NCERT Solutions for Class 6 Maths Chapter 2: Whole Numbers Ex 2.1

Welcome to the world of Whole Numbers! After learning about counting numbers, we are now ready to take the next step. What happens when you have nothing? We give that 'nothing' a special name in maths: zero! When we add zero to our collection of counting numbers (1, 2, 3, ...), we get a brand new set called Whole Numbers. This chapter is the foundation for almost all the maths you will ever learn. In this specific guide for Exercise 2.1, we will become experts on the basics. You will learn what comes just before (predecessor) and just after (successor) any whole number. We will also learn how to arrange and compare these numbers using a super helpful tool called the number line. Let's begin this exciting journey and build a strong base in mathematics!

From Counting to Completeness: Introducing Whole Numbers

Think about the numbers you first learned: 1, 2, 3, 4, and so on. You use them to count your toys, friends, or chocolates. These are called Natural Numbers or Counting Numbers. But what if you have an empty box of chocolates? How many are there? The answer is 'zero'. The natural numbers don't have a symbol for 'nothing'. To fix this, mathematicians created a new team of numbers called Whole Numbers. It's very simple: take all the natural numbers (1, 2, 3, ...) and just add zero (0) at the beginning. So, the set of whole numbers is 0, 1, 2, 3, 4, ... and it goes on forever. The most important new member is 0, which is the smallest whole number.

Successor and Predecessor: Before and After

Successor
The successor of a whole number is the number that comes immediately after it. You can find it by adding 1 to the number. For example, the successor of 15 is 15 + 1 = 16.
Predecessor
The predecessor of a whole number is the number that comes immediately before it. You can find it by subtracting 1 from the number. For example, the predecessor of 15 is 15 - 1 = 14.

How to Find the Successor and Predecessor

  1. Finding the Successor (The number 'after') — To find the successor of any whole number, simply add 1 to it. Example 1: Find the successor of 8. 8 + 1 = 9. So, 9 is the successor of 8. Example 2: Find the successor of 199. 199 + 1 = 200. So, 200 is the successor of 199.
  2. Finding the Predecessor (The number 'before') — To find the predecessor of any whole number (except 0), simply subtract 1 from it. Example 1: Find the predecessor of 54. 54 - 1 = 53. So, 53 is the predecessor of 54. Example 2: Find the predecessor of 10000. 10000 - 1 = 9999. So, 9999 is the predecessor of 10000.

The Number Line: A Map for Whole Numbers

Imagine a long straight road. This is our number line. We mark a starting point and label it 0. Then, at equal distances to the right, we mark points and label them 1, 2, 3, 4, and so on. This simple drawing is a powerful tool!

  • Comparing Numbers: Any number on the number line is greater than all the numbers to its left. For example, 8 is on the right of 5, so 8 is greater than 5 (8 > 5).
  • Successor & Predecessor: The number immediately to the right of any number is its successor. The number immediately to the left is its predecessor.
  • Addition & Subtraction: Adding a number means moving that many steps to the right. Subtracting means moving that many steps to the left.

Using the number line helps you 'see' the numbers and understand their relationships easily.

Watch Out! Common Mistakes to Avoid

  • The Predecessor of 0: The number 0 does NOT have a predecessor in the set of whole numbers. The whole numbers start at 0, so there is no whole number before it.
  • Whole vs. Natural Numbers: Remember, 0 is a whole number but it is NOT a natural number. All natural numbers (1, 2, 3,...) are whole numbers, but not all whole numbers are natural numbers.
  • Successor of 9999: Don't get confused by large numbers. The successor of 9999 is simply 9999 + 1 = 10000.
  • 'Between' vs 'After': If a question asks for numbers 'between' 10 and 14, the answer is 11, 12, 13. If it asks for three numbers 'after' 10, the answer is 11, 12, 13.

Practice Questions with Solutions

  • Q: Write the successor of 2440701 and the predecessor of 10000.
  • A: Step 1: To find the successor of a number, we add 1 to it. Successor of 2440701 = 2440701 + 1 = 2440702. Step 2: To find the predecessor of a number, we subtract 1 from it. Predecessor of 10000 = 10000 - 1 = 9999. Final answer: The successor of 2440701 is 2440702. The predecessor of 10000 is 9999.
  • Q: Which whole number is on the right of 503 on the number line?
  • A: Step 1: On a number line, numbers increase as we move from left to right. This means any number to the right of a given number is greater than that number. Step 2: We need to find the smallest whole number greater than 503. This is found by adding 1 to 503. So, 503 + 1 = 504. Final answer: The whole number on the right of 503 on the number line is 504.
  • Q: Use the appropriate symbol (>, <, or =) to compare the following pairs of numbers: a) 89765 ____ 89756 b) 10001 ____ 9999
  • A: Step 1: For a) 89765 and 89756. Both numbers have 5 digits. Compare digits from left to right. The first four digits (8, 9, 7) are the same. Comparing the tens digit, 6 in 89765 is greater than 5 in 89756. So, 89765 > 89756. Step 2: For b) 10001 and 9999. 10001 has 5 digits, while 9999 has 4 digits. A whole number with more digits is always greater than a whole number with fewer digits. Therefore, 10001 > 9999. Final answer: a) 89765 > 89756, b) 10001 > 9999.

Frequently Asked Questions

What is the main difference between whole numbers and natural numbers?

The only difference is the number 0. Natural numbers are the counting numbers starting from 1 (1, 2, 3,...), while whole numbers include 0 along with all the natural numbers (0, 1, 2, 3,...).

Does every whole number have a predecessor?

No. Every whole number except 0 has a predecessor that is also a whole number. The number 0 is the smallest whole number and does not have a whole number before it.

Are all natural numbers also whole numbers?

Yes, absolutely! The set of whole numbers is made by adding 0 to the set of natural numbers. So, every natural number like 1, 2, 50, or 1000 is also a whole number.