• Written By Priya_Singh
  • Last Modified 27-10-2022

Conversion of Units: Definition, Measurements and Examples

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Unit of Conversion is a multi-step process involving multiplication or division by a numerical factor. Weight, distance, and temperature can all be measured in various ways. When it comes to calculations in Mathematics or other subjects, or in day-to-day lives, the knowledge of conversion of units plays a vital role.

A certain quantity can have different values when expressed in other units. So, for carrying out any mathematical operation on two quantities, we must always convert all the values to a common unit before carrying out the calculations.

Thus, the conversion of units is a fundamental and crucial concept that needs to be learnt to solve any mathematical problem. This article will learn about the unit conversion with various solved examples.

What is Unit Conversion?

Conversion of one unit to another unit of measurement for the same quantity using multiplication/division by conversion factors is known as unit conversion.
The units are expressed using scientific notation and converted into numerical values as per the quantities.

For Example: We can convert meter to centimeter by using the relation \({\rm{1 m}}\,\,{\rm{ = }}\,{\rm{100}}\,{\rm{cm}}\,\) as
\({\rm{50 cm}}\,{\rm{ = }}\,{\rm{50}}\,\, \times \,1\,{\rm{m = 50}}\,\, \times \,100\,{\rm{cm}}\,{\rm{ = }}\,{\rm{5000}}\,{\rm{cm}}\)

What is Conversion of Units Table?

When the bigger units are converted to smaller units multiplication method is used. Similarly, when the smaller units are converted to bigger units, the division method is used. The conversion of units table is given below:

Length units How to convert
From \({\rm{mm}}\) To \({\rm{cm}}\,\) Divide by \(10\)
From \({\rm{cm}}\,\) To \({\rm{m}}\,\) Divide by \(100\)
From \({\rm{m}}\) To \({\rm{km}}\) Divide by \(1000\)
From \({\rm{km}}\) To \({\text{mile}}\) Multiply by \({\rm{0}}{\rm{.62}}\)
Area Units  
From \(mm^2\) To \(cm^2\) Divide by \(100\)
From \(cm^2\) To \(m^2\) Divide by \(10,000\)
From \(m^2\) To \(km^2\) Divide by \(1,000,000\)
Volume Units  
From \({\rm{c}}{{\rm{m}}^3}\) To \({\rm{d}}{{\rm{m}}^3}\) Divide by \(1000\)
From \({\rm{d}}{{\rm{m}}^3}\)
To \({{\rm{m}}^3}\)
Divide by \(1000\)
From \({\rm{d}}{{\rm{m}}^3}\) To \({\text{Litre}}\) Multiply by \(1\)
From \({\rm{d}}{{\rm{m}}^3}\) To \({\rm{c}}{{\rm{m}}^3}\) Multiply by \(1000\)
From \({{\rm{m}}^3}\) To \({\rm{d}}{{\rm{m}}^3}\) Multiply by \(1000\)
Mass Units  
From \({\rm{mg}}\) To \({\text{g}}\) Divide by \(1000\)
From \({\rm{g}}\) To \({\rm{kg}}\) Divide by \(1000\)
From \({\rm{kg}}\) To tonne Divide by \(1000\)
Temprature Units  
From \(^ \circ {\rm{C}}\) To Kelvin \(({\rm{K}})\) Add \(273\)
\({\rm{(K)}}\) To \(^ \circ {\rm{C}}\) Minus \(273\)
From \(^ \circ {\rm{C}}\) To \(^ \circ {\rm{F}}\) \({\left( {\frac{9}{5}} \right)^ \circ }{\text{C}} + 32\)
From \(^ \circ {\rm{C}}\) To \(^ \circ {\rm{C}}\) \(\left( {\frac{5}{9}} \right)\left({^ \circ {\text{F}} – 32} \right)\)
Pressure Units  
From \({\text{Pa}}\) To \({\rm{kPa}}\) Divide by \(1000\)

What is Conversion of Units in CGS System?

The centimetre-gram-second unit system is a variation of the metric system that is based on the following

Centimetre \({\rm{(cm)}}\) as the unit of length.
Gram \({\rm{(g)}}\) as the unit of mass.
Second \({\rm{(s)}}\) as the unit of time.

What is Conversion of Units in SI System?

The SI system stands for “The System International Units”. It is a metric system that is based on the following:

QuantityUnitAbbreviation
Masskilogram\({\rm{Kg}}\)
Lengthmetre\({\rm{m}}\)
Timesecond\({\rm{s}}\)
TemperatureKelvin\({\rm{K}}\)
Amountmole\({\rm{mol}}\)
CurrentAmpere\({\rm{A}}\)
IntensityCandela\({\rm{Cd}}\)

What is Conversion of Unit Chart?

The following is a list of conversion units that are commonly used to measure various parameters:

Volume Unit Conversion
\(1\) millilitre \(0.001\) litre
\(1\) centilitre \(0.01\) litre
\(1\) decilitre \(0.1\) litre
\(1\) decalitre \(10\) litres
\(1\) hectolitre \(100\) litres
\(1\) kilolitre \(1000\) litres
\(1\) gallon \(3.785\) litres
\(1\)cubic foot \(28.316\) litres
Length Unit Conversion
\(1\)` millimetre\(0.001\) metre
\(1\) centimetre\(0.01\) metre
\(1\) decimetre\(0.1\) metre
\(1\) decametre\(10\) metres
\(1\) hectometre\(100\) metre
\(1\) kilometre\(1000\) metres
\(1\) inch\(2.54 \times {10^{ – 2}}\) metres
\(1\) foot\(0.3048\) metres
\(1\) angstrom\(1 \times {10^{ – 10}}\) metres
\(1\) fermi\(1 \times {10^{ – 15}}\) metres
\(1\) light year\(0.941 \times {10^{15}}\) metres
\(1\) mile\(1.609344\) kms
Mass Unit conversion
\(1\) milligram\(0.001\) gram
\(1\) centigram\(0.01\) gram
\(1\) decigram\(0.1\) gram
\(1\) decagram\(10\) grams
\(1\) hectogram\(100\) grams
\(1\) kilogram\(1000\) grams
\(1\) stone\(6350.29\) grams
\(1\) pound\(453.592\) grams
\(1\) ounce\(28.3495\) grams
Time Unit Conversion
\(1\) minute \(60\) seconds
\(1\) hour \(60\) minutes
\(1\) day \(24\) hours
\(1\) week \(7\) days
\(1\) year \(365\) days
Energy unit conversion
\(1\) BTU (British thermal unit) \(1055\) Joule
\(1\) erg \(1 \times {10^{ – 7}}\) Joule
\(1\) foot-pound \(1.356\) Joule
\(1\)  calorie \(4.186\) Joule
\(1\) Kilowatt-hour \(3.6 \times {10^6}\) Joule
\(1\) electron volt \(1.602 \times {10^{ – 19}}\) Joule
\(1\) litre atmosphere \(101.13\) Joule
Area Unit Conversion
\(1\) sq. inch \(6.4516 \times {10^{ – 4}}\;\) square metre
\(1\) sq. foot \(9.2903 \times {10^{ – 2}}\) square metre
\(1\) acre \(4.0468 \times {10^3}\) square metre
\(1\) hectare \(1 \times {10^4}\) square metre
\(1\) sq. mile \(2.5888 \times {10^6}\) square metre
\(1\) barn \(1 \times {10^{ – 28}}\) square metre
Power Unit Conversion
\(1\) erg/sec \(1 \times {10^{ – 5}}\) watt
\(1\) BTU/hr \(0.2930\) watt
\(1\) foot-pound/sec \(1.356\) watt
\(1\) horsepower \(745.7\) watt
\(1\) calorie/sec \(4.186\) watt
Force Unit Conversion
\(1\) dyne \(1 \times {10^{ – 5}}\) Newton
\(1\) pound \(4.448\) Newton

Conversion of Units of Measurement

We usually use Centimetres, Metres and Kilometres to measure any length.
Where Kilometre \( > \) Metre \( > \); Centimetre
\({\rm{(km)}}\,\,\,\,\,\,\,\,{\rm{(m)}}\,\,\,\,\,\,\,\,\,\,{\rm{(cm)}}\) Similarly, mass of an object is measured in kilograms \({\rm{(kg)}}\) and gram \({\rm{(g)}}\) Also,\({\rm{kg}}\,\,{\rm{ < }}\,\,{\rm{g}}\) And capacity (liquid) is measured in kilolitre \({\rm{(kL)}}\) and litre \({\rm{(L)}}\). Also, \({\rm{kL}}\,{\rm{ > }}\,{\rm{L}}\)

So, the three basic units of measurement are:
1. Metre-To measure the length.
2. Gram-To measure the weight.
3. Litre-To measure the capacity (liquid).

 \(1000\) Thousand\(100\) Hundred\(10\) Ten\(1\) One\(\frac{1}{{10}}\) Tenth\(\frac{1}{{100}}\) Hundredth\(\frac{1}{{1000}}\) Thousandth
Metric UnitKilo (\( \times 1000\))Hecto (\( \times 100\))Deca (\( \times 10\))Basic Unit \((1)\)Deci (\( \div 10\))Centi (\( \div 100\))Milli (\( \div 1000\))
LengthKilometreHectometreDecametreMetreDecimetreCentimetreMillimetre
MassKilogramHectogramDecagramGramDecigramCentigramMilligram
Capacity or volumeKilolitreHectolitreDecalitreLitreDecilitreCentilitreMillilitre

Measure of Length:

\(10\) Millimetres\(= \)\(1\) centimetre \({\rm{(cm)}}\)
\(10\) Centimetres\(= \)Decimetre \({\rm{(dm)}}\)
\(10\) Decimetres\(= \) Metre \({\rm{(m)}}\)
\(10\) Metres\(= \) Decametre \({\rm{(dam)}}\)
\(10\) Decametres\(= \) Hectometre \({\rm{(hm)}}\)
\(10\) Hectometres\(= \) Kilometres \({\rm{(km)}}\)

Measure of Mass:

\(10\) Milligrams\(= \)\(1\) Centigram \({\rm{(cg)}}\)
\(10\) Centigrams\(= \)\(1\) Decigram \({\rm{(dg)}}\)
\(10\) Decigrams\(= \)\(1\) Gram \({\rm{(g)}}\)
\(10\) Grams\(= \)\(1\) Decagram \({\rm{(dag)}}\)
\(10\) Decagrams\(= \)\(1\) Hectogram \({\rm{(hg)}}\)
\(10\) Hectograms\(= \)\(1\) Kilogr \({\rm{(kg)}}\)

Measure of Capacity:

\(10\) Millilitres\(= \)\(1\) Centilitre \({\rm{(cL)}}\)
\(10\) Centilitres\(= \)\(1\) Decilitre \({\rm{(dL)}}\)
\(10\) Decilitres\(= \)\(1\) Litre \({\rm{(L)}}\)
\(10\) Litres\(= \)\(1\) Decalitre \({\rm{(daL)}}\)
\(10\) Decalitres\(= \)\(1\) Hectolitre \({\rm{(hL)}}\)
\(10\) Hectolitres\(= \)\(1\) Kilolitres \({\rm{(kL)}}\)

Solved Examples On Conversion of Units

1. Convert the bigger unit into smaller unit: \(2\,{\text{kg}}\,500\,{\text{g}}\) to grams.

Solution: We have: \(2\,{\text{kg}}\,500\,{\text{g}}\)
We know that \(1\,{\text{kg}}\, = 1000\,{\text{g}}\)
So, \(2\,{\text{kg}}\, = 2000\,{\text{g}}\)
Hence, \(2\,{\text{kg}}\,500\,{\text{g=2500}}\,{\text{g}}\)

2. Convert the bigger unit into smaller unit:\(5\,{\text{m}}\,6\,{\text{cm}}\) to \({\text{cm}}\)

Solution: We have: \(5\,{\text{m}}\,6\,{\text{cm}}\)
We know that \(1\,{\text{m}} = 100\,{\text{cm}}\)
So, \(5\,{\text{m}} = 500\,{\text{cm}}\)
Now, \(500\,{\text{cm + 6}}\,{\text{cm}}\)
\( = 506\,{\text{cm}}\)
Hence, \(5\,{\text{m}}\,6\,{\text{cm}} = 506\,{\text{cm}}\)

3. Convert the smaller unit into bigger unit: \(2\,{\text{m}}\,45\,{\text{cm}}\) to \({\text{m}}\)

Solution: We have: \(2\,{\text{m}}\,45\,{\text{cm}}\)
We know that \(1\,{\text{cm}}\, = \frac{1}{{100}}\,{\text{m}}\)
So,\({\text{2}}\,{\text{m}}\, + \frac{{45}}{{100}}\,{\text{m}}\)
\({\text{=2}}\,{\text{m}}\, + 0.45\,{\text{m}}\)
\({\text{=2}}.45\,{\text{m}}\)
Hence, \({\text{2}}\,{\text{m}}\,{\text{45}}\,{\text{cm=2}}.45\,{\text{m}}\)

4. Convert the smaller unit into bigger unit: \(75000\,{\text{mL}}\) to \({\text{L}}\).

Solution: We have \(75000\,{\text{mL}}\)
We know that \({\text{1}}\,{\text{mL=}}\frac{1}{{1000}}\,{\text{L}}\)
So, \({\text{75000}}\,{\text{mL=}}\frac{{75000}}{{1000}}\,{\text{L}}\)
\({\text{75}}\,{\text{L}}\)br>

5. A gardener watered \(25\) nursery plants with one container of water. If the capacity of the container was about \({\text{75}}{\text{.250}}\,{\text{L}}\), and all plants got an equal quantity of water then how much water did each plant get?

Solution: For \(25\) nursery plants water available was \({\text{75}}{\text{.250}}\,{\text{L}}\))
For 1 nursery plant water available was \({\text{75}}{\text{.250}}\,{\text{L}} \div {\text{25}}\)
\({\text{=3}}{\text{.010}}\,{\text{L}}\)
Hence, \(1\) nursery plant will get\({\text{=3}}{\text{.010}}\,{\text{L}}\) water.

Summary

In the given article, the topics covered are about the conversion of units, explained about conversion of units. Then, we discussed the conversion table, conversion of units in CGS (centimetre-gram-second system) system, conversion of units in SI (System International Units) system, and explained the conversion chart and the conversion units of measurement. Later the solved examples are given, followed by frequently asked questions. Understanding the conversion of units is the essential thing that is very useful in our daily lives.

FAQs

Q.1. How do you calculate unit conversion?
Ans: The multiplication method is used to convert the bigger units to smaller units whereas the division method is used to convert the smaller units to bigger units.

Q.2. What is conversion formula?
Ans: The conversion formula is given below:
Conversion rate \(= \,\left( {\frac{{conversion}}{{total\,visitors}}} \right)\,\, \times \,100\)

Q.3. What is the conversion of units in maths?
Ans: When solving mathematical problems, it is necessary to convert units into smaller or larger units as required. And this process of converting units in mathematics is known as unit conversion.

Q.4. What are \(7\) basic units of measurements?
Ans: The seven basic SI units which are comprised are given below:
a. Length – meter \(({\rm{m}})\) b. Time – second \(({\rm{s}})\) c. Mass – kilogram \(\left( {{\rm{kg}}} \right)\) d. For substance – mole \(({\rm{mole}})\) e. Electric current – ampere \(({\rm{A}})\) f. Temperature – kelvin \(({\rm{K}})\) g. Luminous intensity – candela \(({\rm{cd}})\).

Q.5. What is unit converter?
Ans: Conversion of Units is the multi-step process that converts units of measurement for the same quantity. This usually includes division or multiplication by a numerical factor.

Q.6. How do you convert double units?
Ans: The double units can be converted in the following way:
\({\rm{36 km}}\,{\rm{/}}\,{\rm{hour}}\,{\rm{ = }}\,36\,\, \times \,\frac{{1000\,{\rm{m}}}}{{60\,\, \times \,\,60\,\sec {\rm{ond}}}}\, = \,10\,{\rm{m /}}\,{\rm{second}}\) So, here we can see that we must convert both units individually to convert double units.

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