NUMBER SYSTEMS

Whole numbers

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.

Natural numbersA 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, ...}

IntegersA 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

Rational numbersIn 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.

QUESTIONS 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/qExample : 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.