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Tamil Nadu (TNBSE)Class 7 Mathematics★ 6-10 marks in the TN Class 7 Term 3 exam through decimal operation and rounding sums

Number System (Term 3) - Decimal Operations

Samacheer Kalvi (TN State Board) Class 7 Maths — Term 3 Chapter 1, Number System (Decimal Operations). Addition, subtraction, multiplication and division of decimal numbers and rounding of decimals, with worked examples, exercises and quick revision.

⏱ 14 min readEasy difficulty✓ Free · NCERT-aligned

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Study Guide

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Key points, glossary and the questions most likely to show up.

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By the end of this chapter you'll be able to…

1Add and subtract decimals by aligning points
2Multiply decimals and place the point correctly
3Divide decimals including by a decimal divisor
4Multiply and divide by powers of ten
5Round decimals to a given place

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Why this chapter matters

Computing with decimals is essential for money, measurement and data work. The four decimal operations and rounding are directly tested in the TN Class 7 Term 3 exam.

Before you start — revise these

A 5-minute refresher here will save you 30 minutes of confusion below.

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Term 2 — Number System (Decimals)

Decimal place value.

Number System (Decimal Operations) — Class 7 Maths (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 7 Mathematics, Term 3 — Chapter 1. The four operations on decimals, and rounding.

1. About this chapter

This chapter covers addition, subtraction, multiplication and division of decimal numbers, and rounding decimals.

2. Adding and subtracting decimals

Line up the decimal points (and add trailing zeros so each number has the same number of decimal places), then add or subtract as with whole numbers, keeping the point in line.
Example: 12.5 + 3.75 → 12.50 + 3.75 = 16.25.

3. Multiplying decimals

Multiply as whole numbers, then place the point so that the number of decimal places in the answer equals the total in the two factors.
Example: 1.2 × 0.3 → 12 × 3 = 36, total 2 decimal places → 0.36.
Multiplying by 10, 100, 1000 moves the point right 1, 2, 3 places (3.4 × 100 = 340).

4. Dividing decimals

To divide by a whole number, divide normally and keep the point in line (4.8 ÷ 2 = 2.4).
To divide by a decimal, make the divisor a whole number by moving both points the same number of places (6 ÷ 0.2 = 60 ÷ 2 = 30).
Dividing by 10, 100, 1000 moves the point left (45.6 ÷ 10 = 4.56).

5. Rounding decimals

To round to a given place, look at the next digit: if it is 5 or more, round up; if less than 5, round down.
Example: 3.47 rounded to one decimal place → 3.5 (next digit 7 ≥ 5).

6. Worked examples

Example 1. Add 7.6 + 12.45. 7.60 + 12.45 = 20.05.

Example 2. Multiply 2.5 × 0.4. 25 × 4 = 100, 2 decimal places → 1.00 = 1.

Example 3. Round 5.682 to two decimal places. Next digit 2 < 5 → 5.68.

7. Exercises (Samacheer Kalvi)

Add: 15.7 + 2.85 + 0.6.
Subtract: 20.5 − 13.78.
Multiply: (a) 3.4 × 2.5 (b) 0.6 × 0.05.
Divide: (a) 9.6 ÷ 4 (b) 8 ÷ 0.4.
Round 12.346 to (a) one decimal place (b) two decimal places.

8. Common mistakes

Mistake: Not aligning decimal points when adding. Fix: Line up the points and pad with zeros before adding/subtracting.
Mistake: Misplacing the point in multiplication. Fix: The answer has as many decimal places as the two factors together.
Mistake: Rounding the wrong way at 5. Fix: A next digit of 5 or more rounds up.

9. Quick revision

Term 3 · Ch 1 · decimal operations.
Add/subtract: line up the points; multiply: total decimal places of the factors; divide by a decimal: make the divisor whole.
×10/100/1000 moves the point right; ÷10/100/1000 moves it left.
Round: next digit ≥ 5 rounds up, < 5 rounds down.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Add / subtract

line up the decimal points

Pad with zeros.

Multiply

decimal places in answer = sum of those in factors

Multiply digits first.

Divide by a decimal

make the divisor whole (move both points)

Then divide normally.

Rounding

next digit ≥ 5 → round up, < 5 → round down

To the required place.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Not aligning decimal points when adding

✓ Line up the points and pad with zeros before adding or subtracting.

WATCH OUT

✗ Misplacing the point in multiplication

✓ The answer has as many decimal places as the two factors together.

WATCH OUT

✗ Rounding the wrong way at 5

✓ A next digit of 5 or more rounds up.

NCERT exercises (with solutions)

Every NCERT exercise from this chapter — what it covers and how many questions to expect.

Add and subtract

Decimal addition and subtraction.

Questions

Multiply and divide

Decimal multiplication and division.

Questions

Rounding

Round to given decimal places.

Questions

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· Add

Add 15.7 + 2.85 + 0.6.

▶ Show solution

19.15.

Q2EASY· Subtract

Subtract 20.5 − 13.78.

▶ Show solution

6.72.

Q3EASY· Multiply

Multiply 3.4 × 2.5.

▶ Show solution

8.5.

Q4MEDIUM· Divide

Divide 8 ÷ 0.4.

▶ Show solution

80 ÷ 4 = 20.

Q5EASY· Round

Round 12.346 to two decimal places.

▶ Show solution

12.35 (next digit 6 ≥ 5).

Q6EASY· Powers of ten

Find 3.4 × 100.

▶ Show solution

340.

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•Term 3 Chapter 1 of Samacheer Kalvi Class 7 Maths.
•Add/subtract decimals by lining up the decimal points.
•Multiplying: the answer's decimal places equal the total in both factors.
•Dividing by a decimal: make the divisor a whole number, moving both points equally.
•× by 10/100/1000 moves the point right; ÷ moves it left.
•Round: next digit ≥ 5 rounds up, < 5 rounds down.

Tamil Nadu (TNBSE) marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: 6-10 marks across decimal operations and rounding

Question type	Marks each	Typical count	What it tests
Add / subtract	1-2	2	Aligning points
Multiply / divide	1-2	2-3	Placing the point
Rounding	1	1-2	Rounding rule

Prep strategy

Align decimal points for ± and pad with zeros
Count decimal places for ×
Make the divisor whole for ÷ by a decimal
Apply the 5-or-more rounding rule

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Money

Adding bills and splitting costs use decimal operations.

Measurement

Working with lengths and weights in decimals.

Estimation

Rounding gives quick, sensible approximations.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

Pad with zeros and align points for ±
Count decimal places for ×
Shift points to make the divisor whole for ÷
State the rounding rule used

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

Evaluate 2.5 × 0.4 ÷ 0.2 step by step.
Round 9.999 to two decimal places and explain the carry.

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

TN Class 7 Term 3 ExamHigh

NMMS / Foundation MathsMedium

School unit testsHigh

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Questions students ask

The real ones — pulled from the Q&A community and tutor sessions.

Multiply the numbers ignoring the points, then count the total decimal places in the two factors and put that many decimal places in the answer.

Multiply both the dividend and the divisor by 10 (or 100…) to make the divisor a whole number, then divide normally — e.g. 8 ÷ 0.4 becomes 80 ÷ 4 = 20.

Practice more, ask doubts, find a tutor

Tamil Nadu (TNBSE) Class 7 mock tests

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