Introduction

A decimal number line is a straight line where numbers are placed in order from smallest to largest.
It is divided into equal parts to show decimal values between whole numbers.

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Why Use a Decimal Number Line?

• To compare decimals easily.
• To understand place value visually.
• To plot decimal points correctly.
• To connect fractions and decimals.

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Structure of a Decimal Number Line

0    0.1   0.2   0.3   0.4   0.5   0.6   0.7   0.8   0.9    1
|----|----|----|----|----|----|----|----|----|----|----|

• Whole numbers are placed at bigger marks.
• Tenths (0.1) → Divide each whole number into 10 equal parts.
• Hundredths (0.01) → Each tenth is further divided into 10 equal parts.

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Steps to Plot a Decimal on a Number Line

1. Find the two whole numbers the decimal is between.
2. Divide the space between them into 10 parts for tenths or 100 parts for hundredths.
3. Count forward from the left whole number.
4. Mark the exact decimal value with a dot or arrow.

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Examples

Example 1: Plot 3.4

• Between 3 and 4.
• Divide into 10 equal parts (tenths).
• Count 4 parts after 3 → 3.4.

Example 2: Plot 2.35

• Between 2.3 and 2.4.
• Divide into 10 equal parts (hundredths).
• Count 5 parts after 2.3 → 2.35.

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Key Tips

• Moving right = value increases.
• Moving left = value decreases.
• Always check the scale before plotting.
• 0.5 = ½, 0.25 = ¼ → use fraction knowledge to help.

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Common Mistakes to Avoid

• Miscounting the small divisions.
• Forgetting to check whether divisions represent tenths or hundredths.
• Placing decimals in the wrong section between whole numbers.

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Real-life Applications

• Measuring length (2.5 m, 1.75 cm).
• Reading weight (1.2 kg, 0.85 g).
• Handling money (₹3.50, ₹4.75).
• Reading temperature (37.5°C).

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Practice Questions

A. Plot these on a number line:

1. 1.7
2. 0.25
3. 4.6
4. 2.05

B. Answer:

1. Which is greater: 3.45 or 3.5?
2. Mark 0.42 on a number line between 0 and 1.