Units, Measurements and Conversions

Introduction

This article Units, Measurements and Conversions primarily introduces to the units that whole world is using in measuring quantities, for example how far is my city from another city, how heavy is the box of apples, how much time the train takes from one city to another city.

In general, we all know how all of these are measured lets say how far is my city from another city is measured in mile or kilometer, how heavy is the box of apples is measured as gram or kilogram and how much time the train takes from one city to another city is measured in minutes or hours.

So, the mile, kilometer, gram, kilogram, minutes and hours are known as units. These units are placed next to the number value of the quantity measured, for example the distance between two city is 10 kilometer then 10 is the number value and kilometer is the unit.

We will learn about various units that are used in day to day measurements, learn about which are the things that we can measure in measurements of quantities and to make them useful the units can be changed from one into another in conversion of units.

Units

Let’s start with definition of Unit. Unit is a standard that is used to measure quantities. Length is measured in centimeter, so centimeter is called as unit of length. Mass of an object is measured in kilogram, so kilogram is unit of mass. Time is measured in seconds, so seconds is unit of time. There are other units available to measure temperature, volume which are also frequently used in mathematics.

There are short forms available for all units. Kilometer are written as km, kilogram is written as kg and there are more abbreviations of units which we will summarize in following tables.

Basic units used in Maths

Quantity Name of Unit Symbol of Unit
Length Meter m
Mass Kilogram kg
Time Seconds s
Volume Litre l
Temperature Degree Celsius \(^o\)C

In the above table we have shown only one unit of length, mass, time, volume and temperature i.e. m, kg, s, l and \(^o\)C respectively, but there are more units available to measure these quantities. Let’s have a look at next tables which lists more units.

Units of Length

Name of Unit Symbol of Unit
Meter m
Centimeter cm
Millimeter mm
Kilometer km
Miles mi
Yards yd
Foot ft
Inch in

Units of Mass

Name of Unit Symbol of Unit
Kilogram kg
Gram g
Milligram mg
Pounds lbs
Ounce oz

Units of Time

Name of Unit Symbol of Unit
Hour hr
Minute m
Second s

Units of Volume

Name of Unit Symbol of Unit
Litre l
Millilitre ml
Cup C or c
Pint pt
Gallon gal

Units of Temperature

Name of Unit Symbol of Unit
Celsius \(^o\)C
Farenheit F
Kelvin k

Measurement of quantities

In the above topic units, we learned how units are used to express measurements of different type of quantities. A unit whether it is of length, mass or time, is available as even more than one unit. Like the available units of length are millimeter, centimeter, meter and kilometer.

In Measurement of quantities we will learn how these different type of units help in measurement. Can all types of units of length can be used in measuring distance between two cities or measuring length of a pencil? The real answer is no, we should not use all units of length to measure all types of lengths. The different units are meant to measure things depending upon if it is big or small. Let’s discuss them one by one.

Measurement of length

Distance between two cities are very long and the length of a pencil is lump sump about the length of a hand. If it is too long like distance between two cities we use kilometer or miles and for the length of a pencil which is short can be measured in centimeter. This is how we should know the purpose of a unit to measure things, is it meant to measure big like city distances or small like length of a hand.

Generally, we can notice kilometer or miles units while travelling on road, the milestones are written in kilometer that the destination city is 60 mile or 96 km far from here, the milestones are never written in millimeter or centimeter. Following is the table to take a quick look which units are considered as best to measure different types of length from daily life.

Quantity Best suitable units
Distance between two cities kilometer
Length of a car meter
Height of a person centimeter, meter

Measurement of mass

Heavy things like a big box of bananas are measured in kilogram and things with less weight like a pencil are measured in gram. Following is the table for few examples to take a quick look which units are considered as the best to measure mass.

Quantity Best suitable units
Mass of person kilogram
Mass of toothpaste gram
Mass of big box of bananas kilogram

Measurement of time

Long durations of time like how many vacations I will get is calculated in days not in hour or minutes or seconds. Shorter durations like cooking time to cook a cake is in minutes. Following is the table that has few examples of which units are considered as the best to measure time.

Quantity Best suitable units
Time to travel one country to another hour
Time to start a car’s engine second
Time to walk to next door market minute

Measurement of area

In geometry we come across many measurements that need area calculations like area of circle, surface area of sphere or area of lawn and there are many such examples. So, area is quantity that is measured in units of metre square (\(m^2\)) or centimeter square (\(cm^2\)).

Measurement of volume

In geometry volume measurements like volume of sphere or volume of cylinder or volume of a cup is measured in units of metre cube (\(m^3\)) or (\(cm^3\)).

Measurement of angle

Angles are also a quantity that can be measured and have units of degree (\(^o\)) or radian.

Conversion of units

Conversion of units are basically a necessary process to follow when one unit needs to be converted into another unit. Conversion of units can only be carried on same type of quantities, like length units can be converted into one another, mass units into another mass units. Conversion of units from one to another unit never changes the magnitude of measurement, the length or mass of a quantity remains the same.

Conversions are needed usually in cases such as while comparing which is bigger 2 cm or 2 m. For two measurements to be compared has to posses the same units. In above example 2 m needs to be converted into cm then we can compare its value with 2 cm and can check which is bigger.

Example

Which is bigger 2 m or 2 cm?

Convert 2 m into centimeter units.

We know 1 m = 100 cm. (See here)

2m can be written as 2 x 1 m

Therefore, 2 m = 2 x 1 m = 2 x 100 cm = 200 cm

2 m = 200 cm

Now, we can compare 2 cm and 200 cm and 200 cm is clearly bigger than 2 cm. That means 2m is bigger than 2 cm.

The above example is the basic conversion process to change one unit into another type of units. In all conversions we always need to know a unit conversion value, e.g. 1 m = 100 cm, it says one unit of meter is equal to 100 centimeter. So, this is unit conversion of 1m into centimeter.

Conversion of units of length

Length conversion table is an excellent tool that helps converting the units of length into each other.

Conversion table for length
Conversion table for length

In the conversion table we can move in left or right direction. Move right to convert kilo into centi, move left to convert deci into hecto. Then, we count the number of positions we move from left to right or right to left.

We add that much number of 0s next to 1 and make number like 10, 100, 1000 or 10000 etc. If the movement is from right to left then the unit to be converted is multiplied by this number and if the movement is from left to right then the unit number is divided by this number.

Example

Example of left to right movement

Convert 20 kilometer into centimeter.

So, the problem is to convert kilo into centi.

Step1: Find the direction of movement.

Here, as we need to change kilo into centi, so the direction of movement is left to right.

Step2: Find the number of positions to be moved.

Starting point is kilo and end point is centi. So, we start counting after hecto as Ist position, then deca as 2nd position, meter as 3rd position, deci as 4th position and centi as 5th position. The total number of positions moved are 5 from kilo to centi.

Step3: Make the conversion number.

So, the conversion number is formed by adding number of 0s next to 1 and the number of 0s are equal to the number of positions moved.

i.e. conversion number = 100000

Step4: Multiply the old unit with conversion number to get new units because we moved from left to right.

New units = 20 x 100000 = 2000000 centimeter

Example

Example of right to left movement

Convert 6 meter into hectometer.

So, the problem is to convert meter into hecto.

Step1: Find the direction of movement.

Here, as we need to change meter into hecto, so the direction of movement is right to left.

Step2: Find the number of positions to be moved.

Starting point is meter and end point is hecto. So, we start counting after deca as Ist position, then hecto as 2nd position. The total number of positions moved are 2.

Step3: Make the conversion number.

i.e. conversion number = 100

Step4: Divide the old unit with conversion number to get new units because we moved from right to left.

New units = \(\frac{6}{100}\) hectometer

Conversion of units of mass

Following figure shows the conversion table to convert units of mass. The steps to convert units of mass are same as those are explained in Conversion of units of length.

Conversion table for mass
Conversion table for mass

Conversion of units of volume

Following figure shows the conversion table to convert units of volume. The steps to convert units of volume are samesame as those are explained in Conversion of units of length.

Conversion table for volume
Conversion table for volume