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Unit Conversion refers to the process of changing one unit to another through various mathematical operations as per the requirement of processes. Conversion of units includes multiple steps like division or multiplication by a numerical factor and selection of the correct number of specific digits. Unit of Measurement is required to measure physical quantities such as temperature, area, volume, mass, and speed. Some units of measurement do not follow the standards applicable to certain applications and processes which is why it is necessary to convert them.
- The conversion of units plays an important role while performing calculations in our daily lives.
- For instance, a person aware of the metric system only won’t be able to easily understand the height of the building given as 40 feet.
- When feet is converted to metres, it is easy for him to understand and further apply the knowledge.
- A quantity can have different values when expressed in different measurement units.
- Before carrying out mathematical operations on quantities, they must be converted to a common unit.
Key Terms: Conversion of Units, Length, meter, feet, temperature, mass, volume, force, power, density
What is Unit Conversion?
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Conversion of units or unit conversion refers to the process of changing one unit to another measurement unit by multiplication or division by the conversion factors. Units are converted to numerical values and are expressed with scientific notations.
- Conversion of Units Table is used to convert the units.
- When bigger units are converted to smaller ones, the multiplication method is used.
- In the same way, when the smaller units are converted to bigger units, the division method is used.
ExampleMeter is converted to centimetres by the relation 1 m = 100 cm. |
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Unit Conversion of Length Units
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There are several direct methods to measure lengths such as a meter scale, vernier calliper, Screw Gauge, and a spherometer. Large distances are measured by the parallax method. There exists a wide range of lengths, from a tiny nucleus with the size of 10-16 m to 1026 m which is the size of the observable universe.
- To convert from mm to cm – divide by 10
- To convert from cm to m – divide by 100
- To convert from m to km – divide by 1000
- To convert from km to mile – multiply by 0.62
| Unit | Conversion Unit |
|---|---|
| 1 millimeter | 0.001 meter |
| 1 centimeter | 0.01 meter |
| 1 decimeter | 0.1 meter |
| 1 decameter | 10 meters |
| 1 hectometer | 100 meters |
| 1 kilometer | 1000 meter |
| 1 mile | 1.609344 kms |
| 1 light year | 0.946 x 1016 meter |
| 1 fermi | 1 x 10-15 meter |
| 1 angstrom | 1 x 10-10 m |
| 1 foot | 0.3048 m |
| 1 inch | 2.54 x 10-2 m |
Solved ExampleCalculate the height of the person 5’4 tall in metres. Solution – The conversion of height from feet to metres is done as – First, convert the number of feet to metres. Then, convert the number of inches to metres. Converting feet to metres, 5 ft × 0.305 = 1.53 metres Converting inches to centimetres, 3 inches × 2.54 = 7.62 cm = 0.0762 metres Adding these two, 1.53 metres + 0.0762 metres = 1.6062 metres. Therefore, the height in metres is 1.6062 metres. |
Mass Unit Conversion
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The basic property of matter which is not dependent on pressure or temperature is mass. Kilogram or kg is the SI unit of mass. Gravitational methods are used to measure bodies with large masses whereas a spectrograph is used to measure the mass of small objects.
- From mg to g – Divide by 1000
- From g to kg – Divide by 1000
- From kg to tonne – Divide by 1000
The mass conversion table is below:
| Unit of Mass | Conversion (grams) |
|---|---|
| 1 milligram | 0.001 gram |
| 1 centigram | 0.01 gram |
| 1 decigram | 0.1 gram |
| 1 decagram | 10 gram |
| 1 hectogram | 100 gram |
| 1 kilogram | 1000 gram |
| 1 stone | 6350.29 gram |
| 1 pound | 453.592 grams |
| 1 ounce | 28.3495 grams |
Read More: Fundamental Forces in Nature
Time Unit Conversion
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Time interval is measured by a clock that follows the atomic standard of time. Accurate measurement depends on the limit or resolution of the measuring instrument although all the measurements are approximate due to errors in the measurement. There are two types of errors in the measurement of time: systematic errors and random errors.
- Systematic errors are again subdivided into personal errors, instrumental errors, and imperfections in experimental technique or procedure.
- The least-count error is a list of random errors.
The time unit conversion table is as follows:
| Time | Time Conversion |
|---|---|
| 1 minute | 60 seconds |
| 1 hour | 60 mins or 3600 seconds |
| 1 day | 24 hours |
| 1 week | 7 days |
| 1 year | 365 days |
Density Unit Conversion
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By dividing the mass and volume of a substance, density can be obtained. The important density unit conversions are tabulated below.
| Density Unit | Conversion (cubic meter) |
|---|---|
| 1 slug / cubic ft | 515.4 kilogram /cubic meter |
| 1 pound/cubic in | 2.768 x 104 kilogram/cubic metre |
Viscosity Unit Conversion
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The viscosity Unit is pascal-second. The viscosity Unit Conversion Table is given below –
| Velocity Unit | Conversion (kg/ms) |
|---|---|
| 1 poise | 0.1 kg/m.s |
| 1 slug/ft | 4.79 x 101 kg/m.s |
Force Unit Conversion
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Force is defined as the product of mass and acceleration which can be expressed as Force = mass x acceleration = mass x (length)/(time). The conversion of unit of force is given in the table below.
| Force Unit | Conversion (Newton) |
|---|---|
| 1 dyne | 1 x 10-5 newton |
| 1 pound | 4.448 newton |
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Power Unit Conversion
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Power unit conversion table is as given below.
| Power Unit Conversion | Conversion (Watt) |
|---|---|
| 1 calorie/sec | 4.168 watt |
| 1 horsepower | 745.7 watt |
| 1 foot-pound/sec | 1.356 watt |
| 1 BTU/hr | 0.2930 watt |
| 1 erg/sec | 1x 10-5 watt |
Area Unit Conversion
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The area is considered the total amount of space that is covered by a two-dimensional shape. The unit conversion of the area is tabulated below:
| Area Unit Conversion | Conversion (Square meter) |
|---|---|
| 1 sq. inch | 6.4516 x 10-4 square meter |
| 1 sq. foot | 9.2903 x 10-2 square meter |
| 1 barn | 1 x 10-28 square meter |
| 1 sq. mile | 2.5888 x 106 square meter |
| 1 hectare | 1 x 104 square meter |
| 1 acre | 4.0468 x 103 square meter |
Energy Unit Conversion
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The most common energy unit is Kilowatt Hour. A unit of power can be converted into a unit of energy.
| Energy Unit Conversion | Conversion (Joule) |
|---|---|
| 1-litre atmosphere | 101.13 joule |
| 1 electron volt | 1.602 x 10-19 joule |
| I kilowatt hour | 3.6 x 106 joule |
| 1 calorie | 4.168 joule |
| 1 erg | 1 x 10-7 joule |
| 1 foot-pound | 1.356 joule |
| 1 BTU | 1055 joule |
Volume Unit Conversion
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Volume is a physical quantity that is free of mass and time. It has three dimensions in length and zero dimensions in mass and time. The conversion table of unit of volume is given below.
| Measurement of Volume | Conversion (Liter) |
|---|---|
| 1 cubic foot | 28.316 liter |
| 1 gallon | 3.785 liter |
| 1 cubic inch | 1.639 x 10-2 liters |
| 1 kiloliter | 1000 liters |
| 1 hectoliter | 100 liters |
| 1 decaliter | 10 liters |
| 1 centiliter | 0.01 liter |
| 1 milliliter | 0.001 liter |
Things to Remember Based on Unit Conversion
- A dimensional equation is an equation obtained by solving a physical quantity with its dimensional formula.
- Unit of measurement is used to measure physical quantities.
- Unit conversion is necessary to find numerical solutions directly and easily.
- Three basic units of measurement are meter, gram and litre.
- When bigger units are converted to smaller ones, multiplication is used.
- When smaller units are converted to bigger ones, the division is used.
Previous Year Questions (PYQs)
- A man of mass of 100 kg is standing on a platform… (BITSAT 2012)
- Four identical particles each of mass ''m'' are arranged…
- Two particles of mass 5 kg and 10 kg respectively are… (NEET 2020)
- What is the distance of the centre of mass of a half ring from the centre…
- A boy of mass 50kg is standing at one end of the boat of… (CBSE Class XII)
- Four particles of masses m, 2m, 3m and 4m are arranged… (AMUEEE 1999)
- The centre of mass of three particles of masses 1 kg, 2 kg… (JCECE 2010)
- Three particles of masses 1 kg, 2 kg and 3 kg are situated at the corners…
- The motion of the centre of mass is the result of… (JKCET 2007)
- A uniform disc of radius R is put over another uniform disc of...
Sample Questions Based on Unit Conversion
Ques: How many square yards are there in a room of 10 ft by 12 ft which has an area of 120 ft? (1 Mark)
Ans: 120 ft 2 = 120 ft 2 x 1 yard2 / (3)2 ft 2
= 120 yard2/9
=13.33 yard2
Ques: Calculate the density of a substance of 5.74 g which occupies 1.2 cm3. (1 Mark)
Ans: Density = mass/volume
= 5.74/1.2 g cm-3
= 4.8 g cm-3
Ques: Calculate the height of a person in meters whose height is 5’3”. (2 Marks)
Ans: By converting feet to meters, 5ft x 0.305 = 1.53 meter
By converting inches to centimeters, 3 inches x 2.54 = 7.62 cm = 0. 0762 meters
Adding the two conversions, 1.53 meter + 0.0762 meters = 1.6062 meters
Ques: Calculate the size of the atom if the size of a nucleus is scaled to the tip of a pin. The range of the nucleus is 10-15 to 10-14 m and the size of the pin is assumed to be in the range 10-5 m 10-4 m. (2 Marks)
Ans: Range of the nucleus = 10-15 to 10-14 m and range of the pin = 10-5 m 10-4 m.
The scaling up is happening with 1010. The size of an atom with 10-10 m will be scaled up to a size of 1 m. the size of the tip of a sharp pin is equal to the size of the nucleus in an atom.
Ques: Under normal atmospheric pressures, frozen carbon dioxide or dry ice changes its state at 75.8 degrees Celsius. Calculate the temperature in Fahrenheit. (2 Marks)
Ans: To convert celcius to farenheit,
°F = 9/5° C + 32 = 1.8°C + 32
Thus,
°F = 1.8 (-78.5) + 32
= 141.3 + 32
= -109.3 °F
At the temperature of -109.3 °F, dry ice sublimes under normal condition
Ques: A simple pendulum has a period of oscillation given as T = 2Π√(l/g) . The value of L is given as 20.0 cm which is equivalent to 1 mm accuracy. The period of 100 oscillations is noted as the 90s. find the accuracy in % error. (2 Marks)
Ans: g = 4Π2 (L/T2)
T= t/n and \(\Delta\)T = \(\Delta\)t/n
Therefore, \(\Delta\)T/T = \(\Delta\)t/t
\(\Delta\)g/g = (\(\Delta\)L/L) + 2(\(\Delta\)T/T)
= 0.1/20.0 + 2(1/90)
= 0.027
Thus, the % error in g = 100 x ?g/g = 100 x 0.027 = 2.7 %
Ques: If the heart beats once in 0.8 sec, calculate the number of times the heart of a human being will beat. (2 Marks)
Ans: The heartbeats once in 0.8 sec
Therefore, the number of times the heart beats in 0.8 sec = 1/(0.8 ) = 10/8 beats
Therefore, the number of times the heart beats in 10 years
10/8 x 365 x 24 x 60 x 60 beats = 3.942 x 108 beats
Ques: The measurement of a swimming pool is 11.0 feet by 11.0 feet and a depth of 8.00 feet. Calculate the volume of water required to fill the swimming pool. Given: 1 litre = 103cm3, 1 inch = 2.54 cm,1 foot = 12 inches. (3 Marks)
Ans: By converting the feet measurements, 11.0 feet = 11.0 feet x 12inch/1 foot x 2.5cm/1 inch
= 11.0 feet
= 335cm
8.00 feet = 8.00 feet x 12inch/1 foot x 2.5cm/1 inch
= 8.00 feet
= 243 cm
The volume of the swimming pool = 11.0 feet x 11.0 feet x 8.00 feet
= 335 cm x 335 cm x 243cm
= 27,270,675 cm3
Volume in liters = 2.7 x 107 cm3 = 2.7 x 107 cm3 . 1 litre/103cm3
The volume of the swimming pool = 2.7 x 104 litres
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