Chapter 3 — A Peek Beyond the Point

Ganita Prakash • Grade 7 • Part I • 2026–27

🔎 Why a decimal point?

A whole unit is not always enough. A 2 m ribbon may need to be cut to 2.5 m, ₹10 may become ₹10.50, and a 5 kg object may weigh 5.75 kg. Decimals allow us to represent parts of a whole using the same place-value idea as whole numbers.

1. Decimal place-value chart

In 4.735, the 7 represents 7 tenths, 3 represents 3 hundredths and 5 represents 5 thousandths. Thus 4.735 = 4 + 7/10 + 3/100 + 5/1000.

2. Equivalent decimals

Adding zeros to the right of the last decimal digit does not change the number: 0.5 = 0.50 = 0.500. This is useful when comparing or adding decimals because equal numbers of decimal places make the place values easier to see.

3. Comparing decimals

Do not judge a decimal by the number of digits after the point. 4.8 is greater than 4.08.

4. Addition and subtraction

Align decimal points, not merely the last digits. Example: 12.50 + 3.75 = 16.25. For subtraction, 20.00 − 7.85 = 12.15.

5. Decimals on a number line

Between 2 and 3, tenths divide the interval into ten equal parts. The point 2.6 is six tenths after 2. If we divide each tenth again, hundredths can be located precisely.

🧠 Worked Examples

1. Write 6.304 in expanded form: 6 + 3/10 + 0/100 + 4/1000.
2. Compare 7.09 and 7.9: write 7.09 and 7.90; therefore 7.09 < 7.9.
3. Add 8.75 + 2.6: write 8.75 + 2.60 = 11.35.
4. Subtract 15 − 6.48: write 15.00 − 6.48 = 8.52.

🎯 Explore

1. Which is closer to 5: 4.91 or 5.09? Explain.
2. Find three different decimals between 2.4 and 2.5.
3. Use money to explain why ₹7.5 and ₹7.50 represent the same amount.

🧩 Concept MCQs

1. In 5.407, the 4 represents — A. 4 tenths B. 4 hundredths C. 4 ones D. 4 thousandths
2. Which is greatest? A. 3.08 B. 3.8 C. 3.18 D. 3.108
3. 6.4 is equal to — A. 6.04 B. 6.40 C. 6.004 D. 64
4. For 9.5 + 2.75, the correct aligned form is — A. 9.50 + 2.75 B. 9.5 + 27.5 C. 95 + 2.75 D. 9.05 + 2.75

Answers: 1-A, 2-B, 3-B, 4-A

📌 Case-based Challenge

A student has ₹500. They buy a book for ₹248.75 and a notebook for ₹96.50.

1. Write the total expenditure.
2. Find the money left.
3. Explain why aligning decimal points is important.
4. Estimate first and use your estimate to check the exact answer.

📝 Worksheet

1. Write five decimals in expanded form.
2. Compare and arrange six decimals.
3. Add five pairs of decimals.
4. Subtract five pairs of decimals.
5. Locate given decimals on a number line.

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