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Summary- Real Numbers
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Providing a brief Summary on the chapter real numbers, and go through for before the exams
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Coordinate Geometry Notes Class 10 (Sophmore Year)
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12th MATHAMATICS NOTES
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Real NumbersReal numbers are numbers that can be found on the number line.
This includes both the rational and irrational numbers.
Irrational Numbers
An irrational number is number that cannot be expressed as a ratio of integers,
i.e. as a fraction.
Therefore, irrational numbers, when written as decimal numbers, do not
terminate, nor do they repeat.
For example:- The number √2=1.41421356..... does not end.
The same can be said for any irrational number.
Express rational numbers on number line
Let's see to how express any irrational number on number line
For example:- Take √2 as irrational number
1. Draw a number line, mark the origin and other integers.
2. Now, find distance between 0 and 1 using compass.
3. Draw a perpendicular to 1 of the same length as between 0 and 1.
4. Join origin and other end of the new line i.e. perpendicular. You will get a figure
as shown.
5. Name origin as A, 1 on the number line as B and end of perpendicular as C.
6. Distance between A and C is √2 .
7. Use compass to find distance between A and C.
8. Place compass at A and mark the same length as between A and C on the
number line.
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