3. Real numbers
The collection of irrational and rational numbers
are called as real numbers.
Every real number can be represented by a
unique point on a number line.
Two German Mathematician Cantor and
Dedekind showed that corresponding to
every real number there is a point on the real
number line.
4. Terminating and non terminating
decimals
The decimal expansion of a rational
number is either terminating or non
terminating recurring.
Irrational numbers are non
terminating and non repeating.
6. If the denominator in the rational number in the
lowest form is the multiple of 2 or 5 or both then
the number is terminating
Eg 3/ 128
The denominator can be represented in the form
of 27 ,hence the number is terminating.
7. Rationalising the denominator
If we have a number 1/√7
We can rationalize the denominator by
multiplying the number by √7
We get 1/√7 x √7/ √7
√7/ 7
8. Every point on a number line represents a
real number.
We can represent √2 , √3, √5 on a number
line
10. Conclusion
Rational numbers are either terminating or
non terminating repeating decimals
Irrational numbers are non terminating non
repeating decimals.
Every real numbers can be represented on a
number line
Every point on a number line represents a
real numbers.