Whole Numbers : Expanded form of Numbers

maths > wholenumbers

Expanded form of Numbers

what you'll learn...

overview

This page introduces the concept of "number of digits" in a number and 2-digit numbers, 3-digit numbers, etc.

In the previous pages, the numbers were introduced with grouping of

• $10$ $10$ units to $1$ $1$ ten,

• $10$ $10$ tens to $1$ $1$ hundreds

• and so on.

That lead to numbers in standard numerical format.

In this page, the understanding of standard numerical format in reverse is explained with the two expanded forms

• $7253 = 7000 + 200 + 50 + 3$ $7253 = 7000+200 + 50 +3$

• = $7$ $7$ thousands, $2$ hundreds, $5$ tens, 3 units.

Then the two popular systems of large numbers is introduced.

• Indian system of large numbers.

• International system of large numbers.

Expanded form of a number

The number $65$ has $2$ digits.

The number $24$ is made of two digits $2$ and $4$ . This is another example of a $2$ digit number.

The number $423$ , has $3$ digits.

The digits in the number $264$ are $2$ , $6$ , and $4$ . This is another example of a $3$ digit number. This represents

$2$ hundreds

$6$ tens

$4$ units.

The expanded form of the given number $2735$ .

$2735$

$quad =2000 + 700 + 30 + 5$

$quad =2$ thousands $+ 7$ hundreds $+ 3$ tens $+ 5$ units

to expand means: to make something large by giving more details. Expanded form of a number provides the place value of each digits of the number.

What is the number $652734$ in expanded form?
The answer is " $600000+50000$ $+2000$ $+700$ $+30+4$ ".

Expanded form: provides the place value of each digits of the number.
Eg: $1234 = 1000+200+30+4$

What is the expanded form of $872$ ?
The answer is ' $8$ hundred, $+7$ ten, $+2$ '

What is the expanded form of $46427$ ?
The answer is $40000 + 6000+400+20+7$
= $4$ ten thousand $+6$ thousand $+4$ hundred $+2$ ten $+7$

Indian System

Large Numbers - Indian System :

$1$ - unit

$10$ - ten

$100$ - hundred

$1,000$ - thousand

$10,000$ - ten thousand

$1,00,000$ - lakh

$10,00,000$ - ten lakh

$1,00,00,000$ - crore

International System

Large Numbers - International System :

$1$ - unit

$10$ - ten

$100$ - hundred

$1,000$ - thousand

$10,000$ - ten thousand

$100,000$ - hundred thousand

$1,000,000$ - million

$10,000,000$ - ten million

$100,000,000$ - hundred million

$1,000,000,000$ - billion

Summary

• 2-digit number: A number with only tens and units places.

• 3-digit number: A number with only hundreds, tens, and units places.

Expanded forms of a number

$7253$

$= 7000+200 + 50 +3$

$= 7$ thousands, $2$ hundreds, $5$ tens, 3 units.

$=$ seven thousand, two hundred, fifty three.

• Indian system of large numbers.
» $1$ - unit
» $10$ - ten
» $100$ - hundred
» $1,000$ - thousand
» $10,000$ - ten thousand
» $1,00,000$ - lakh
» $10,00,000$ - ten lakh
» $1,00,00,000$ - crore

• International system of large numbers.
» $1$ - unit
» $10$ - ten
» $100$ - hundred
» $1,000$ - thousand
» $10,000$ - ten thousand
» $100,000$ - hundred thousand
» $1,000,000$ - million

» $10,000,000$ - ten million
» $100,000,000$ - hundred million
» $1000,000,000$ - billion

Outline

The outline of material to learn whole numbers is as follows

Note: click here for detailed outline of Whole numbers

• Introduction

→ Numbers

→ Large Numbers

→ Expanded form

→ Face and place values

→ Approximation and Estimation

• Comparison

→ Comparing two numbers

→ Number line

→ Predecessor & Successor

→ Largest & Smallest

→ Ascending & Descending

• Addition Subtraction

→ Addtion: First Principles

→ Addition: Simplified Procedure

→ Subtraction: First Principles

→ Subtraction: Simplified Procedure

• Multiplication Division

→ Multiplication: First Principles

→ Multiplication: Simplified Procedure

→ Division: First Principles

→ Division: Simplified Procedure

• Numerical Expression

→ Introducing Numerical Expressions

→ Precedence

→ Sequence

→ Brackets