Activity: To Make a Paper Scale of Given Least Count
Materials Required
- A4 size white paper or drawing paper
- Ruler with millimeter divisions
- Sharp pencil
- Fine-tip pen or marker
- Scissors
- Transparent tape (optional, for reinforcement)
- Calculator
Theoretical Background
A measurement scale is a tool used to measure length accurately. The least count of a scale is the smallest measurement that can be taken directly from the scale.
Understanding Least Count
The least count of a measuring instrument represents its precision. It is defined as the smallest division that can be measured directly using that instrument.
For a standard ruler (scale), the least count is typically 1 mm or 0.1 cm.
If we want to create a paper scale with a different least count (e.g., 0.2 cm or 0.5 cm), we need to design it such that:
\[ \text{Least Count} = \frac{\text{True Length}}{\text{Number of Divisions}} \]
Vernier Principle
We'll be using a principle similar to the Vernier scale, where we create an auxiliary scale that allows measurements smaller than the main scale divisions.
For a paper scale with least count 0.2 cm:
\[ 10 \text{ divisions on our scale} = 9 \text{ divisions on true scale} \]
\[ 1 \text{ division on our scale} = \frac{9}{10} \text{ division on true scale} \]
\[ \text{Least count} = 1 \text{ mm} - \frac{9}{10} \text{ mm} = 0.1 \text{ mm} = 0.01 \text{ cm} \]
Procedure
A. Creating a Paper Scale with Least Count 0.2 cm
- Draw a straight line about 15 cm long near the edge of the paper.
- Mark a starting point and label it as 0.
- Using your standard ruler, mark primary divisions at every 1 cm interval.
- For each 1 cm interval, divide it into 5 equal parts (each part will be 0.2 cm).
- Label each division properly.
- Draw appropriate tick marks with varying heights for better readability.
- Cut along the edge to produce your paper scale.
For a scale with least count 0.2 cm:
\[ \text{Number of divisions per cm} = \frac{1 \text{ cm}}{0.2 \text{ cm/division}} = 5 \text{ divisions} \]
So, we need to divide each centimeter into 5 equal parts, with each part representing 0.2 cm.
B. Creating a Paper Scale with Least Count 0.5 cm
- Draw a straight line about 15 cm long near the edge of the paper.
- Mark a starting point and label it as 0.
- Using your standard ruler, mark primary divisions at every 1 cm interval.
- For each 1 cm interval, divide it into 2 equal parts (each part will be 0.5 cm).
- Label each division properly.
- Draw appropriate tick marks with varying heights for better readability.
- Cut along the edge to produce your paper scale.
For a scale with least count 0.5 cm:
\[ \text{Number of divisions per cm} = \frac{1 \text{ cm}}{0.5 \text{ cm/division}} = 2 \text{ divisions} \]
So, we need to divide each centimeter into 2 equal parts, with each part representing 0.5 cm.
Diagrams and Illustrations
Example of a Paper Scale with Least Count 0.2 cm
Example of a Paper Scale with Least Count 0.5 cm
Worksheet Activities
Activity 1: Making a Paper Scale with Least Count 0.2 cm
| Step | Observation/Calculation | Check (✓) |
|---|---|---|
| Length of scale drawn | _____ cm | |
| Number of primary divisions | _____ divisions | |
| Number of subdivisions per cm | _____ subdivisions | |
| Calculated least count | _____ cm |
Activity 2: Making a Paper Scale with Least Count 0.5 cm
| Step | Observation/Calculation | Check (✓) |
|---|---|---|
| Length of scale drawn | _____ cm | |
| Number of primary divisions | _____ divisions | |
| Number of subdivisions per cm | _____ subdivisions | |
| Calculated least count | _____ cm |
Activity 3: Verification Exercise
Use your constructed paper scales to measure the following objects and record your readings:
| Object | Measurement with 0.2 cm scale | Measurement with 0.5 cm scale | Measurement with standard ruler |
|---|---|---|---|
| Length of your pencil | _____ cm | _____ cm | _____ cm |
| Width of your textbook | _____ cm | _____ cm | _____ cm |
| Length of your eraser | _____ cm | _____ cm | _____ cm |
Conclusion and Learning Outcomes
In this activity, you have:
- Created paper scales with specific least counts of 0.2 cm and 0.5 cm
- Applied mathematical concepts to create accurate measurement tools
- Understood the principle and importance of least count in measurements
- Practiced precision in measurements and scale creation
Note: The accuracy of your paper scale depends on the precision of your drawing and division. For better results, work on a flat surface and use a sharp pencil for marking divisions.
Self-Assessment Questions
- What is the least count of your standard ruler? How does it compare to the paper scales you created?
- If you want to create a paper scale with a least count of 0.25 cm, how many divisions would you need per centimeter?
- Calculate the least count of a scale where 4 divisions equal 1 cm.
- What are some practical applications where different least counts might be useful?
- If you were to create a paper scale with least count 0.1 cm, describe the process and calculations involved.
For question 3, the calculation would be:
\[ \text{Least Count} = \frac{\text{Length}}{\text{Number of Divisions}} = \frac{1 \text{ cm}}{4} = 0.25 \text{ cm} \]
For question 5, to create a paper scale with least count 0.1 cm:
\[ \text{Number of divisions per cm} = \frac{1 \text{ cm}}{0.1 \text{ cm/division}} = 10 \text{ divisions} \]