Unit Conversion

In the area of science and mathematics, it is needed many times to convert the units of some measurement into other units. It is termed as unit conversion. Sometimes it is more important while solving the problem. To carry out the calculations, mathematical conversions are being done. For example, to find the area of a rectangle, suppose the length is given in cm, and breadth is given in meter. Then for finding the area of it in a square meter, we have to convert cm unit to another meter unit. Therefore, one has to learn the concept and method of the conversion of units.

The use of one unit depends on the situation, like finding the area of a room expressed in meters but the length measurement expressed in centimetres. While understanding the concept of conversion of units we have to understand the relationship between units. This article will discuss the concept of unit conversion in a systematic manner with examples.

Introduction to the Unit Conversion

There are few things which we have to measure in our day-to-day activities. These are as follows:

• Speed
• Temperature
• Area
• Volume
• Mass

To measure the above quantities, we need units of measurements. Many times, when the units used for the measurement, which are not matching with the measurement given. Then some standard conversion procedures should be used for certain processes and applications. Converting these units to some extent, and it is understandable directly and applied properly.

To better understand it, let us consider the example of a person who is knowing only the metric system. The person cannot easily compute the height of a building measuring as 25 feet. Then, here converting 25 feet to meters will help the person to understand the height of the building.

Thus, unit conversion is the multi-step process which involves the multiplication or division by some numerical factor. Then selection of the correct number with the significant digits, and finally the rounding off of the values. Hence this multi-step process will have procedures including the rounding off the process for technical documents, specifications etc. Also, the necessary conversion factors will be specified in this procedure.

Importance of Mathematical Conversions

For most quantities, a unit is very much necessary to communicate the values of that physical quantity. Imagine we need to buy some rope to tie something onto the roof of the car. How would we tell the salesperson how much rope we need without using some unit of measurement?

But, all quantities will require the unit of their own. Using the physical laws we may represent the units of quantities as the combinations of units of the other terms. Therefore, only a small set of units is needed. These units will work as the base units, and other units will work the derived units. Derived units are a matter of convenience, as they should be expressed in terms of the basic units.

Different systems of units are based on the different choices of base units. The widely applicable system of units is the International System of Units or the SI. There are seven SI base units, and all other SI units further can be derived easily from these base units.

The seven base SI units are as follows:

• Length: m (meter)
• Mass: kg (kilogram)
• Time: s (second)
• Electric Current: A (Ampere)
• Thermodynamic Temperature: K (degrees Kelvin)
• Amount of Substance: mol (mole)
• Luminous Intensity: cd (candela)

Thus to get the accuracy and avoid confusion in the measurement. Then we need to convert one unit to another. For instance, we may not measure the length of a pencil in the unit of kilometres. Therefore, we have to convert the kilometre into the centimetre unit. Normally, the conversion of one unit to another unit of the same quantity is performed using the multiplicative conversion factors.

Unit Conversion Procedure

If someone has an amount of unit of A, then how much will be the value in unit B?

Such problems will be answered through the unit conversion process. It is involving the following points:

• Dimensional Analysis
• Principle for quantities defined as equalities
• Conversion Factor giving the expression for the relationship between units.

Steps for the conversion is as follows:

• What do you have? This will be the Starting Units.
• What do you want? This will be the Desired Units.
• Identify the Conversion Factor. This will be the ratio or linking Units.
• Cancel the units where we may do the mathematical process.

The process of conversion depends on the specific situation as well as the intended purpose. This may be governed by some regulations and the published standards. Some conversions from one system of units to another need to be exact, without increasing or decreasing the precision value of the first measurement. Sometimes, it is termed as the soft conversion. By contrast, a hard conversion may not be exactly equivalent.

The conversion factor will be doing the change of the units of the measured quantity, without changing its value. Because of the identity property of the multiplication process, the value of a quantity will not change with the multiplication by one. Also, if the numerator and denominator of a fraction are equal to each other, then the fraction will be one.

FAQs about Unit Conversion

Q.1: Convert 2 cm to the km unit.

Step 1: Draw the line or box as shown below,

km

hm

dam

m

dm

cm

mm

Step 2: Then put 1 at the larger unit, which has to be converted.

Here we want to convert cm to the  km unit,

As km is the larger unit, so we need to put 1 under the corresponding column (km).

km 1

hm

dam

m

dm

cm

mm

Step 3: Now put 0 for all units till the smaller unit reached.

As we want to convert cm to km, hence put 0 till the corresponding smaller unit of cm.

km 1

hm 0

dam 0

m 0

dm 0

cm 0

mm

Thus, we see the conversion from a smaller to a larger unit. So, we need to divide the given length by 100000 conversion factor.

So, 2 cm =  \(\frac{2}{10000}\) km

i.e. 2 cm = 0.00002 km

Q.2: Convert the 5 grams to the milligrams.

Solution: We have to convert 5 grams to milligrams, means from larger unit to smaller unit.

As we know, 1 g = 1000 mg

Therefore 5 g = 5 × 1000 = 5000 mg

Q.3: What are the software tools needed for the unit conversion?

Solution: These are found in the function libraries of the applications like the spreadsheets databases and in the macro packages and plugins for many other applications. There are many standalone applications available also, offering thousands of the various units with conversions. Dimensional analysis is the process involving the conversion between units.

The International System of Units specifies many base units from which all other units of measurement are obtained. Derived units are hence based on those base units. The unit analysis in the form of proportional reasoning where a given measurement can be multiplied by the known proportion or ratio to give the result of having a different unit. The dimensional analysis also involves the use of conversion factors. These are the ratios of related physical quantities expressed in the desired units.