3.23 x106 3,230,000

6.003 x109 6,003,000

Summary

To express a positive number greater than or equal 1 to 10 in the standard form the given number can be express as A x10n ,where n is positive

To express a positive number less than 1 in standard form, the given number can be express as A x10n , where n is negative

Express single number to standard form

To convert a number given in the form to single number, see whether n is positive or negative.

If n positive, shift the decimal point n places to the rightIf n negative, shift the decimal point n places to the left

Kena tahu cara tukar unit suatu kuantiti kepada unit yang lain

Misalnya, diketahui 1 kg = 103 g, 1 cm = 10-2 m. Ketumpatan aluminium adalah 2.70 g/cm3.

Express the density of Aluminum in kg/m3. 2.70 g/cm3 = 2.70 (10-3 kg)/(10-2 m)3

= 2.7 (10-3/ 10-6) kg/m3

=2.7 x 103 kg/m3

Unit Conversion

Example:

530pF is equal to?

Solution:

530 pF = 530 x 10-12 F

530 pF = 5.30 x 102 x 10-12

= 5.3 x 102+(-12)

= 5.3 x 10-10

Prefix p is equivalent to 10-12

So convert 530 into standard form

ab x ac = ab+c

Next example…..Q: Convert 100 cm3 to m3

Solution:

• we already know c = 10-2

• 100 x 10-2 m3 ( this answer is wrong)

• In this case:

cm3 = (cm)3

= (10-2m)3

= 10-6m3

100cm3 = 100 x 10-6m3

= 1x 10-4m3 (ni baru betul..)