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Tamil Nadu (TNBSE)Class 7 Mathematics★ 6-10 marks in the TN Class 7 Term 2 exam through decimal place value, comparison and conversion sums

Number System (Term 2) - Decimal Numbers

Samacheer Kalvi (TN State Board) Class 7 Maths — Term 2 Chapter 1, Number System (Decimals). The decimal number system and decimal place value, representing decimals on the number line, comparing decimals, and converting between decimal fractions and common fractions, with worked examples, exercises and quick revision.

⏱ 14 min readEasy difficulty✓ Free · NCERT-aligned

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

1State decimal place values
2Represent decimals on the number line
3Compare decimal numbers correctly
4Convert decimals to fractions
5Convert fractions to decimals

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Why this chapter matters

Decimals are used in money, measurement and data every day. Place value, comparing decimals and converting between decimals and fractions are directly tested in the TN Class 7 Term 2 exam.

Before you start — revise these

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

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Term 1 — Number System (Integers)

Place value basics.

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

TN State Board (Samacheer Kalvi) Class 7 Mathematics, Term 2 — Chapter 1. Understanding and comparing decimal numbers.

1. About this chapter

This chapter covers the decimal number system, decimal place value, decimals on the number line, comparing decimals, and converting between decimal and common fractions.

2. Decimal place value

A decimal number has a whole-number part and a fractional part separated by a decimal point, e.g. in 34.56, the places after the point are tenths (5/10) and hundredths (6/100).
Place values after the point: tenths, hundredths, thousandths … (each ten times smaller).

3. Decimals on the number line

Each unit on the number line can be divided into ten equal parts to mark tenths; dividing further gives hundredths.
So 0.4 lies four-tenths of the way from 0 to 1.

4. Comparing decimals

Compare the whole-number parts first; if equal, compare the tenths, then hundredths, and so on.
Example: 3.45 and 3.5 → wholes equal (3), tenths 4 < 5, so 3.45 < 3.5.

5. Converting fractions and decimals

Decimal → fraction: write the digits over the place value and simplify, e.g. 0.75 = 75/100 = 3/4.
Fraction → decimal: divide, e.g. 3/4 = 0.75; a fraction with denominator 10, 100, 1000 converts directly (7/10 = 0.7).

6. Worked examples

Example 1. Write the place value of 7 in 5.073. The 7 is in the hundredths place → 7/100 = 0.07.

Example 2. Which is greater, 6.8 or 6.75? Wholes equal; tenths 8 > 7, so 6.8 > 6.75.

Example 3. Convert 0.25 to a fraction. 0.25 = 25/100 = 1/4.

7. Exercises (Samacheer Kalvi)

Write the place value of each digit in 12.345.
Mark 0.6 and 0.65 on the number line.
Compare: (a) 4.5 and 4.45 (b) 0.9 and 0.90.
Convert to fractions: (a) 0.8 (b) 0.125.
Convert to decimals: (a) 3/5 (b) 7/20.

8. Common mistakes

Mistake: Thinking more digits after the point means a bigger number. Fix: 0.5 > 0.45, even though 0.45 has more digits — compare place by place.
Mistake: Forgetting trailing zeros don't change the value. Fix: 0.9 = 0.90 = 0.900.
Mistake: Wrong place value when converting to a fraction. Fix: 0.07 = 7/100, not 7/10.

9. Quick revision

Term 2 · Ch 1 · decimals.
Place values after the point: tenths, hundredths, thousandths.
Compare wholes first, then tenths, then hundredths.
Decimal ↔ fraction: 0.75 = 75/100 = 3/4; 3/4 = 0.75. Trailing zeros don't change value.

Key formulas & results

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

Decimal place value

tenths, hundredths, thousandths after the point

Each ten times smaller.

Comparing

compare wholes, then tenths, then hundredths

Place by place.

Decimal → fraction

0.75 = 75/100 = 3/4

Over the place value.

Fraction → decimal

3/4 = 0.75 (divide)

Or use /10, /100.

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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

✗ Thinking more digits after the point means a bigger number

✓ 0.5 > 0.45 — compare place by place, not by the number of digits.

WATCH OUT

✗ Forgetting trailing zeros do not change the value

✓ 0.9 = 0.90 = 0.900.

WATCH OUT

✗ Wrong place value when converting to a fraction

✓ 0.07 = 7/100, not 7/10.

NCERT exercises (with solutions)

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

Place value

Identify place values of digits.

Questions

Comparing decimals

Compare and order decimals.

Questions

Conversions

Decimal ↔ fraction conversions.

Questions

Practice problems

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

Q1EASY· Place value

Write the place value of 7 in 5.073.

▶ Show solution

Hundredths place → 0.07 (7/100).

Q2EASY· Compare

Which is greater, 6.8 or 6.75?

▶ Show solution

6.8 (tenths 8 > 7).

Q3EASY· Convert

Convert 0.25 to a fraction.

▶ Show solution

25/100 = 1/4.

Q4EASY· Convert

Convert 3/5 to a decimal.

▶ Show solution

0.6.

Q5MEDIUM· Compare

Arrange in ascending order: 4.5, 4.45, 4.05.

▶ Show solution

4.05 < 4.45 < 4.5.

Q6MEDIUM· Convert

Convert 7/20 to a decimal.

▶ Show solution

7/20 = 35/100 = 0.35.

5-minute revision

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

•Term 2 Chapter 1 of Samacheer Kalvi Class 7 Maths.
•Place values after the point: tenths, hundredths, thousandths.
•Compare decimals place by place (wholes, then tenths, then hundredths).
•Trailing zeros do not change a decimal's value (0.9 = 0.90).
•Decimal → fraction: write over the place value and simplify (0.75 = 3/4).
•Fraction → decimal: divide, or rewrite with denominator 10, 100, 1000.

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 place value, comparison and conversion

Question type	Marks each	Typical count	What it tests
Objective	1	3-5	Place value and comparison
Conversion	2	2	Decimal ↔ fraction
Ordering	2	1	Arranging decimals

Prep strategy

Line up decimal points when comparing
Add trailing zeros to equalise places
Use the place value to form the fraction
Divide to convert a fraction to a decimal

Where this shows up in the real world

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

Money

Rupees and paise are written as decimals.

Measurement

Lengths and weights use decimal units.

Data

Averages and readings are often decimals.

Exam strategy

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

Align decimal points when comparing
Use trailing zeros to equalise decimal places
Quote the place value when converting
Simplify the fraction at the end

Going beyond the textbook

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

Write 0.625 as a fraction in lowest terms.
Find a decimal between 0.3 and 0.31.

Where else this chapter is tested

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

TN Class 7 Term 2 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.

No. Compare place by place: the tenths digit of 0.5 is 5, larger than the 4 in 0.45, so 0.5 > 0.45 even though it has fewer digits.

If the denominator is 10, 100 or 1000, write the numerator with the point in the right place; otherwise divide the numerator by the denominator, or make the denominator 10/100/1000.

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