## Key Concepts

- Counting Numbers
- Word form
- Standard form
- Place Value
- Understanding place value chart
- Identifying the value of digit
- Expansion form
- Comparing & Ordering
- Comparing numbers using symbols
- Ordering numbers in ascending and descending order

**Introduction **

In this chapter, we will learn to count numbers up to 10,000 and place values up to 10,000. We will also learn to compare and order numbers.

### Define Counting of Numbers

Counting is the process of determining the number of elements of a finite set of objects. Counting numbers are used to count objects. We have used counting to determine the number of animals or birds.

**Example:** Count the below ducks and write it in a number.

**Sol: **

### 1.1.1. Writing Numbers into Word Form

**Word Form: **Numericals are written in a word form.

**Example: **

1) Write 747 into the word form.

** Sol:** Seven hundred and forty-seven.

2) Write the number shown on a balloon into the word form.

**Sol:**

### 1.1.2 Writing Words into Standard Form

**Standard form**: Words are written into a standard form.

**Examples 1:** Write one hundred and ninety-six into a standard form.

**Sol:** 196

2. Write the number written inside the box into standard form.

**Sol:** 4556

### 1.2 Place Value

**Place value**: Place value is defined as the position of a digit in a number that tells the value of a digit.

The place values start from ones, tens, hundreds, and so on.

#### 1.2.1 Identifying the Place Value of Digit Using Place Value Chart

**Place value chart up to 10,000:**

**Example:** What is the place value of 6 in 45362?

**Sol: **

Here, 6 is in the tens place. Thus, the value of digit 6 is 60.

#### 1.2.2 Writing the Value of a Digit

**Value**: The value can be written by seeing the position of the number.

**Example:** In 4325, what is the value of 3

**Sol:**

Here 3 is in hundreds place so, the value of 3 is 300.

### Expanded Form of Number Using Place Value Strips

**Place value steps:**

**Example:**

**Expanded form**: Expanded form helps the numbers to determine their place value.

Or

Position of a digit in a number series expansion of numbers is based on the place value.

**Example1:** Expand the number 6742.

**Sol:** Th H T O

6 7 4 2

= 6000 + 700 + 40 + 2 = 6742

**Example 2:** Expand the number 15982.

**Sol:** TTH Th H T O

1 5 9 8 2

= 10000 + 5000 + 900 + 80 + 2

= 15982

### 1.3 Comparing and Ordering Numbers

**Comparing Numbers**: To compare means to examine the differences between numbers, quantities or values to decide if it is greater than, smaller than or equal to another quantity.

**Example:** Compare the number 10 ____20

**Sol:** 10 < 20

**Example:** Guess whether Ron is correct or Jone.

**Sol:** 4 < 5 (4 is lesser than 5), 8 < 7 (8 is greater than 7)

So, Ron is correct.

#### 1.3.1. Comparing Numbers Using Symbols of Greater Than, Less Than and Equal To

**Greater than:** This symbol shows the greater number among both numbers (>).

**Less Than:** This symbol shows the lesser number among both numbers (<).

**Equal to:** This symbol is used to equate both numbers

**Examples:** 1) 6051 > 3021 [6051 is greater than 3021]

2) 4052 < 540 [4052 is less than 5402]

3) 998 = 998 [Both the numbers are equal]

#### 1.3.2. Arranging the Numbers in Ascending and Descending Order

**Ascending order**: The numbers are arranged from smaller number to bigger number.

**Example 1:** 52, 58, 56, 54, 51

51, 52, 54, 56, 58.

**Example 2: **

**Sol: **198, 367, 438, 755, 899.

**Descending order**: The numbers are arranged from bigger number to smaller number.

**Example1:** 1052, 1982, 4676, 1824, 1200

**Sol: **4676, 1982, 1824, 1200, 1052

**Example 2:**

**Sol:** 5406, 3200, 3046, 2200, 2046.

#### Exercise:

- Place the digits of 3964 in correct position of the following place value chart.

TH | H | T | O |

2. Compare the numbers 6253 ○ 3256.

3. Which is greater number in 3051 or 6052?

4. Compare the numbers 2532 ○ 2341.

5. Arrange the numbers in ascending order.

291, 213, 277, 230, 245

6. Arrange the numbers in descending order

1624, 1267, 1090, 1410, 989

7. Write one thousand three hundred and forty-five into standard form

8. Write 15426 into Word form.

9. Write 16328 into word form.

10. Write the place value of 7 in 1742.

11. Write the value of 6 in 15620.

12. Expand 6246 according to place value strips.

13. Expand 7248.

14. 6000, 400, 10 and 5 make ___________number.

15. What is the value of each digit

### What have we learnt:

- We understood how to count numbers and how to write numbers in the standard form and word form.
- We learnt how to find the place value and value of the digit using place value chart.
- We understood the comparison of numbers using system and learnt to order of number in ascending and descending order.

### Concept Map :

#### Related topics

#### Addition and Multiplication Using Counters & Bar-Diagrams

Introduction: We can find the solution to the word problem by solving it. Here, in this topic, we can use 3 methods to find the solution. 1. Add using counters 2. Use factors to get the product 3. Write equations to find the unknown. Addition Equation: 8+8+8 =? Multiplication equation: 3×8=? Example 1: Andrew has […]

Read More >>#### Dilation: Definitions, Characteristics, and Similarities

Understanding Dilation A dilation is a transformation that produces an image that is of the same shape and different sizes. Dilation that creates a larger image is called enlargement. Describing Dilation Dilation of Scale Factor 2 The following figure undergoes a dilation with a scale factor of 2 giving an image A’ (2, 4), B’ […]

Read More >>#### How to Write and Interpret Numerical Expressions?

Write numerical expressions What is the Meaning of Numerical Expression? A numerical expression is a combination of numbers and integers using basic operations such as addition, subtraction, multiplication, or division. The word PEMDAS stands for: P → Parentheses E → Exponents M → Multiplication D → Division A → Addition S → Subtraction Some examples […]

Read More >>#### System of Linear Inequalities and Equations

Introduction: Systems of Linear Inequalities: A system of linear inequalities is a set of two or more linear inequalities in the same variables. The following example illustrates this, y < x + 2…………..Inequality 1 y ≥ 2x − 1…………Inequality 2 Solution of a System of Linear Inequalities: A solution of a system of linear inequalities […]

Read More >>
Comments: