Whole Numbers

1. Introduction

   Imagine you have marbles! We use numbers to count them, like 1, 2, 3, and so on. These numbers that help us count are called natural numbers.

   Think of adding one marble to your pile. That's called the successor. So, the successor of 5 is 6 because you add 1. We can also take one away, that's the predecessor. The predecessor of 8 is 7 because you remove 1.

   Every number (except 1) has a successor, but 1 is special! It only has a successor (2) because there's no number before 1 to remove from.

   These numbers can be used to count anything, like people in a room, stars in the sky (if we could!), or even your hair (if you're patient)! And no matter how many things you count, there's always a bigger number possible by adding 1. So, there's no biggest number!

2. Whole Numbers

   Natural numbers: Imagine you have apples and you count them: 1, 2, 3, 4... These counting numbers, starting from 1 and going up forever, are called natural numbers. They don't include zero because we don't start counting from nothing.

   Whole numbers: Now imagine you get a basket and put all your apples in it, even if it's empty. That emptiness is like zero. So, whole numbers include all the natural numbers (1, 2, 3...) AND zero (0). It's like the whole bunch of counting numbers, including zero.

   Key points:

   • All natural numbers are whole numbers (because they're included in the bunch).
   • But not all whole numbers are natural numbers (because zero isn't a counting number).
   • There's no biggest whole number, because you can always add 1 to any number and get a bigger one!

3. The Number Line

   Imagine a ruler! That's our number line. Zero (0) is marked first, then to its right we mark 1, leaving the same space between them (called 1 unit). Keep marking numbers this way, 2, 3, 4... you can go on forever!

   Comparing numbers:

   • Numbers further to the right are bigger! So, 5 is bigger than 3 because it's to the right. We write this as 5 > 3.
   • The opposite is also true! Numbers to the left are smaller. So, 2 is smaller than 7 because it's to the left. We write this as 2 < 7.

   Try it yourself:

   • Which is bigger, 10 or 20?
   • Mark 12, 18, and 30 on your number line. Which is furthest left?
   • Looking at 1005 and 9756, which would be on the right?

   Adding and subtracting:

   • Imagine jumping on the number line! To add 3 and 4, start at 3 and jump 4 times to the right (landing on 7). So, 3 + 4 = 7.
   • Subtracting is like jumping backwards! To find 7 - 5, start at 7 and jump 5 times to the left (landing on 2). So, 7 - 5 = 2.

   Multiplying:

   • Think of jumping bigger jumps! To find 4 x 3, start at 0 and make 4 jumps of 3 units each (landing on 12). So, 4 x 3 = 12.

4. Tips

   How to find the whole numbers between two given whole numbers?

   Let's say you need to count whole numbers between the given whole number 5 and 10. Hence you will look up at the word "between".

   If you simply count from 5 to 10, i.e. 10 - 5, you'll get 5. However, we don't include the given numbers. Therefore, to find the correct count of whole numbers between those two given whole numbers, we subtract 1. In this case, 5 - 1 = 4, which is the correct answer.

5. Points to remember

   • 0 is the smallest whole number.

   Since 0 is less than any positive number, it's the smallest whole number.

   • All natural numbers are whole numbers.

   Natural numbers are 1, 2, 3, and so on.

   • All whole numbers are not natural numbers.

   0 is a whole number but not a natural number.

   • The natural number 1 has no predecessor.

   0 is not a natural number. It is a whole number.

   • The whole number 0 has no predecessor.

   There is no whole number less than 0. So, 0 has no predecessor.

   • The successor of a two-digit number is not always a two-digit number.

   the successor (after number) of 99 is 100, which is not a two-digit number.

   • The predecessor of a two-digit number is not always a two-digit number.

   the predecessor (before number) of 10 is 9, which is not a two-digit number.

   • Every whole number has a successor.

   Least whole number is 0. Thereafter there is no limit of whole number.

   • Every whole number except zero has a predecessor.

   There is no whole number less than 0. So, 0 has no predecessor.

   • The numbers 1, 2, 3,... which we use for counting are known as natural numbers.
   • If you add 1 to a natural number, we get its successor. If you subtract 1 from a natural number, you get its predecessor.

6. Exercise

   The next three natural numbers after \(10999\) are:
   \(11000 \)
   \( 11001 \)
   \( 11002 \)
   

   [Remember, natural numbers start from 1 and continue infinitely, increasing by 1 each time.]

   The three whole numbers occurring just before \(10001\) are:
   \( 10000 \)
   \( 9999 \)
   \( 9998 \)
   

   The smallest whole number is \(0\).

   [Remember, 0 is not a natural numbers.]

   We can count them all: \(33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52\).
   We can also solve this problem mathematically.
   The number of whole numbers between \(32\) and \(53\) is:
   \(\text{Number of whole numbers} = (\text{higher number} - \text{lower number}) - 1 \)
   \(\text{Number of whole numbers} = (53 - 32) -1 \)
   \(\text{Number of whole numbers} = 21 - 1 \)
   \(\text{Number of whole numbers} = 20 \)
   There are \(20\) whole numbers between \(32\) and \(53\).

   (a) Successor of 2440701: \(2440701 + 1 = 2440702\).
   (b) Successor of 100199: \(100199 + 1 = 100200\).
   (c) Successor of 1099999: \(1099999 + 1 = 1100000\).
   (d) Successor of 2345670: \(2345670 + 1 = 2345671\).
   

   (a) Successor of 94: \(94 - 1 = 93\).
   (b) Successor of 10000: \(10000 - 1 = 9999\).
   (c) Successor of 208090: \(208090 - 1 = 208089\).
   (d) Successor of 7654321: \(7654321 - 1 = 7654320\).
   

   (a) \( 530 > 503 \).
   (b) \( 370 > 307 \).
   (c) \( 98765 > 56789 \).
   (d) \( 983415 < 1002301 \).