The document explains whole numbers, natural numbers, integers, and rational numbers, detailing their definitions and examples. It provides specific methods to find rational numbers between given numbers, demonstrated through examples between 3 and 4, and between 3/5 and 4/5. The document concludes with a note on the ability to find multiple rational numbers by calculating the averages of given numbers.

2. 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.

3. 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, ...}

5. 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

6. 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.

7. 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.

8. 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

9. (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

10. (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

11. 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.