A Peek Beyond the Point - Class 7 Mathematics (CBSE)

Based on the 2026-27 Class 7 Mathematics sequence for NCERT Ganita Prakash. These notes are written for students: understand the idea first, then practise enough examples to become accurate.

1. Why this chapter matters

Whole numbers are not enough for measuring length, money, mass, temperature, or sports timing. Decimals help us write numbers between whole numbers. This first decimal chapter builds the idea of tenths and hundredths using grids, number lines, money, and metric units.

In school tests, this chapter can appear as direct calculations, reasoning questions, short explanations, activity-based questions, and word problems. The safest preparation is not to memorise a single trick, but to know what each idea means and when to use it.

2. Core ideas

Decimal place value

The first digit after the decimal point is tenths, the second is hundredths, and the third is thousandths. In 8.37, 3 means three tenths and 7 means seven hundredths.

Decimals as fractions

0.4 = 4/10, 0.37 = 37/100, and 2.05 = 2 + 5/100. This link prevents decimal rules from feeling mysterious.

Comparison

Compare whole-number parts first. If they are equal, compare tenths, then hundredths, then thousandths. Extra zeros at the end do not change value: 3.5 = 3.50.

3. Rules and formulas to remember

• Tenths: 0.1 = 1/10. One whole divided into 10 equal parts.
• Hundredths: 0.01 = 1/100. One whole divided into 100 equal parts.
• Metric link: 1 cm = 0.01 m. Decimals are common in measurement.
• Money link: 1 paise = Rs. 0.01. Hundred paise make one rupee.

4. Worked examples

Example 1: Write 7 tenths as a decimal.

7 tenths = 7/10 = 0.7.

Example 2: Write 4.09 in expanded form.

4.09 = 4 + 0/10 + 9/100 = 4 + 9/100.

Example 3: Which is greater: 5.6 or 5.47?

Whole parts are equal. Tenths: 6 tenths > 4 tenths, so 5.6 is greater.

Example 4: Convert 342 cm to metres.

100 cm = 1 m, so 342 cm = 3.42 m.

5. Activity corner

Shade decimal grids: first shade 0.3, then 0.30. Students see that both cover the same area, which explains why trailing zeros do not change a decimal.

When writing an activity answer, include three things:

• What you did.
• What you observed.
• What mathematical rule or pattern the activity shows.

6. Common mistakes and how to avoid them

• Mistake: Thinking 5.47 is greater than 5.6 because 47 is greater than 6 Fix: Compare place by place: 5.60 is greater than 5.47.
• Mistake: Forgetting zero as a placeholder Fix: 4.09 is not 4.9. The zero shows no tenths.
• Mistake: Reading decimals as whole numbers Fix: Read 2.35 as two point three five or two and thirty-five hundredths, not two point thirty-five.

7. How to write high-scoring answers

1. State the given information in mathematical form.
2. Write the rule, formula, diagram, table, or operation you are using.
3. Show every step clearly.
4. Keep units such as cm, m, rupees, degrees, or minutes where needed.
5. Check whether the answer is reasonable.

8. Practice set

1. Write 63/100 as a decimal.
2. Write 8.04 in words.
3. Arrange 2.4, 2.04, 2.40, 2.44 in ascending order.
4. Convert 7 m 35 cm to metres.
5. Write 0.8 as an equivalent decimal with two decimal places.
6. Explain why 0.5 = 0.50.

9. Answer key

1. Write 63/100 as a decimal. Answer: 0.63.

2. Write 8.04 in words. Answer: Eight and four hundredths.

3. Arrange 2.4, 2.04, 2.40, 2.44 in ascending order. Answer: 2.04, 2.4/2.40, 2.44.

4. Convert 7 m 35 cm to metres. Answer: 7.35 m.

5. Write 0.8 as an equivalent decimal with two decimal places. Answer: 0.80.

6. Explain why 0.5 = 0.50. Answer: Both represent half of a whole, or 50 hundredths.

10. Quick revision

• Main themes: decimals, tenths, hundredths, decimal comparison, measurement.
• Redo the worked examples without looking at the solutions.
• Explain the activity in your own words.
• Correct the common mistakes once before the test.
• Create one new word problem from daily life and solve it step by step.