Why Correct Scale Matters in Graphs and Exams
In Math, a scale is used to represent the relationship between the measurement of a model to the corresponding measurement of the actual objects. Without scale, there is no use of blueprints and maps. The scale helps us to represent real-world things on paper with comparatively smaller dimensions. Scale is most commonly used in maps and blueprints used for construction and buildings.
What is Scale Drawing in Math?
The scale is defined as the ratio of the length in a drawing or model to the actual length of an object in the real world.
For example, in scale drawing, anything you draw on a paper with a size of “1” would have a size of “10” in the real world. Hence, the measurement of 150 mm on the drawing would be 1500 mm in the real world.
Scale Drawing Vs Original
Let’s now learn how to write scales in drawing.
How To Write Scales?
A ratio is used to write scales. In other words, the scale is written as the length in the drawing, then a colon (:), then the actual length. This implies that:
The scale of Drawing = Length of Drawing: Actual Length
Similarly, we have:
Map Scale= Map Distance: Actual Distance
How Is Scale Expressed?
A scale is expressed in the following two ways.
You can use units in scale such as 1 cm to 1 km.
Also, without clearly mentioning units such as 1: 100 000. (This implies that the real distance is 100 000 times the length of 1 unit on a drawing).
Let us understand with an example.
Example 1:
Express 5 cm to 5 m in ratio form.
Solution:
5 cm to 5 m = 5 cm : 5 m
= 5 cm : 500 cm ( 1 m = 100 cm, hence 5m = 500 cm)
= 1 : 100
Example 2:
Simplify the scale 5 mm: 2 m.
Solution:
5mm : 2 m = 5mm : 2000 mm ( 1 m = 1000 mm, hence 2 m = 2000 mm)
= 1 mm : 400 mm
= 1 : 400
Example 3:
Simplify the scale 5 cm: 4 km
Solution:
5 cm : 4 km = 5 : 400000 cm ( 1 km = 100,000 cm, hence, 4 km = 400,000 cm)
= 1cm : 80000 cm
= 1: 80000
How To Calculate The Scales of Drawings Using a Calculator?
To calculate the scales of drawing using calculator:
Divide the measurement by the scale if you want to minimize the drawing in size, or
Multiply the measurement by the scale if you want to increase the drawing in size.
Example 1:
A 100 mm line is to be drawn at a scale of 1: 5.
Solution:
To draw a 100 mm line at a scale of 1: 5 (i.e. 5 times less than its original size), we will divide 100 mm by 5.
= 100 mm 5
= 20 mm
Therefore, a 20 mm line is drawn.
Example 2:
A 100 mm line is to be drawn at a scale of 5 : 1.
Solution:
To draw a 100 mm line at a scale of 5: 1 (i.e. 5 times more than its original size), we will multiply 100 mm by 5.
= 100 mm 5
= 500 mm
Therefore, a 500 mm line is drawn.
How To Interpret Scale Drawing?
We can easily interpret scale drawing if the required information is given. Let us consider an example that represents how a scale is used to prepare the blueprint of a house and how to calculate and interpret the required dimensions.
Example: To prepare the blueprint of a house, Hitesh has used a scale of 1:100. The dimensions of the master bedrooms in the floor plan are represented as 6 units by 4 units. Find the actual dimensions of the master bedroom.
Solution:
Step 1: The scale 1:100 implies that for every 100 units in the real world, the house represents 1 unit on the blueprint drawing. In other words, it implies that 100 units of an actual house is equal to 1 unit of a blueprint drawing.
Step 2: Now, we will calculate the actual dimensions of the master bedroom using scale 1:100. Here, the scale factor is 100, therefore, we will multiply the blueprint dimensions by 100.
Therefore,
Actual length of master bedroom = 6 100 = 600 units
Actual width of master bedroom = 4 100 = 400 units
Hope you have understood what scale is, and how ratio is used to write scale in Math. With this understanding, you can now easily draw the blueprints of the original design with precise measurements.
FAQs on How to Write Scale in Graph: Step-by-Step Guide
1. What is a scale on a graph?
A scale on a graph is the ratio that defines the relationship between the measurements on the graph and the actual values of the data being represented. It tells you how many units of data are represented by a single unit of length (e.g., one centimetre or one big square) on the graph paper for both the x-axis and y-axis.
2. How do you write the scale for a graph on graph paper?
The scale should be clearly written, usually at the top right corner of the graph paper, so anyone can understand how to read it. You should specify the scale for each axis separately if they are different. For example:
- On x-axis: 1 cm = 5 years
- On y-axis: 1 cm = 1000 people
3. What does a graph scale like '1 cm = 10 units' mean?
A scale of '1 cm = 10 units' means that every one-centimetre distance measured on the graph axis represents an actual value of 10 units of the data. For instance, if you are plotting temperature on the y-axis, a bar that is 4 cm high would represent a temperature of 4 x 10 = 40 degrees.
4. Do the x-axis and y-axis need to have the same scale?
No, the x-axis and y-axis do not need to have the same scale. In fact, they often have different scales because they usually represent different types of quantities with different ranges. For example, an x-axis might show 'Number of Overs' in a cricket match (e.g., 1 unit = 1 over), while the y-axis shows 'Runs Scored' (e.g., 1 unit = 10 runs).
5. How do you choose the right scale for a bar graph or histogram?
To choose the right scale for a bar graph or histogram, follow these steps:
- Identify the highest data value you need to plot on an axis.
- Count the number of available squares or divisions on your graph paper for that axis.
- Divide the highest value by the number of divisions to get an idea of the value per division.
- Round this up to a convenient number (like 2, 5, 10, or 20) to make plotting the points easy. The goal is to use most of the available space without making the graph look cramped or empty.
6. Why is choosing a proper scale so important for a graph?
Choosing a proper scale is crucial for three main reasons:
- Accuracy: It ensures the data is represented truthfully without distortion. An improper scale can make small changes look huge or significant changes look minor.
- Clarity: A good scale makes the graph easy to read and understand. The labels and points are clear and well-spaced.
- Efficiency: It ensures the graph effectively uses the available space on the paper, making it look professional and tidy.
7. What happens if you choose a wrong scale for your graph?
Choosing a wrong scale can make your graph misleading. If the scale is too large (e.g., 1 cm = 1000 when data only goes up to 50), all your data points will be cramped in a tiny section, making it impossible to see details. If the scale is too small (e.g., 1 cm = 2 when data goes up to 200), the graph will be too big to fit on the page, or the visual trend will be exaggerated and hard to interpret as a whole.
8. What is the difference between a graph's scale and a scale factor in geometry?
While both terms involve ratios, they are used in different contexts. A graph's scale is used for data representation; it's a ratio that links graph distance to a data quantity (e.g., 1 cm on the graph equals 5 kg of weight). A scale factor is a multiplier used in geometry to resize a shape; it changes the dimensions of an object proportionally (e.g., a scale factor of 3 triples the length of all sides of a triangle).
9. Is there a standard formula for determining the best scale for any graph?
No, there is no single formula to find the perfect scale. Choosing a scale is a matter of judgement based on the range of your data (the difference between the highest and lowest values) and the size of your graph paper. The primary goal is to select a simple, round number that allows you to cover at least 75% of the graph area for clear visualisation.
10. How do you show a break in the scale on a graph, and when is it used?
A break in the scale is shown using a small zigzag line or a 'kink' on the axis, usually near the origin (0). This technique is used when the data values to be plotted start far from zero. For example, if you are plotting student marks that are all between 80 and 100, you can use a kink to skip the empty space from 0 to 79. This allows you to use a larger, more detailed scale for the values that matter.
