Construct a simple scale of 1:5 to show decimeters and centimeters and to read upto 1 meter! Show the length of 7.4 decimeters on it.
Answers
Answer:
Plain Scales: Plain scales read or measure upto two units or a unit and its sub-division, for example centimetres (cm) and millimetres (mm). When measurements are required upto first decimal, for example 2.3 m or 4.6 cm etc. It consists of a line divided into number of equal main parts and the first main part is sub-divided into smaller parts. Mark zero (O) at the end of the first main part. From zero mark numbers to the main parts or units towards right and give numbers to the sub-divisions or smaller parts towards left. Give the names of the units and sub-units below clearly. Indicate below the name of the scale and its R.F clearly.
The construction of the plain scale is explained below by a worked example.
W E 1.1 A 3 cm long line represents a length of 4.5 metres. Extend this line to measure upto 30 metres and show on it units of metre and 5 metre. Show the length of 22 metres on this line. Fig 1.10
i) The scale has to represent meter and 5 meters, hence it is a Plain scale.
ii) Given that 3 cm represents 4.5 meters or 450cm, Hence 1 cm represents 450/3=150 cm, hence scale is 1 cm=150 cm or 1:150: R.F=1/150
iii) Maximum length to read is 30 meters; Length of the scale is 20 cm. i.e. (1/150)x30x100 = 20cm
Construction:
Draw a straight line of 20cm length and divide into 6 equal parts.
Divide again first part into 5 equal parts. Give numbers as shown. To represent 22 meters, take 4 main parts to represent 20 meters and 2 small parts to represent 2 meters. Give names as A and B so that the distance between A and B is 22 meters as shown.
Note: Assume height of the plain scale as 1 cm.
Construct a plain scale of 1:5 to show decimeters and centimeters and to read upto 1 metre. Show the length of 7.4 decimeters on it.
i) The scale has to represent decimeter and 1/10 of decimeter.
ii) Given that the scale is 1:5 that is R.F=1/5
iii) Maximum length to read is 1 meter; Length of the scale=(1/5)x1x100=20cm
Construction:
Draw a straight line of 20cm length and divide into 10 equal parts.
Divide again first part into 10 equal parts. Give numbers as shown. To represent 7.4 decimeters, take 7 main parts to represent 7 decimeters and 4 small parts to represent 0.4 decimeters. Give names as A and B so that the distance between A and B is 7.4 decimeters as shown.
Diagonal Scales:
Diagonal scales are used to read or measure upto three units.
For example: decimeters (dm), centimeters (cm) and millimeters (mm) or miles, furlongs and yards etc. This scale is used when very small distances such as 0.1 mm are to be accurately measured or when measurements are required upto second decimal.
For example: 2.35dm or 4.68km etc.
Small divisions of short lines are obtained by the principle of diagonal division, as explained below:
Principle of diagonal scale: To divide a given line AB into small divisions in multiples of 1/10 its length for example 0.1AB; 0.2AB etc. as shown in
Explanation:
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- Plain scales read or measure up to two units or a unit plus its subdivisions, such as centimetres (cm) and millimetres (mm) (mm).
- When exact measures to the first decimal are required, such as 2.3 m or 4.6 cm, etc.
- It is made up of a line that is divided into a number of equal main sections, with the first main portion being further divided into smaller parts.
- Mark zero (O) at the end of the first main part. From zero mark numbers to the main parts or units towards right and give numbers to the sub-divisions or smaller parts towards left.
- Give the names of the units and sub-units below clearly.
- Indicate below the name of the scale and its R.F clearly.
Construct a plain scale of 1:5 to show decimeters and centimeters and to read upto 1 metre. Show the length of 7.4 decimeters on it.
i) The scale has to represent decimeter and 1/10 of decimeter.
ii) Given that the scale is 1:5 that is R.F=1/5
iii) Maximum length to read is 1 meter; Length of the scale= (1/5)x1x100=20cm
Construction:
- Draw a straight line of 20cm length and divide into 10 equal parts.
- Divide again first part into 10 equal parts.
- To represent 7.4 decimeters, take 7 main parts to represent 7 decimeters and 4 small parts to represent 0.4 decimeters.
- Give names as A and B so that the distance between A and B is 7.4 decimeters.
Diagonal Scales:
- Diagonal scales are used to read or measure upto three units.
- For example, decimeters (dm), centimeters (cm) and millimeters (mm) or miles, furlongs and yards etc.
- This scale is used when very small distances such as 0.1 mm are to be accurately measured or when measurements are required upto second decimal.
For example: 2.35dm or 4.68km etc.
- Small divisions of short lines are obtained by the principle of diagonal division, as explained below:
- Principle of diagonal scale, To divide a given line AB into small divisions in multiples of 1/10 its length for example 0.1AB; 0.2AB etc.
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