Contents
Physics Topics can help us understand the behavior of the natural world around us.
What is a Measurement ? and How Distance Between Points Should be Measured ?
The length of the space between two points (or two places) is called distance. For example, the length of space between two places, Delhi and Agra, is 200 kilometres, so we say that the distance between Delhi and Agra is 200 kilometres. If the two points (or two places) are close by, the distance between them will be small.
On the other hand, if the two points (or two places) are far off, then the distance between them will be large. Actually, the terms “distance” and “length” are used in the same sense. So, when we say “measurement of distances”, we actually mean “measurement of lengths”. We will now learn the meaning of the term “measurement”.
Measurement
Measurement is a process of ‘comparing an object’ with a standard ‘unit of measurement’. For example, when we go to a cloth shop to buy cloth for making our school uniform, then the shopkeeper measures the cloth by comparing it with a standard unit of measuring length called “metre”. And when we go to a tailor for the stitching of school uniform, he takes our measurements by using a measuring tape.
The tailor has to make the measurements correctly for the proper stitching of clothes. If any of the measurements are made wrongly by the tailor, then the stitched clothes may not fit us properly. This is just one example of the importance of making proper measurements in our daily life.
Need of Standard Units of Measurement
In our daily life, we can use a variety of objects as units of measurement of length. For example, we can measure the length of an object by using ‘hand-span’, ‘forearm-length’ (called cubit), or ‘foot-step’ (called pace) as the emits of measuring length (see Figure).
In this case, the length of each one of these objects becomes a unit of measurement of length. But hand-span, forearm-length (cubit) and foot-step (pace) cannot be used as standard units of measurements because their length is not the same for all the persons. The length of hand-span, forearm-length (cubit) and foot-step (pace) of different persons is different (see Figure).
It varies from person to person. Thus, hand-span, forearm-length (cubit) and foot-step (pace) are not the standard units of measuring length. The length of foot, the length of fist (muthi) and the width of finger (angul) were also used as units of measurement in ancient times. These units also vary from person to person and hence they are not standard units of measuring length.
A unit of measurement which has a fixed value which does not change from person to person or place to place, is called a standard unit of measurement. For example, ‘metre’ is a standard unit of measuring length. Whether a metre is used by one person or another person, whether the metre is used in one country or another country, it always represents exactly the ‘same length’.
The length of metre does not change from person to person or place to place. In fact, wherever we go in the world, a metre has a fixed length, which never changes. Thus, a ‘metre’ means the ‘same length’ to everyone. So, metre is a standard unit of measuring length. It is necessary to have standard units of measurements for the sake of uniformity in measurements.
Every Measurement Consists of a Number and a Unit
The result of every measurement consists of two parts : The first part of the measurement consists of a number (1,2,3,4 … etc.) which tells us the ‘magnitude of measurement’ and the second part tells us the ‘name of the unit of measurement’. Thus, every measurement consists of a number and a unit.
For example, if the length of a table is expressed as 2 metres, then 2 is the number and metre is the unit. The number ‘2’ tells us the magnitude of the length of the table and ‘metre’ tells us the unit in which the length has been measured. By saying that the length of table is 2 metres, we mean that the length of the table is 2 times the length of unit of length called ‘metre’.
Please note that a measurement is not complete unless both, the number and the unit are mentioned. For example, if we say that the length of the table is ‘2’, it does not make any sense. But if we say that the length of table is ‘2 metres’, then the measurement is complete. So, we must write the units of measurement while expressing the lengths of various objects.
SI Unit of Length
In order to have a uniformity in the measurement of various physical quantities like length, mass and time, etc., the scientists all over the world have adopted ‘International System of Units’. The units of this system are called SI units (SI units is the short form of the French name ‘Systeme International d’ Unites’).
We can now say that the SI units are the standard units of measurement which are used in all the countries of the world. The SI unit of measuring length is metre. The symbol of metre is m. One sample of standard ‘metre’ is kept at the National Physical Laboratory in New Delhi.
The ‘metre’ measure used everywhere in our country is an exact copy of this National standard. The SI unit of measuring mass is ‘kilogram’ (kg) ; and the SI unit of measuring time is ‘second’ (s). We will study the SI units of mass and time in detail in higher classes.
Prefixes Used with SI Units
‘Prefix’ is a kind of word used ‘before the name’ of an SI unit to get a bigger value or a smaller value of the unit. Here we will give the meaning of only three common prefixes : kilo, centi and milli.
(i) Kilo is a prefix which denotes one thousand. That is :
‘kilo’ means ‘one-thousand’ or 1000
So, when we write ‘kilo’ before the unit of length ‘metre’, it becomes ‘kilometre’, which means 1000 metres. Thus, 1 kilometre = 1000 metres.
(ii) Centi is a prefix which denotes one-hundredth. That is :
‘centi’ means ‘one-hundredth’ or \(\frac{1}{100}\)
So, if we write ‘centi’ before the unit of length ‘metre’, it becomes ‘centimetre’ which means one-hundredth of a metre or \(\frac{1}{100}\) metre. In other words,
1 metre = 100 centimetres
(iii) Milli is a prefix which denotes ‘one-thousandth’. That is :
‘milli’ means ‘one-thousandth’ or \(\frac{1}{1000}\)
So, if we write ‘milli’ before the unit of length ‘metre’, it becomes ‘millimetre’ which means one-thousandth of a metre or \(\frac{1}{1000}\) metre. In other words,
1 metre = 1000 millimetres
Please note that the unit ‘kilometre’ is written in short form as ‘km’ ; the unit centimetre’ is written in short form as ‘cm’; whereas the unit ‘millimetre’ is written in short form as ‘mm’. Let us solve some problems now.
Example Problem 1.
The height of a person is 1.65 m. Express it in cm and mm.
Solution:
(i) In the first case we have to convert the height of 1.65 m (1.65 metres) into cm (centimetres). Now, we know that :
1 m = 100 cm
So, 1.65 m = 100 × 1.65 cm
= 165 cm
Thus, a height of 1.65 metres is equal to 165 centimetres.
(ii) In the second case, we have to convert the height of 1.65 m (1.65 metres) into mm (millimetres). Now, we know that :
1 m = 1000 mm
So, 1.65 m = 1000 × 1.65 mm
= 1650 mm
Thus, a height of 1.65 metres is equal to 1650 millimetres.
Example Problem 2.
The distance between Radha’s home and her school is 3250 m. Express this distance in km.
Solution:
In this problem, the distance is given in metres (m) and we have to convert it into kilometres (km). Now, we know that
1000 m = 1 km
Or, 1 m = \(\frac{1}{1000}\) km
So, 3250 m = \(\frac{1}{1000}\) × 3250 km
= 3.250 km
Thus, a distance of 3250 metres is equal to 3.250 kilometres.