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The numbers {0, 1, 2, 3, ...} etc.
There is no fractional or decimal part. And no
negatives.
Example: 5, 49 and 980 are all whole numbers.

A natural number is a number that occurs
commonly and obviously in nature. As such, it is a
whole, non-negative number. The set of natural
numbers, denoted N, can be defined in either of
two ways:
N = {0, 1, 2, 3, ...}
N = (1, 2, 3, 4, ...}

A number with no fractional part.
Includes:
• the counting numbers {1, 2, 3, ...},
• zero {0},
• and the negative of the counting numbers {-1, -2, -3, ...}
We can write them all down like this: {..., -3, -2, -1, 0, 1, 2, 3,
...}
Examples of integers: -16, -3, 0, 1, 198

In mathematics, a rational number is
any number that can be expressed as the
quotient or fraction p/q of two integers, p and q,
with the denominator q not equal to zero. Since q
may be equal to 1, every integer is a rational
number.

Question – 1- Is zero a rational number? Can you write it
in the form of p/q, where p and q are integers and q ≠ 0?
Answer –
We know that, rational number is a number which can be
written in the form of p/q, where q is not equal to zero.
Thus,
(a) Yes, zero is a rational number, as it can be written in
the form of p/q.
(b) Since, 0 (zero) is an integer thus, zero can be written in
the form of p/q
Example : 0/1, 0/2, 0/3, etc. where 0 (zero) is an integer.

Question – 2 - Find six rational numbers between 3 and 4.
Answer –
First method to find rational number between two number:
A rational number between two numbers can be found by calculating average of
two given numbers.
Thus, six rational numbers between given two numbers i.e. 3 and 4 can be
calculated as follows:
(1) First rational number between 3 and 4 can be calculated by finding average
between them.
(2) As 7/2 is a rational number between 3 and 4, consequently, rational number
between 3 and 7/2 will be
one of the rational number between 3 and 4, which can be found by calculating
average between 3 and 7/2

(3) Again as 7/2 is a rational number between 3 and 4, consequently,
rational
number between 4 and 7/2 will be the rational number between 3 and 4,
which can be found by average between 4 and 7/2
(4) Similarly, rational number between 3 and 13/4 will be the rational
number between 3 and 4, since 13/4 is a rational number between 3
and 4. Thus next rational number between 3 and 4 can be found by
calculating average between 3 and 13/4

(5) Similarly, rational number between 4 and 13/4 will be the rational number
between 3 and 4, which can be found by calculating average between 4 and
13/4
(6) Similarly next rational number between 3 and 4 can be found by calculating
average between 3 and 15/4, since 15/4 is a rational number between 3 and 4
which we calculated in the step (3).
Thus, six rational numbers between 3 and 4 are 7/2, 13/4, 15/4, 25/8, 29/8
and 27/8.
One can find as many rational number between given any two numbers by
calculating average as above

Question – 3 - Find five rational numbers
between 3/5 and 4/5.
Answer:
First method to find rational number between two number:
Since we have to find 5 rational numbers between 3/5 and 4/5, so we will
multiply the
numerator and denominator of or the given numbers by 5+1, i.e. equal to 6.
We get,
Now, we have to find 5 rational numbers between 18/30 and 24/30, which will
come as
Thus, five rational numbers between 3/5 and 4/5 are
You can find as many rational numbers between given numbers using method
given above.

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Bhavya maths

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