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In real life situations, we come across many instances where representing the opposites are of great need. If we measure the heights of buildings, mountains, etc., above sea-level, we have to measure depth below sea-level. When temperatures are measured above 0°C, the temperatures go down below 0°C in certain places. To represent all these distinctly, we need some other measures along with whole numbers, i.e., as the opposites of them. Hence, negative numbers are created. Thus, we have -1 as the opposite of +1, -2 as the opposite of +2, -3 as the opposite of +3 and so on.
Note: Zero is considered neither negative nor positive.
Connection of Negative Numbers in Daily Life:
The negative numbers show the oppositeness of the positive numbers. Hence, the positive and negative quantities are used in opposite sense.
For example:
✅ Temperature above 0°C is taken as positive, while that below 0°C is taken as negative.
✅ Profit is expressed as positive, while loss is expressed as negative.
✅ Depositing money in a bank is considered positive, while withdrawal of money is taken as negative.
✅ Walking towards north is considered as positive, while towards south as negative. Similarly, walking towards east is considered as positive and walking towards west is negative.
✅ Height above sea-level is taken as positive, while that below sea-level is taken as negative.
Representation Of Negative Numbers On Number Line:
The numbers less than 0 can be represented as the negative numbers. So, -1, -2, -3, -4, -5, … are the negative numbers, which are shown by affixing minus sign (-) with the natural numbers.
These negative numbers can be represented on the number line as shown below. On moving 1 step towards left starting from 0 we get -1, 2 steps towards left starting from 0 we get -2, 3 steps towards left starting from 0 we get -3, so on.
Thus, all other negative numbers can be represented on the number line to the left of 0.
Ordering of Negative Numbers:
Just like whole numbers, a negative number on the number line is greater than the number to its left or less than the number to its right.
For example, -1 > -2 or -2
Hence, we have the following ordering of negative numbers:
-1 > -2 > -3 > -4 > -5 … or … -5
Oppositeness of Positive and Negative Numbers on Number Line:
Look at the number line below:
On the number line, 0 is considered the starting point. To the right of 0, the points as 1, 2, 3, 4, 5, 6, … are labelled. To the left of 0, lies -1. It is at the same distance from 0 as 0 from 1. To the left of -1, lies -2, -3, -4, and so on. From the number line, it is clear that the numbers -1, -2, -3, .. are equidistant from 0 as the numbers 1, 2, 3, … but in opposite direction. Thus, the numbers to the left of 0, i.e., -1, -2, -3, … are opposites of the numbers to the right of 0, i.e., 1, 2, 3, … and vice-versa.
Note: Zero is neither positive nor negative.
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