Chapter 13 · ICSE Class 5 Math

Large Numbers and Operations

Big numbers are grouped differently depending on the system you use. Enter a number and switch between the Indian and International place value systems.

The Place Value Machine
1,23,45,678
12345678

Try it: switch systems and watch the same number get grouped differently!

The Indian place value system grouped as crores, lakhs, thousands, and ones for the number 3457621 The number 34,57,621 split into groups: 3 crore-related digit, 45 lakhs, 76 thousands, and 21 ones, showing how digits are grouped in pairs after the first three 3 45 76 621 Crore Lakh Thousand Hundred, Ten, One Read as: 34 lakh, 57 thousand, 6 hundred 21
13.1

Indian vs. International place value

Large numbers are grouped differently depending on the system used. The Indian system groups digits as ones, tens, hundreds, thousands, lakhs, and crores. The International system groups digits as ones, tens, hundreds, thousands, millions, and billions.

Indian System
1,23,45,678

Groups of 2 after the first 3 digits: ones, thousands, lakhs, crores.

International System
12,345,678

Groups of 3 throughout: ones, thousands, millions.

Why it matters — Newspapers and Indian banks often use lakhs and crores, while international news and world statistics often use millions and billions — knowing both helps you read numbers correctly everywhere.
13.2

Roman numerals

Roman numerals use letters to represent numbers, a system from ancient Rome still used today on clocks, book chapters, and monuments.

RomanValueRomanValue
I1L50
V5C100
X10D500
M1000
1Adding symbols

When a smaller symbol comes after a larger one, add: VI = 5 + 1 = 6

2Subtracting symbols

When a smaller symbol comes before a larger one, subtract: IX = 10 − 1 = 9

13.3

BODMAS / DMAS — order of operations

BODMAS tells us the correct order to solve a maths expression with multiple operations: Brackets, Orders (powers), Division, Multiplication, Addition, Subtraction.

1Solving with BODMAS

Solve: 4 + 6 × 2. Multiplication first: 6 × 2 = 12. Then add: 4 + 12 = 16

2Brackets first

Solve: (4 + 6) × 2. Brackets first: 4 + 6 = 10. Then multiply: 10 × 2 = 20

Watch out — Solving strictly left to right without following BODMAS gives the wrong answer! 4 + 6 × 2 is NOT 20 (that's what left-to-right gives) — it's 16, because multiplication comes before addition.
13.4

More worked examples

1Reading a large number in the Indian system

Write 4523891 with Indian place value commas.

45,23,891 — forty-five lakh, twenty-three thousand, eight hundred ninety-one

2Converting a Roman numeral

Convert XL to a number. X comes before L (smaller before larger), so subtract: 50 − 10 = 40

3A mixed BODMAS problem

Solve: 20 − 8 ÷ 2 + 3. Division first: 8 ÷ 2 = 4. Then left to right: 20 − 4 + 3 = 19

Practice

Exercises

Tap a question to reveal its answer once you've tried it yourself.

Assess

Sample tests

Two 20-mark, 30-minute tests. Reveal answers question by question.