ICSE Class 6 Physics Chapter 1 Measurement

Measurement

Syllabus

1. Measurement - Its importance - units of measurement - the need for standard units of measurement - S.I. Units - length, mass, area, volume, time, temperature - correct abbreviations - rules to follow to write units correctly. Simple multiples and sub-multiples of these units, understanding the prefixes - centi, milli and kilo.

2. Measurement of length

Using a ruler correctly, without parallax error (E).

Estimating distances keeping in mind the size of 1 cm and 1 mm (E). Measuring small lengths - e.g., thickness of a coin, diameter of a wire (E). Measuring the length of line it is not straight, using a string (E).

3. Measuring mass, area, volume / capacity - units, multiples and sub-multiples and correct abbreviations.

Survey to find out which items are sold by mass and which by volume (E). Finding approximate areas of irregular shapes using a square centimetre grid (E).

4. Measuring time - common units.

Reading a twenty-four hour clock - air/train schedules (E).

Measuring time for common, daily activities (E).

Learning to count seconds - approximately (E).

5. Measuring temperature - Celsius scale - the two fixed points. Commonly measured temperatures - maximum-minimum thermometer - temperature of the human body.

Reading a laboratory thermometer (E). Reading a clinical thermometer (E).

6. Approximations - when do we need very accurate measurements ?

Taking many measurements and finding an average.

Finding the average pulse of the class and the range of the pulse rate of the students (E).

Standard Weights and Measures - to avoid being cheated in commercial transactions.

Teacher's Note

Measurement connects abstract numbers to real-world objects, helping students understand that mathematics is a practical tool for solving everyday problems.

Measurement - Its Importance

Measurement is necessary in our life. Daily, we come across many things which we have to measure. When we visit a grocery shop to buy rice, sugar, etc., we ask the shopkeeper to weigh them because we have to calculate the amount to be paid with respect to their weight. Similarly, we need to measure the height and weight of students in our school to check up their body growth. Thus, measurement is an essential need to keep accuracy in our various day-to-day activities. Without actual measurement, we cannot make a correct judgement about the length, height, area, volume, mass and temperature of a given object. Our rough estimate may give a wrong answer. Let us consider some more examples to know the importance of measurement.

Teacher's Note

Students learn that vague estimations can lead to serious consequences, from ill-fitting clothes to incorrect medical dosages.

Example 1: Two lines are given below. Can you guess which line is longer?

At a glance, line B seems to be longer than line A. Now measure both the lines with the help of a scale. You will find that both of them are equal.

Example 2: Some orange juice is kept in two glasses, as shown below. Can you guess which glass has more juice? It is difficult to answer without measuring their actual volumes.

Example 3: A tailor has to stitch a new dress for you. Think! What will happen if he stitches it without taking your measurement?

Example 4: When you feel sick, your mother measures your body temperature with the help of a thermometer. The thermometer shows 101°F temperature. Do you have fever (temperature)? Yes, since the normal body temperature is 98.6°F. It means that on measuring your body temperature, she would know exactly whether you have fever or not.

It is clear from the above examples that measurement has great importance in our daily life.

We frequently come across questions like, how big or small, how long or short, how many in number, etc. Measurement is the only solution to all these questions.

Measurement is a comparison of an unknown quantity with a known fixed quantity of the same kind.

Physical Quantity

A quantity that can be measured is called a physical quantity. Length, time, volume, and temperature are some examples of physical quantity.

Physical quantities are of two types

1. Fundamental physical quantities or fundamental quantities

The quantities which are completely independent of each other and do not depend upon any other quantity are known as fundamental quantities e.g., mass, length, time, temperature, etc.

2. Derived physical quantities or derived quantities

The quantities which are obtained by combining two or more fundamental quantities are known as derived quantities. For example, area (depends on length and breadth), density (depends on mass and volume), speed (depends on distance and time), etc. are derived quantities.

Units Of Measurement

When we measure any physical quantity, what we actually do is that we compare it with a known standard. The standard of comparison is called a unit. The need of a standard unit was felt because units kept changing from place to place. A unit is a fixed quantity which is accepted as a standard by people all over the world.

Teacher's Note

Understanding units helps students appreciate why international standards exist - so a kilogram means the same thing everywhere in the world.

Nowadays, to measure length, we use the unit "metre" (m). People in ancient times used their footstep, arm length (cubit), hand span, ropes, sticks, etc. to measure length. One cubit was the length from the elbow to the tip of the middle finger of a person's hand.

Similarly, a hand-span was the length from the tip of the thumb to the tip of the little finger when they are stretched completely.

In the past, when an object was measured with a hand-span, its length varied from person to person. The simple reason for the variation was the difference in the size of the hand-span of each person. Thus, this system of measurement was felt inconvenient as well as inaccurate.

To avoid confusion, scientists evolved rulers. Now, if we take two rulers and measure the same object, say, a table, both the rulers will give us the same measurement. Why? It is simple, because the rulers are calibrated (marked) with the standard units of measurement but hand-spans are not.

Similarly, you cannot use a bowl to measure the exact volume of a liquid like milk or oil.

When we had no means of weighing, seeds and stones were the only standards to measure mass.

Hence, to express the result of a measurement of a physical quantity, we must know:

(a) the unit in which the quantity is to be measured.

(b) the numerical value which expresses how many times the above mentioned unit is contained in the given quantity.

Example: If the length of a piece of cloth is 10 metres, it means that the length is measured in the unit metre and this unit is contained 10 times in the length of that piece of cloth.

Thus, a measurement consists of two parts - the magnitude (or number) and a unit. The physical quantities are the product of magnitude and the unit, i.e.

\[Q = n \times u\]

Where, Q => Physical quantity

n => Magnitude

u => Unit

For example - When we measure the mass of sugar as 15 kg, then,

15 - is the magnitude,

kg - is the unit and

mass - is the physical quantity.

Need for Standard Units of Measurement

In the past, different units were used for measurement in different countries. To maintain uniformity in measurement, scientists from all over the world accepted some of the units as standard units. Considering the fundamental quantities as length, mass and time, the three systems - MKS (Metre, Kilogram and Second), CGS (Centimetre, Gram and Second) and FPS (Foot, Pound and Second) were developed.

Out of the three systems, the MKS system was widely accepted. Since the comparison of data was difficult with a large number of units, the General Conference of Weights and Measures, in 1960, adopted a system of units commonly known as S.I. units. S.I. stands for Syste-me Internationale d-Unites (in French) or International System of Units (in English). The S.I. units of measurement are standard units and are adopted for the purpose of uniformity.

The unit that could be used everywhere as a basic unit of measurement is called a standard unit.

Fundamental Units of S.I. System

The units that we use to measure fundamental quantities are called fundamental units.

The S.I. system has nine basic or fundamental units. Commonly used fundamental units and their standard symbols are given in Table 1.1.

Some standard conventions followed in the usage of S.I. units.

Whenever we write S.I. units and their symbols, we follow certain conventions. These conventions are as follows:

Symbols used for units are always written in small letters (other than the names of scientists). For example:

Symbol of kilogram - kg and not Kg

Symbol of metre - m and not M

Symbol of second - s and not S

Symbol for a unit named after a scientist is always written with a capital letter. For example:

Symbol of Fahrenheit - °F, and not °f

Symbol of Ampere - A and not a

Symbol of Newton - N and not n

Symbol of Kelvin - K and not k

Symbols are not followed by full stops. For example:

Symbol of Fahrenheit - °F and not °F.

Symbol of metre - m and not m.

Symbol of kilogram - kg and not kg.

However, we may use a full stop if the unit is written at the end of a sentence.

Symbols for units remain unaltered in the plural, that is, the symbols for units are never written in plural, but when written in words, plurals are used. For example:

Symbol for 10 kilograms is 10 kg (and not 10 kgs)

Symbol for 20 metres is 20 m (and not 20 ms)

If we are writing the full form of a unit, we start with a small letter. For example:

kelvin and not Kelvin,

metre and not Metre,

newton and not Newton,

celsius and not Celsius.

Negative powers are used for compound units formed by dividing one unit by the other. For example, the unit of speed is metre/second. It is expressed as m-1.

The National Physical Laboratory (NPL), New Delhi, is responsible for maintaining the national standards for all the basic (base) units in India.

Multiple Units

To measure the distance between two far-off cities, say, Delhi to Mumbai, measuring in metres is not only difficult but very inconvenient too. Hence, we use some bigger unit, say, kilometre, which is a multiple of metre.

1 kilometre = 1000 metres or 103 m

In short, 1 km = 1000 m

Units which are used to measure large quantities are called multiple units.

Example: If the distance between Delhi and Agra is 200,000 metres, for convenience, it is expressed as 200 kilometres or 200 km.

Sub-multiple Units

Similarly, if we are trying to measure the length of an eraser or a pen, or, say, our nails, we again cannot depend on the unit metre but we need some smaller or sub-multiple units like centimetre (cm), millimetre (mm), decimetre (dm), etc.

Units which are used to measure smaller quantities are called sub-multiple units.

1 m = 100 cm or 1000 mm

1 cm = 10 mm

For example, if the diameter of a coin is 2 x 10-2 metres, it is expressed as 2 centimetres or 2 cm.

Some very old units are still accepted in terms of S.I. standards for our convenience. For example:

1 yard = 0.9144 m-

1 inch = 2-54 cm-

1 pound = 0-454 kg-

1 foot = 30-48 cm-

Example: Tanu-s house is 3250 metres from her school. Express this distance in kilometres.

Solution: Distance = 3250 m.

we know, 1 km = 1000 m

So, Distance = \[\frac{3250}{1000}\] km = 3.25 km

Teacher's Note

Learning about multiple and sub-multiple units helps students understand why we express a city's distance in kilometers but a pencil's thickness in millimeters.

This is a preview of the first 3 pages. To get the complete book, click below.