MATHS
QUERY

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
cities is 10 kilometers, 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.

Let’s start with the definition of Unit. **Unit is a standard that is used to measure quantities**. Length is
measured in centimetres, so centimetre is called a unit of length. Mass of an object is measured in kilograms,
so kilogram is unit of mass.
Time is measured in seconds, so seconds is a 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 is written as km, kilogram is written as kg and there
are more abbreviations of units which we will summarize in following tables.

Quantity | Name of Unit | Symbol of Unit |
---|---|---|

Length | Meter | m |

Mass | Kilogram | kg |

Time | Seconds | s |

Volume | Litre | l |

Temperature | Degree Celsius | °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 °C respectively, but there are more units available to measure these quantities. Let’s have a look at the next tables which list more different units.

Name of Unit | Symbol of Unit |
---|---|

Meter | m |

Centimeter | cm |

Millimeter | mm |

Kilometer | km |

Miles | mi |

Yards | yd |

Foot | ft |

Inch | in |

Name of Unit | Symbol of Unit |
---|---|

Kilogram | kg |

Gram | g |

Milligram | mg |

Pounds | lbs |

Ounce | oz |

Name of Unit | Symbol of Unit |
---|---|

Hour | hr |

Minute | m |

Second | s |

Name of Unit | Symbol of Unit |
---|---|

Litre | l |

Millilitre | ml |

Cup | C or c |

Pint | pt |

Gallon | gal |

Name of Unit | Symbol of Unit |
---|---|

Celsius | °C |

Farenheit | F |

Kelvin | k |

In the above topic units, we learned how units are used to express measurements of
different types 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 types of units help in measurement. Can all types
of units of length 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.

Distance between two cities is very long and the length of a pencil is a 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 centimetres.
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
kilometres 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 at 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 |

Heavy things like a big box of bananas are measured in kilograms and things with less weight like a pencil are measured in grams. Following is the table for a 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 |

Long durations of time like how many vacations I will get are calculated in days not in hours 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 |

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}.

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}.

Angles are also a quantity that can be measured and have units of degree ° or radian.

Conversion of units is 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 possess the same units. In the 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 centimetres.

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

Conversion table for length

In the conversion table we can move in the 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 numbers 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, 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 the 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 the 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 the 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 the meter into hecto.
**Step1:** Find the direction of movement.

Here, we need to change the meter into hecto, so the direction of movement is right to left.
**Step2:** Find the number of positions to be moved.

Starting point is the meter and the 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 the conversion number to get new units because we moved from
right to left.

New units =
$\frac{6}{100}$
hectometer

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

Conversion table for mass

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

Conversion table for volume