Measurements - Class 6 Notes & Olympiad Questions

Measurement

a) Measurement is the process of determining the quantity or size of something by comparing it to a known or standard value. In other words, it involves using a reference point or unit to express a physical quantity accurately.
b) In the past, people used various units to measure length, such as hand spans, cubits (the distance from the elbow to the tip of the middle finger), or feet. However, these units were not consistent across individuals and lacked accuracy due to variations in body proportions. To address this, scientists established a system of standard units of measurement to ensure uniformity and precision.

c) The International System of Units (SI) is the globally accepted standard system of measurement used by scientists worldwide. It provides a set of base units for measuring physical quantities such as length, mass, time, and temperature. Some of the SI units include:

1. Length: The unit for measuring length is the metre (m).
2. Mass: The unit for measuring mass is the kilogram (kg).
3. Time: The unit for measuring time is the second (s).
4. Temperature: The unit for measuring temperature is Kelvin (K).

d) These SI units form the foundation of modern scientific measurement and enable consistency and comparability across different fields of study.

Measurement of Length

a) Length is a measurement that refers to the distance between two points or objects.
b) In the International System of Units (SI), the standard unit for length is the metre (m), denoted by 'm'. It provides a consistent and universally accepted reference for measuring length.
c) There are various measuring devices that can be used to measure the length of an object. Common tools include a metre scale, measuring tape, Vernier callipers, and screw gauges.

d) Depending on the precision required, different devices may be used. For very small lengths, Vernier callipers and screw gauges are particularly useful.
e) In addition to the metre, there are several other units commonly used for measuring length. These units are derived from the metre and have specific relationships with it. The relationship between these units and the standard unit (metre) is as follows:

f) For example, to convert a metre to a kilometre, you divide the given value by 1000 since there are 1000 metres in 1 kilometre.

Similarly, to convert kilometres to metres, you multiply the given value by 1000, since there are 1000 metres in 1 kilometre.

g) These units provide a convenient way to express length in different contexts and scales. By using appropriate unit conversions, measurements can be easily converted from one unit to another based on their relationships with the standard unit (metre).

Correct Way to Measure Length

To measure length accurately, it is important to follow the correct procedure. Here are some key steps to ensure accurate length measurement:

1. Ensure proper contact

a) When using a measuring device, such as a scale or measuring tape, make sure it is placed in direct contact with the object along its entire length.
b) Avoid any gaps or overlaps that could lead to inaccurate measurements.

2. Compensation for scale imperfections

a) If the measuring scale is broken or worn out at the ends, it may affect the measurement.
b) In such cases, it is necessary to consider the zero mark as the full mark and subtract the value accordingly to obtain the correct reading.

3. Avoid parallax errors

a) Parallax errors occur when the eye is not directly above the point where the measurement is being taken.
b) This can lead to inaccurate readings. To avoid parallax errors, ensure that the eye is positioned directly above the point being measured.
c) This can be achieved by aligning the eye with the measuring device, such as a scale, in a way that the scale appears as a straight line without any apparent distortion.

Measurement of Length of Curved Line

a) When measuring the length of a curved line, you cannot directly use a metre scale or ruler. Instead, you can use a thread and a metre scale to measure the length indirectly.
b) First, place the thread along the curved line, following its shape as closely as possible. Mark the starting and ending points of the thread on the line to define the segment you want to measure.
c) Next, remove the thread from the curved line without altering its shape and place it on a flat surface. Straighten the thread as much as possible.
d) Using a metre scale or ruler, measure the length of the thread from the starting point to the ending point. Make sure the scale is in contact with the thread to get an accurate measurement.

Measurement of Mass

a) Measurement of mass involves determining the amount of matter present in an object. There are several devices that can be used to measure mass, including beam balances, spring balances, and electronic balances.

b) In the International System of Units (SI), the standard unit of mass is the kilogram (kg).
c) Other commonly used units of mass include the milligram (mg) and gram (g). Additionally, larger units such as the tonne or metric ton (t) are used for measuring very large masses.
d) Some conversion factors for mass are:

1. 1 gram (g) = 1000 milligrams (mg)
2. 1 kilogram (kg) = 1000 grams (g)
3. 1 quintal = 100 kilograms (kg)
4. 1 metric ton = 10 quintals

Measurement of Time

a) Time is a measure of the interval between two events or the duration of an event.
b) Various methods have been used throughout history to measure time. In ancient times, people relied on instruments like sundials and water clocks.
c) In modern times, we use a variety of timekeeping devices such as pendulum clocks, digital watches, and stopwatches.

d) The International System of Units (SI) establishes the second (s) as the standard unit of time.
e) Some common units of time and their relationships:

1. 1 minute = 60 seconds
2. 1 hour = 60 minutes
3. 1 day = 24 hours
4. 1 year = 365 days (in the Gregorian calendar)
5. 1 decade = 10 years
6. 1 century = 10 decades
7. 1 millennium = 10 centuries

Measurement of Temperature

a) Temperature is a measure of the degree of hotness or coldness of a body. It indicates the amount of thermal energy present in an object or substance.
b) Temperature can be measured using various instruments, including clinical thermometers for measuring body temperature and laboratory thermometres for scientific and industrial applications.

c) The International System of Units (SI) defines the Kelvin (K) as the standard unit of temperature.
d) In everyday use, the Celsius (°C) scale is commonly used. On the Celsius scale, the freezing point of water is defined as 0°C and the boiling point of water is defined as 100°C.
e) The normal body temperature for a healthy human is typically around 37°C.

Measurement of Area

a) Area refers to the extent or amount of surface occupied by an object or a shape. It is a measurement of the two-dimensional space within the boundaries of the object or shape.
b) The International System of Units (SI) defines the square metre (m²) as the standard unit of area.
c) It represents the area covered by a square with sides measuring one metre. Other common units of the area include the square centimetre (cm²), square millimetre (mm²), and square kilometre (km²). These units are used to measure areas of different magnitudes.

Measurement of the Area of an Irregular Surface

When dealing with irregular surfaces, one method to measure the area is by using graph paper. The steps to follow are:

a) Place the graph paper over the irregular surface, aligning it so that the edges of the surface are within the boundaries of the graph paper.
b) Observe the grid of small squares on the graph paper. Each square represents a unit of area.
c) Count the number of complete squares that are fully or partially covered by the irregular surface. Count only the squares that are fully within the boundaries of the surface.
d) If there are squares that are only partially covered, estimate the fraction of each square that is covered. For example, if a square is half-covered, consider it as half a square unit.
e) Add up the total number of complete squares and the partial squares to get an approximate measure of the area of the irregular surface.