 # Conversion of Units

## What is Conversion of Units?

Units in Mathematics is used to measure any physical quantity. Any quantity that can be measured is called a physical quantity. The fundamental physical quantities are mass, length, and time. Every physical quantity has a separate unit to measure that quantity. Each unit in Mathematics can be expressed using a dimensional formula in terms of Mass, Length, and Time.  When two quantities of the same unit are taken as a ratio, the result obtained is dimensionless. In many Mathematical problems, the quantities involved in the calculation of the final result are not measured in the same standard unit. In those cases, the conversion of units of measurement to one standard form is required. A unit conversion chart or unit conversion table is used to perform this action.

## Examples of an Instance Where Conversion of Units of Measurement is Used:

• To measure the perimeter of a scalene triangle with sides 10 cm, 0.2 m, and 15 mm. In this problem, the sides of the triangle are measured with three different units. So, unit conversion charts for length should be used for the conversion of units of measurement of length either to a meter or centimeter or millimeter.

• Finding the total weight of 3 boys weighing 45 kg, 3400 g, and 0.07 tons respectively. In this case, the mass unit conversion table should be used to convert the weights of all the three boys to one unit of measuring mass.

### Unit Conversion Chart for Mass:

Any matter which occupies space is said to have mass. Mass of a substance is measured in kilograms in the International System of units. Unit conversion table for various other units of measuring mass is given below.

 SI unit of Mass = kilograms (kg) 1 kilogram = 1000 gram (g) 1 gram = 1000 milligram (mg) 1 pound = 453.59237 gram = 16 ounces 1 ton = 2000 pounds

### Conversion of Units Example Problems (Mass):

1. Convert 7.23 kgs into milligrams.

Solution:

1 kg = 1000 g and 1 gm  = 1000 mg

So, 1 kg = 1000 x 1000 = 106 mg

7.23 kg = 7.23 x 106 mg = 7230000 mg

1. A boy visits a grocery shop and purchases 2 kg onion, 500 g brinjal, and 25 mg of elaichi. He puts these items into a bag measuring 20 g after paying the bill. What is the total weight carried by the boy in kilograms?

Solution:

Weight of the onion = 2 kg

Weight of the brinjal = 500 g

Weight of elaichi = 25 mg

Weight of the bag =  20 g

Recall what is conversion of units factor for mass.

1 kg = 1000 g and 1 g = 1000 mg

So 1 g = 0.001 kg and 1 mg = 0.000001 kg

Weight of onion = 2 kg

Weight of brinjal = 500 g = 500 x 0.001 = 0.5 kg

Weight of elaichi = 25 mg = 25 x 0.000001 = 0.000025 kg

Weight of the bag = 20 g = 20 x 0.001 = 0.02 kg

Total weight = 2 + 0.5 + 0.000025 + 0.02 = 2.520025 kg

### Unit Conversion for Length:

Length is one of the physical quantities which has several units of measurement. The SI unit of length is meter (m). The unit conversion table for length is as below:

 SI unit = meter (m) 1 kilometer (km) = 1000 meter = 0.62137 mile 1 meter = 100 centimeter (cm) 1 centimeter = 10 millimeter (mm) 1 nanometer = 1 x 10-9 meter 1 picometer = 1 x 10-12 meter 1 inch = 2.54 meter 1 Angstrom = 1 x 10-10 meter

### Conversion of Units Example Problems (Length):

1. In one of the conversion of units example problems, it is given that an object travels 5 cm to the north, 7 m to the east and 0.5 km to the south. What is the total distance travelled by the object in meters?

Solution:

In this problem, the unit conversion table for length is used.

1 cm = 0.01 m and 1 km = 1000 m

So, the total distance travelled by the object is

= 5 cm + 7 m + 0.5 km

= 5 x 0.01 + 7 + 0.5 x 1000

= 0.05 + 7 + 500

= 507.05 m

### Fun Facts:

• Unit conversion table for time also can be written by prefixing the SI unit of time i.e. seconds with required conversion factors.

• There are certain prefixes which are generally used to represent the units in terms of the basic unit of measurement. For example kilo refers to 103, milli refers to 10-3, mega refers to 106, micro refers to 10-6, nano refers to 10-9, centi refers to 10-2, pico refers to 10-12 etc.

1. What is Conversion of Units and Why is It Important?

Conversion of units of measurement refers to transforming the particular measurements of any specific physical quantity in one form of units. Conversion of units is generally done by multiplying the measured quantity with the conversion factors as prescribed in the unit conversion table.

• Conversion of units in Mathematics plays a key role in understanding the unit of measurement of a quantity to be chosen in different instances.

For example, the length of a pencil can be measured in centimeters whereas it is not appropriate to use centimeters for measuring the length of a road from your school to home.

• It also helps in comparing the quantities with the idea of the units used to measure them.

• Conversion of units to one form helps to avoid confusion and eases the problem-solving techniques.

1. Which are the Different Systems of Measuring the Unit?

There are different systems used to measure a physical quantity. They are:

1. Metric System of Units

There are many other subsystems in the metric system of units. The Metric system of units is widely used in almost all countries. Several metric systems of unit measurement are the MKS system, CGS system, and the SI system. The SI system of units is internationally accepted and hence it is called the international system of units.

1. Imperial and US Customary Units

Imperial and US Customary units are derived from early English units and are closely related to each other. Imperial units are used in the UK whereas the customary units are used in the United States of America.

1. Natural Units

Natural units are used to measure the physical quantities in terms of natural constants. Natural units include geometric units, Planck’s unit, Stoney units, Schrodinger units, and electronic units.