The scale of a drawing is given as 1 : 20. What is the representative fraction?
1/20
Understanding Drawing Scale and Representative Fraction
A drawing scale represents the ratio between the length of an object on a drawing and its actual length in reality. It tells us how much smaller (or larger) the drawing is compared to the real object. Scales are often expressed in different ways, such as:
- Engineers' Scale: e.g., 1 cm = 5 m
- Graphical Scale: A line divided into segments representing real-world distances.
- Representative Fraction (RF): A ratio or fraction where both sides have the same units, e.g., 1:100 or 1/100.
Calculating Representative Fraction from Scale
The question provides the scale of a drawing as a ratio: 1 : 20.
This ratio means that 1 unit of length on the drawing corresponds to 20 units of the same length in reality.
The Representative Fraction (RF) is defined as the ratio of the length of the drawing to the corresponding actual length of the object, with both lengths expressed in the same units.
Mathematically, the Representative Fraction (RF) is given by:
\(\text{RF} = \frac{\text{Length on drawing}}{\text{Corresponding actual length}}\)
In the given scale 1 : 20:
- Length on drawing = 1 unit
- Corresponding actual length = 20 units
Since the units are already the same (it's a ratio of units), we can directly substitute these values into the RF formula:
\(\text{RF} = \frac{1 \text{ unit}}{20 \text{ units}}\)
The units cancel out, leaving a dimensionless fraction:
\(\text{RF} = \frac{1}{20}\)
Analyzing the Options
Let's examine the provided options to find the calculated representative fraction.
- Option 1: 1/200
- Option 2: 1/20
- Option 3: 5/20
- Option 4: 20/2
Our calculated representative fraction is 1/20. Comparing this with the options, we find that Option 2 matches our result.
Let's look at why the other options are incorrect based on the given scale 1:20:
- 1/200: This would correspond to a scale of 1:200, not 1:20.
- 5/20: This fraction simplifies to 1/4. This would correspond to a scale of 1:4, which means the drawing is 1/4th the size of the object. This is not the given scale.
- 20/2: This fraction simplifies to 10/1. This would mean the drawing is 10 times larger than the object (a scale of 10:1), which is the opposite of what 1:20 implies (drawing is smaller).
Conclusion
The scale 1 : 20 directly translates to a representative fraction of 1/20. The representative fraction is simply this ratio expressed as a fraction.
| Scale Format | Meaning | Representative Fraction (RF) |
|---|---|---|
| 1 : 20 | 1 unit on drawing = 20 units in reality | 1/20 |
| 1 : 100 | 1 unit on drawing = 100 units in reality | 1/100 |
| 1 : 1000 | 1 unit on drawing = 1000 units in reality | 1/1000 |
Revision Table: Key Concepts for Scale and RF
| Term | Definition | Example (from 1:20 scale) |
|---|---|---|
| Drawing Scale | Ratio of drawing length to actual length | 1 : 20 |
| Representative Fraction (RF) | Drawing length / Actual length (same units) | 1/20 |
| Units | Must be the same for both drawing and actual length in RF calculation | If drawing is 1 cm, actual is 20 cm. If drawing is 1 inch, actual is 20 inches. RF is still 1/20. |
Additional Information: Applications of Representative Fraction
The Representative Fraction (RF) is a universal way to express scale because it is dimensionless and unit-independent. This makes it very useful in various applications like:
- Mapping: RF is commonly used on maps to indicate the scale. A map with an RF of 1/100,000 means 1 unit on the map represents 100,000 units in the real world, regardless of whether the unit is cm, inch, etc.
- Technical Drawings: While scales like 1:10 or 1:50 are common, the underlying concept can be expressed as an RF.
- Model Making: If a model is built to a scale of 1:25, the RF is 1/25.
Understanding RF allows for easy conversion between drawing measurements and real-world measurements, regardless of the units being used, as long as consistency is maintained within the ratio.
Important Questions from Linear Measurement
The engineer's chain is typically:
Correction for pull or tension in a tape is given by
Cross-staff is used for:
An Engineer measured the distance between two locations on a plan having a scale of 1 cm = 50 m as 600 m. Later, however, he found that he used a wrong scale of 1 cm = 30 m to measure the distance. The true distance between the locations is:
The length of the chain is equal to _____.
