Number System Lesson With Expanded Form and Names

Lesson Overview

• Comparing and Ordering Numbers
• Place Value and Face Value
• Predecessor and Successor
• Writing Number Names
• Writing Numbers from Words
• Increase or Decrease in Population Problems

Numbers are the foundation of mathematics. We use them every day to count, compare, calculate, and solve problems. The number system helps us understand how numbers are built, what each digit means, and how to read and write very large or very small numbers.

In this lesson, you will explore:

• Place value and face value
  
• Comparing large numbers
  
• Expanded form
  
• Writing number names
  
• Solving word problems with big numbers
  

Let's begin by learning how to compare numbers and understand which ones are greater or smaller.

Comparing and Ordering Numbers

When you are given a group of numbers, it's important to know which is the greatest and which is the smallest.

➤ Step-by-step method:

1. Count the digits – The number with more digits is usually greater.
   
2. If the numbers have the same number of digits, compare from left to right, starting with the largest place value.
   

Example 1:

Compare: 234, 543, 657, 456

All are three-digit numbers. So, check the hundreds place:

• 2 in 234
  
• 5 in 543
  
• 6 in 657
  
• 4 in 456
  

6 is the largest → 657 is the greatest number

Example 2:

Compare: 4567, 3456, 2345, 1234

All are four-digit numbers. Check from the thousands place:

• 4, 3, 2, 1 → 1234 is the smallest number
  

Comparing helps you put numbers in order from smallest to largest or largest to smallest, which is very useful in sorting and organizing data.

Place Value and Face Value

Every digit in a number has:

• A place value (its position in the number)
  
• A face value (the digit itself)
  

➤ Place Value Chart (up to 6 digits):

Example 1: What is the place value of 5 in 4567?

• Number: 4 5 6 7
  
• 5 is in the hundreds place
  
• Place value = 5 × 100 = 500
  
• Face value = 5
  

Example 2: What is the place value of 4 in 56743?

• 4 is in the tens place
  
• Place value = 4 × 10 = 40
  

Understanding place value helps you read large numbers correctly and know the worth of each digit in the number.

Take This Quiz:

Number System Math Practice Test! Quiz

Predecessor and Successor

The predecessor is the number that comes just before, and the successor is the number that comes just after a given number.

Example:

• Number: 100
  
• Predecessor = 100 − 1 = 99
  
• Successor = 100 + 1 = 101
  

This concept helps in number sequencing and basic math operations.

Writing Number Names

There are two systems for writing large numbers in words:

Indian System:

• Groups: Ones, Tens, Hundreds, Thousands, Lakhs, Crores
  
• Example: 45,678 = "Forty-five thousand six hundred seventy-eight"
  

International System:

• Groups: Ones, Tens, Hundreds, Thousands, Millions, Billions
  
• Example: 756,432 = "Seven hundred fifty-six thousand four hundred thirty-two"
  

Tips:

• Start from the left
  
• Break the number into groups of three
  
• Use hyphens for numbers between 21 and 99 (e.g., sixty-seven)
  

Practicing number names strengthens your understanding of place value and helps in reading large numbers easily.

Expanded Form and Standard Form

• Standard form: Writing the number normally
  
• Expanded form: Breaking it into parts to show each digit's value
  

Example: 6549

Expanded Form:

• 6 × 1000 = 6000
  
• 5 × 100 = 500
  
• 4 × 10 = 40
  
• 9 × 1 = 9
  So: 6000 + 500 + 40 + 9 = 6549
  

Expanded form helps you see how a number is built, digit by digit.

Writing Numbers from Words

To write a number in digits from its word form, follow these steps:

Example:

"Forty-five thousand six hundred seventy-eight"
Break it down:

• 45,000
  
• 600
  
• 78
  

Write in digits: 45,678

Another example:
"Seven hundred fifty-six thousand four hundred thirty-two" = 756,432

Solving Problems Using Large Numbers

Sometimes, you'll see word problems where you must calculate totals using large numbers.

Example:

A box has 500,000 tablets. Each weighs 50 mg.
What is the total weight?

Step 1: Multiply
500,000 × 50 = 25,000,000 mg

Step 2: Convert mg to grams
1,000 mg = 1 g → 25,000,000 ÷ 1,000 = 25,000 g

Step 3: Convert grams to kilograms
1,000 g = 1 kg → 25,000 ÷ 1,000 = 25 kg

So, the total weight = 25 kg

This problem uses multiplication and unit conversions together.

Increase or Decrease in Population Problems

You may be given a number that increases or decreases over time.

Example:

Population in 2002 = 235,471
Increased by = 72,958
Total in 2012 = 235,471 + 72,958 = 308,429

To solve:

• Add the increase to the original number
  
• Line up digits by place value to avoid errors
  

Word problems like this teach you how to apply addition in real situations.

Take This Quiz:

Math: Can You Pass The Number System Quiz?

Multiplication with Large Numbers

Some problems involve multiplying a large number by another number to find a total.

Example:

A newspaper has 12 pages. Each day, 12,000 copies are printed.
How many total pages are printed?

Step 1: Multiply
12 × 12,000 = 144,000 pages

Use place value strategies:

• 12 × 12 = 144
  
• Add three zeros from 12,000 → 144,000
  

Always double-check your work when dealing with large numbers.