What are Units? 

Standard units are also called SI units. SI units are used for measuring a physical quantity satisfying certain conditions. There are two types of units: fundamental units and derived units. Fundamental units are physical quantities that are independent, that is, they do not depend on other quantities like mass, length, or time. There are plenty of quantities in our lives which need to be measured and compared. Measuring is the comparison of a particular physical quantity with its reference value. A unit is a measure of a fixed physical quantity. A physical quantity is the product of a unit and the numerical value we need to compare with.  

The derived unit is a physical quantity that depends on fundamental quantities like speed, acceleration, and area. 

Why Do We Need a Standard Unit of Measurement? 

In our day to day, we frequently describe things in terms of their length, volume, weight, and power. SI units enable us to specifically measure these and many other phenomena in a way that can be mutually agreed upon, or considered standard from a scientific perspective. Likewise, we are also frequently presented with a need to compare things in terms of features. Hence, standard conversions are needed. The words that we use to describe different quantities help us to understand how measure, and ultimately convert them as needed. 

There are plenty of systems with various units, like measuring quantities of an object's length, area, and weight. Throughout most of the world, weight is mainly expressed in grams and kilograms, but in other countries like the United States, weight is measured it in pounds. Similarly, currency differs from country to country. That is why we generally follow the international system of units which are used as the standard units of measurement and hence this is used for standard conversion.  

The seven base units for conversion to its standard units are: 

• Length - meter
• Mass - kilogram
• Time - seconds
• Temperature - kelvin
• Electric current - ampere
• Amount of substance - mole
• Luminosity intensity - candela 

From these fundamental units, there arises the derived units for the other factors and hence conversions are used.  

Types of Unit Systems 

There four types of unit systems or metric systems we use in mathematics and physics, which are CGS unit systems where the unit of length is centimeter, unit of mass is gram, and unit of time is seconds. The FPS system where the unit length is foot, the unit of mass is a pound, and the unit of time is second. The SI unit is the system of units universally followed internationally. It is also called the MKS unit where the unit of length is in meter, the unit of mass is in kilogram and the unit of time is in seconds. The SI system is always used in the calculation of physical quantities and it is known as the rational system of units. The fundamental SI units are meter, kilogram, second, ampere, kelvin, candela, and mole. Certain general rules and guidelines should be followed for using notations for physical quantities and standard symbols for SI units.  

Metric system 

This system was introduced in the early 1800s. It is the system used for measuring quantities like distance, weight, temperature, and length The fundamental units of metrics are meter, kilogram, and second where it is used for measuring the length, mass, and time respectively. For the smaller quantity conversion, decimal conversions are used to calculate and assign the value.  

The metric numbers for the fundamental unit mass, length, and time are 

Mass or weight

Kilogram - 1000, hectogram - 100, decagram - 10, unit or gram - 1, decigram - 0.1, centigram - 0.01 and milligram - 0.001 

Length 

Kilometer - 1000, Hectometer - 100, Decameter - 10, Meter - 1, Decimeter - 0.1, Centimeter 0.01, Millimeter - 0.001 

Time

1 minute: 60 seconds, 1 hour - 3600 seconds or 60 minutes, 1 day: 24 hours or 86,400 seconds, 1 week: 7 days, 1 year: 12 months or 365 days. 

Volume

Kiloliter - 1000, hectoliter - 100, decaliter - 10, liter - 1, deciliter - 0.1, centiliter - 0.01, and milliliter - 0.001 

The conversion ratios or conversion calculators used is the ratio equal 1, this is also called unit factors. This is used for the conversion of various units, between different systems. It is similar to the equivalent values between the metric and CGS unit system conversion.

Unit Conversion

The common quantities that are measured have various interdependencies and different units are related in some or the other way. Like Temperature, weight, volume, mass, area, and speed. Sometimes units used for the measurement will be unable to satisfy the measurement preferences for certain applications. So in this case unit conversion is important and hence the conversion occurs between the metric systems.  

When focusing on the fundamental units which are length or distance and weight. There are certain standard unit of measurements used in our day to day lives. 

For Length or distance measurement, it can be measured in inches, foot, cubit, yard, kilometer and miles. 

For weight measurement, it is usually measured in gram, pounds, and kilogram 

For example if we want to convert a person's height which is given as 5'8'' to its standard mode of conversion. Then we need to refer to the metric unit conversion chart on how to understand what’s given and how to convert it to its standard unit of measurement. So the ' is denoted as feet and '' is denoted as inches. So that means the given height is 5 feet and 8 inches. Now we need to convert feet and inches into meters separately and then add both together to get the final value. 

Five feet in meters is calculated by multiplying its standard unit of conversion factor which is; 1 foot is 0.305 meters, hence 5 feet is 5 times 0.305 which equals 1.53 meters. Now the inch conversion has to be calculated, so 8 inches to be converted into meter shall be, 1 inch's conversion unit factor in centimeter, so 1 inch is 2.54 cm. Now in this case there is double-conversion where centimeter has to be converted into the meter, so for 1 cm, its conversion factor is- 1 meter is 100 cm, so 1 cm I s1/100 m. Hence 8 times 2.54 is 20.32cm and in meters is 0.02032 meters hence the converted value is 1.53 +0.02032 is 1.7332 meters is the person's height. 

Practice Problems 

1) Below, arrange the given quantities in descending order that is biggest value to its smallest value 

a) 3 kg b) 4500 g c) 2.5lbs d) 450000 mg 

Solution: The arrangement of the given quantities in descending order are: 

a) 4500 g  b) 3 kg  c) 2.5 lbs  d) 450000 mg 

2) How much is of millilitre is there in 1 kilolitre ? 

Solution: 1000000 milliliter 

1 millilitre = 0.000001  kilolitre 

So, 1000000 milliliters are there in 1 kiloliter 

3) Convert 14 cubic feet to yard using the conversion factor 

Solution: 0.518518 cubic yard

$\text{14 cubic feet = 14 cubic feet x }\frac{0.037037\text{ cubic yard}}{1\text{ cubic feet}}$

$=\text{ 0}\text{.518518 cubic yard}$

Context and Applications    

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for  

• Bachelors in Technology/Engineering 
• Masters in Technology/Engineering 
• Bachelors in Science (Physics and Chemistry) 
• Masters in Science (Physics and Chemistry)