Decimals on Number Line
You already know how to show whole numbers and fractions on a number line. Decimals can also be shown on a number line in the same way.
Since decimals are another way of writing fractions (like 0.5 = 1/2), they fit between whole numbers on the number line.
In Class 6, you will learn to plot decimals with one and two decimal places on a number line by dividing the space between whole numbers into equal parts.
What is Decimals on Number Line - Grade 6 Maths (Decimals)?
Key idea: To plot a decimal on a number line, divide the space between two whole numbers into equal parts.
- For one decimal place (tenths like 0.1, 0.2, ...): divide the space into 10 equal parts.
- For two decimal places (hundredths like 0.01, 0.15, ...): divide each tenth into 10 more parts (total 100 parts between two whole numbers).
Each small part between whole numbers represents:
- 0.1 if divided into 10 parts
- 0.01 if divided into 100 parts
Decimals on Number Line Formula
Steps to plot a decimal on a number line:
- Find which two whole numbers the decimal lies between. Example: 2.7 lies between 2 and 3.
- Divide the space between those whole numbers into 10 equal parts.
- Count the required number of parts from the smaller whole number. Example: 2.7 is 7 parts after 2.
- Mark the point and label it.
For two decimal places:
- First find which two tenths it lies between. Example: 3.45 lies between 3.4 and 3.5.
- Divide the space between 3.4 and 3.5 into 10 equal parts.
- Count 5 parts from 3.4 to reach 3.45.
Tip: The decimal 0.5 is exactly halfway between 0 and 1. Similarly, 3.5 is halfway between 3 and 4.
Types and Properties
Reading decimals from a number line:
- Look at the labels on the number line (the whole numbers).
- Count how many equal parts the space is divided into (usually 10).
- Count which part the point is at from the left whole number.
- Write as a decimal: whole number + (part count ÷ total parts).
Important observations:
- On a number line, numbers increase from left to right.
- 0.3 is to the left of 0.7 (because 0.3 < 0.7).
- Every decimal has a unique position on the number line.
- Between any two decimals, there are infinitely many other decimals.
Solved Examples
Example 1: Plotting 0.3 on a Number Line
Problem: Show 0.3 on a number line.
Solution:
- 0.3 lies between 0 and 1.
- Divide the space from 0 to 1 into 10 equal parts.
- Count 3 parts from 0.
- Mark the point as 0.3.
Answer: 0.3 is at the 3rd mark between 0 and 1.
Example 2: Plotting 2.7 on a Number Line
Problem: Show 2.7 on a number line.
Solution:
- 2.7 lies between 2 and 3.
- Divide the space from 2 to 3 into 10 equal parts.
- Count 7 parts from 2.
Answer: 2.7 is at the 7th mark between 2 and 3.
Example 3: Reading a Decimal from a Number Line
Problem: On a number line, the space between 1 and 2 is divided into 10 parts. A point is at the 4th mark. What decimal is it?
Solution:
Whole number = 1. Parts = 4 out of 10 = 0.4.
Answer: The point is at 1.4.
Example 4: Plotting 0.5 (Halfway Point)
Problem: Where is 0.5 on the number line?
Solution:
0.5 = 5/10 = 1/2. It is exactly halfway between 0 and 1.
Answer: 0.5 is at the middle mark between 0 and 1.
Example 5: Plotting a Hundredths Decimal
Problem: Show 1.25 on a number line.
Solution:
- 1.25 lies between 1.2 and 1.3.
- Divide the space from 1.2 to 1.3 into 10 equal parts.
- Count 5 parts from 1.2.
Answer: 1.25 is halfway between 1.2 and 1.3.
Example 6: Comparing Decimals Using a Number Line
Problem: Which is greater: 0.4 or 0.8? Use a number line to explain.
Solution:
On the number line, 0.4 is at the 4th mark and 0.8 is at the 8th mark between 0 and 1.
Since 0.8 is to the right of 0.4, it is greater.
Answer: 0.8 > 0.4.
Example 7: Plotting Negative Decimals
Problem: Where is −0.6 on the number line?
Solution:
- −0.6 is between −1 and 0.
- Divide the space from −1 to 0 into 10 equal parts.
- Count 4 parts from −1 towards 0 (since −0.6 is 4 parts from −1, or 6 parts left of 0).
Answer: −0.6 is at the 6th mark to the left of 0.
Example 8: Finding Decimals Between Two Values
Problem: Name three decimals between 3 and 4.
Solution:
Divide the space from 3 to 4 into 10 parts.
Three decimals between 3 and 4: 3.2, 3.5, 3.9.
Real-World Applications
Where decimals on number lines are used:
- Thermometers: Temperature is read on a number line marked in decimal degrees.
- Rulers: Millimetre marks on a ruler show tenths of a centimetre (0.1 cm, 0.2 cm, etc.).
- Speedometers: Speed is shown on a number line scale.
- Kitchen scales: Weight shown in decimals (0.5 kg, 1.2 kg).
- Maps: Distances between places may be shown as decimal values.
Key Points to Remember
- Decimals are plotted on a number line between whole numbers.
- For tenths (1 decimal place), divide the space into 10 equal parts.
- For hundredths (2 decimal places), divide each tenth into 10 more parts.
- On a number line, numbers increase from left to right.
- 0.5 is halfway between 0 and 1.
- You can use number lines to compare decimals — the number on the right is greater.
- Between any two decimals, there are infinitely many other decimals.
Practice Problems
- Plot 0.6, 0.2, and 0.9 on a number line from 0 to 1.
- Plot 3.4 on a number line from 3 to 4.
- A number line from 0 to 1 is divided into 10 parts. A point is at the 8th mark. What decimal is it?
- Plot 1.75 on a number line. (Hint: first find it between 1.7 and 1.8.)
- Name five decimals between 2 and 3.
- Which is greater: 4.3 or 4.7? Show on a number line.
Frequently Asked Questions
Q1. How do I show a decimal on a number line?
Find which two whole numbers it lies between. Divide that space into 10 equal parts. Count the required parts from the smaller whole number. Mark and label the point.
Q2. How many parts should I divide the space into?
For one decimal place (tenths), divide into 10 parts. For two decimal places (hundredths), you need to zoom in further and divide a tenth into 10 more parts.
Q3. Where is 0.5 on the number line?
0.5 is exactly halfway between 0 and 1. It is the same as 1/2.
Q4. Can I show negative decimals on a number line?
Yes. Negative decimals are to the left of 0. For example, −0.3 is between −1 and 0, at the 7th mark from −1 (or 3 marks to the left of 0).
Q5. Are there decimals between 0.1 and 0.2?
Yes, infinitely many! Examples: 0.11, 0.12, 0.15, 0.19, etc. Between any two decimals, you can always find more decimals.
Q6. How does a number line help compare decimals?
On a number line, the number to the right is always greater. So if you plot two decimals, the one further to the right is the larger number.
