Metric System

A physical quantity is something that is measured such as mass, length and time. Each of these units is defined by a number, value or its magnitude and a unit. Each physical quantity has its specific unit and these unit help us to analyze what the given or the asked quantity is.

These units are identified through different systems. Using these different systems in one solution may be confusing, thus, scientists around the world use one system as the commonly used system in dealing with measurements. This system of measurement is the International System of Units (SI).

A list of base quantities with the corresponding unit they are measured is given in the table below.

 Quantity Unit Symbol Mass kilogram kg Length meter m Time second s Electric current ampere A Temperature kelvin K Amount of substance mole mol Luminous intensity candela cd

Prefixes are used to define smaller or larger values or measurement of the same quantities. Below is the list of prefixes and their corresponding factor:

 Prefix Symbol Multiplying Factor pico- p 10-12 nano- n 10-9 micro- µ 10-6 milli- m 10-3 centi- c 10-2 deci- d 10-1 kilo- k 103 mega- M 106 giga- G 109 tera- T 1012

To convert units, the following must be followed:

1. Identify the given unit and the unit in which the given unit must be converted.
2. Detemine the conversion factor. The unit to be converted must be placed in the position(numerator or denominator) in which it can be cancelled out so that the only unit left is the desired unit.

​Example 1.

The length of the pole is 15 meter. What is its length in decimeters?

Given: 15 meters

Desired unit: decimeter

Conversion Factor: 1 dm = 10-1 m

Solution: $$15\;m\;\times\;{1\;dm \over 10^{-1}m}=150\;dm$$

Example 2.

The speed of the race car is 140 km/h. Express the race car's speed in m/s.

Given: speed = 140 km/h

Conversion Factors: 1 km = 103 m and 1 hr = 3,600 s

Solution:

$$140\;\frac{km}{h}\times {10^3\;m \over 1\;km}\times {1\;h \over 3,600\;s}=38.89\;m/s$$

Derived Units

Derived units from the term itself is derived from the base units. It is a combination of two or more base units. These base units are multiplied or divided by one another and not added or subtracted. The following are some commonly used derived units:

Quantity

Unit

Derived Unit

velocity

m/s m; s-1

frequency

herts (Hz) 1/s or s-1

energy

joule (J) kg m2 s-2

force

newton (N) kg m s-2

electric charge

coulomb (C) A s

acceleration

m/s2 m s-2

Example 1.

A 5-kg object is pushed then accelerates at 2 m/s2 . How much force is exerted on the object?

Solution:

$$F=ma=(5\;kg)(2\;m/s^2)=10\;kg\;m/s^2=10\;N$$