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ICSE Class 3 Mathematics★ 6-8 marks in Class 3 Mathematics; place value, comparison, and Roman numerals

Numbers Up to 10,000

Learn about NUMBERS up to 10,000. Understand PLACE VALUE — thousands, hundreds, tens, ones. Expanded form. Comparison and ordering. Skip counting. Roman numerals I to C. ICSE Class 3 Mathematics.

⏱ 10 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…

1Identify place value in 4-digit numbers (thousands to ones)
2Read and write numbers in figures and words
3Write numbers in expanded form
4Compare and order numbers
5Skip count and read Roman numerals I to C

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Why this chapter matters

Numbers up to 10,000 give children the place-value foundation for all later arithmetic. Reading, writing, comparing, ordering, skip counting, and Roman numerals build number sense used in money, measurement, and everyday counting.

Before you start — revise these

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

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Class 2 Mathematics: Numbers up to 1000

3-digit place value and counting

Numbers Up to 10,000

1. Place Value (Thousands, Hundreds, Tens, Ones)

Every number is made of DIGITS. Each digit has a PLACE and a VALUE.

'In the number 3,456 — the digit 3 is in the THOUSANDS place and means 3,000. The digit 4 is in the HUNDREDS place and means 400.'

Place Value Chart:

Thousands (Th)	Hundreds (H)	Tens (T)	Ones (O)
1,000	100	10	1

Example: The number 3,456

3 in Thousands place → 3,000
4 in Hundreds place → 400
5 in Tens place → 50
6 in Ones place → 6

Reading Numbers:

3,456 = Three thousand four hundred fifty-six

Number	In Words
1,000	One thousand
2,345	Two thousand three hundred forty-five
5,678	Five thousand six hundred seventy-eight
9,999	Nine thousand nine hundred ninety-nine
10,000	Ten thousand

'Read the THOUSANDS group first, then the remaining three digits. 4,567 = Four thousand five hundred sixty-seven.'

2. Expanded Form

Write the number as the SUM of its place values.

Examples:

3,456 = 3,000 + 400 + 50 + 6
5,820 = 5,000 + 800 + 20 + 0 (or 5,000 + 800 + 20)
7,009 = 7,000 + 0 + 0 + 9 = 7,000 + 9

Practice:

Write 6,789 in expanded form.

Answer: 6,000 + 700 + 80 + 9

'If a place has ZERO, you can skip it in expanded form. But in the NUMBER, the zero is important because it HOLDS the place!'

Number	Expanded Form
2,305	2,000 + 300 + 0 + 5
4,080	4,000 + 0 + 80 + 0
9,999	9,000 + 900 + 90 + 9
1,001	1,000 + 0 + 0 + 1

3. Comparing Numbers

Rules:

A number with MORE digits is ALWAYS larger.
If both have the SAME number of digits, start comparing from the LEFT.

Examples:

5,678 > 999 (4 digits > 3 digits)
6,789 > 5,789 (same 4 digits — 6 > 5 in thousands)
7,890 < 8,901 (same 4 digits — 7 < 8 in thousands)
4,567 > 4,566 (same up to tens — 7 > 6 in ones)

First Number	Second Number	Which Is Larger?
4,567	4,657	4,657 (4,6 > 4,5)
8,901	8,910	8,910 (8,91 > 8,90)
3,333	3,330	3,333 (3 > 0 in ones)
1,000	10,000	10,000 (5 digits > 4)

4. Ordering Numbers

Ascending Order (Smallest to Largest):

Arrange: 3,456, 2,789, 4,567, 1,234 Answer: 1,234 < 2,789 < 3,456 < 4,567

Descending Order (Largest to Smallest):

Arrange: 3,456, 2,789, 4,567, 1,234 Answer: 4,567 > 3,456 > 2,789 > 1,234

5. Skip Counting

Counting by 2s (Even Numbers):

2, 4, 6, 8, 10, 12, 14, 16, 18, 20...

Counting by 5s:

5, 10, 15, 20, 25, 30, 35, 40, 45, 50...

Counting by 10s:

10, 20, 30, 40, 50, 60, 70, 80, 90, 100...

Counting by 100s:

100, 200, 300, 400, 500, 600, 700, 800, 900, 1000...

Skip by	Start	Next 5 Numbers
2	4	6, 8, 10, 12, 14
5	10	15, 20, 25, 30, 35
10	30	40, 50, 60, 70, 80
100	300	400, 500, 600, 700, 800

6. Roman Numerals (I to C)

Roman numerals use LETTERS for numbers.

Roman	I	V	X	L	C
Value	1	5	10	50	100

Rules:

Add when smaller comes after: VI = 5 + 1 = 6
Subtract when smaller comes before: IV = 5 - 1 = 4

Numbers 1 to 20:

I=1, II=2, III=3, IV=4, V=5, VI=6, VII=7, VIII=8, IX=9, X=10, XI=11, XII=12, XIII=13, XIV=14, XV=15, XVI=16, XVII=17, XVIII=18, XIX=19, XX=20

Tens:

XX=20, XXX=30, XL=40, L=50, LX=60, LXX=70, LXXX=80, XC=90, C=100

7. Common Mistakes

Reading numbers wrong: '4,567 is "four thousand five hundred sixty-seven." NOT "four thousand five hundred and sixty-seven." Avoid using "and" between hundreds and tens.'
Place value confusion: 'In 3,045, the 0 in hundreds means there are NO hundreds. The number is three thousand forty-five.'
Comparing digits incorrectly: '4,567 vs 4,657 — compare the hundreds first. 5 vs 6. 6 is bigger, so 4,657 is larger.'
Roman numeral order: 'IV is 4 (1 before 5). VI is 6 (5 before 1). The order matters!'

8. Key Facts to Remember

'The largest 4-digit number is 9,999. The smallest 4-digit number is 1,000.'
'10 thousands = 10,000 = Ten thousand.'
'Skip counting helps you learn multiplication tables.'
'Roman numerals I, V, X, L, C represent 1, 5, 10, 50, 100.'
'V, L are never repeated. Only I, X, C can be repeated.'

9. Self-Test

Q1: Write 5,678 in words.

Q2: Write in expanded form: 7,305

Q3: Which is larger — 4,567 or 4,657? Why?

Q4: Arrange in ascending order: 3,210, 2,301, 1,230, 3,021

Q5: Write the Roman numerals for: (a) 8 (b) 14 (c) 20 (d) 40

Q6: Convert to Hindu-Arabic: (a) XII (b) XXV (c) XL (d) LXX

Q7: Count by 5s from 15 to 40.

Q8: What is the place value of 7 in 7,845?

Answers:

A1: Five thousand six hundred seventy-eight. A2: 7,000 + 300 + 0 + 5 = 7,000 + 300 + 5 A3: 4,657 — because 6 > 5 in the hundreds place. A4: 1,230 < 2,301 < 3,021 < 3,210 A5: (a) VIII (b) XIV (c) XX (d) XL A6: (a) 12 (b) 25 (c) 40 (d) 70 A7: 15, 20, 25, 30, 35, 40 A8: 7 is in the THOUSANDS place — value = 7,000.

Key formulas & results

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

Place value

Thousands (1000), Hundreds (100), Tens (10), Ones (1)

In 3,456 the 3 means 3,000 and the 4 means 400.

Roman numerals

I=1, V=5, X=10, L=50, C=100

Smaller after = add (VI=6); smaller before = subtract (IV=4).

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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

✗ Saying 'and' in number names (four thousand five hundred AND sixty)

✓ Read it as 'four thousand five hundred sixty-seven', without 'and'.

WATCH OUT

✗ Ignoring zero as a place holder

✓ In 3,045 the 0 shows there are no hundreds; the number is three thousand forty-five.

WATCH OUT

✗ Comparing wrong digits

✓ With the same number of digits, compare from the left, place by place.

NCERT exercises (with solutions)

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

Place value and expanded form

Writing numbers in words, figures, and expanded form

Questions

Comparing, ordering, Roman numerals

Comparison, ascending/descending order, and Roman numerals

Questions

Practice problems

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

Q1EASY· Place Value

What is the place value of 7 in 7,845?

▶ Show solution

7 is in the thousands place; its value is 7,000.

Q2EASY· Expanded Form

Write 7,305 in expanded form.

▶ Show solution

7,000 + 300 + 5.

Q3EASY· Compare

Which is larger, 4,567 or 4,657?

▶ Show solution

4,657, because 6 > 5 in the hundreds place.

Q4MEDIUM· Roman

Write Roman numerals for 8, 14, 40.

▶ Show solution

VIII, XIV, XL.

5-minute revision

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

•Places: thousands, hundreds, tens, ones.
•Expanded form writes a number as the sum of place values.
•More digits means a larger number.
•With equal digits, compare from the left.
•The largest 4-digit number is 9,999; the smallest is 1,000.
•I, V, X, L, C stand for 1, 5, 10, 50, 100.
•V and L are never repeated; I, X, C can be repeated.

ICSE marks blueprint

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

Typical chapter weightage: 6-8 marks, depending on the school paper

Question type	Marks each	Typical count	What it tests
Place value / Expanded form	3-4	2	Reading, writing, and expanding numbers
Comparison / Roman numerals	3-4	2	Ordering numbers and Roman numerals

Prep strategy

Make a place-value chart for practice
Read numbers aloud in words
Compare numbers digit by digit from the left
Memorise Roman numerals I to C and the add/subtract rule

Where this shows up in the real world

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

Counting and money

Place value helps us read prices, scores, and large counts.

Clocks and chapters

Roman numerals appear on clocks, chapters, and king's names.

Comparing amounts

Ordering numbers helps compare distances, weights, and quantities.

Exam strategy

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

Use a place-value chart for tricky numbers
Write number names without 'and'
Compare from the leftmost digit
Apply the add/subtract rule for Roman numerals

Going beyond the textbook

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

Write all 4-digit numbers using the digits 3, 0, 5, 1 once each.
Find the year of your birth in Roman numerals.

Where else this chapter is tested

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

ICSE Class 3 School ExamHigh

Maths Olympiad / IMO (junior)Medium

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Questions students ask

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

Zero is a place holder. In the number 3,045, the zero sits in the hundreds place to show that there are no hundreds. Without it, the number would become 345, which is completely different. So even though zero by itself means nothing, its position keeps the other digits in their correct places, which keeps the value of the whole number correct.

Look at the order of the letters. If a smaller letter comes after a larger one, you add, so VI is 5 + 1 = 6. If a smaller letter comes before a larger one, you subtract, so IV is 5 - 1 = 4. This is why IV is four and VI is six even though they use the same two letters; the order tells you which rule to use.

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