Chapter-1 Number Systems

Solution:

If a number can be expressed in the form p/q, where p and q are both integers and q 0, then we can

say that it is rational.

Considering the situation of "0,"

Zero can be expressed as 0/1, 0/2, 0/3... or as, 0/1, 0/2, 0/3.

We therefore conclude that 0 can be expressed in the p/q form, where q can be either a positive or

negative number, because it meets the necessary condition.

Because of this, 0 is a rational number.

Solution:

There are an unlimited amount of rational numbers between 3 and 4.

To find six rational numbers between 3 and 4, we shall multiply both 3 and 4 by 6+1. (or a total of more

than 6)

i.e., 3 × (7/7) = 21/7

and, 4 × (7/7) = 28/7. Reasonable numbers that fall between 3 and 4 will be between 21 and 28.

The six numbers between 3 and 4 that are rational are therefore 22/7, 23/7, 24/7, 25/7, 26/7, and 27/7.

Solution:

The rational numbers are limitless between 3/5 and 4/5.

We can find 5 rational numbers between the numbers 3/5 and 4/5 by multiplying both of them.

with 5+1=6 (or any number more than 5) (or any number more than 5) (or any quantity higher than 5)

i.e., (3/5) × (6/6) = 18/30

and, (4/5) × (6/6) = 24/30

Between 3/5 and 4/5 are reasonable ranges between 18/30 and 24/30.

Hence, 19/30, 20/30, 21/30, 22/30, and 23/30 are the five rational numbers between 3/5 and 4/5.

Solution:

True

Natural numbers are those that range from one to infinity (without fractions or decimals)

Natural numbers equal 1, 2, 3, and 4...

Whole numbers are those that range from zero to infinity (without fractions or decimals)

Entire numbers equal 0, 1, 2, and 3...

Instead, we may say that entire numbers contain both zero and all the characteristics of natural

numbers.

Every whole number is a natural number, but not every natural number is a whole number.

Solution:

False

Integers, which can have positive, negative, or 0 digits, are a group of numbers that are different from

fractional and decimal numbers.

Integers are defined as 4, 3, 2, 1, 0, 1, 2, 3, 4.

The range of whole numbers is zero to infinity (without fractions or decimals)

The whole number 0, 1, 2, 3, etc.

Since integers can contain both positive and negative numbers, we can say that they are inclusive.

Although all integers are whole numbers, not all whole numbers are integers.

Solution:

False

Any numbers with the format p/q, where p and q are integers and q0, are considered rational numbers.

Rational numbers, thus, are 0, 19, 30, 2, 9, and -12/7.

Whole numbers are those that range from zero to infinity (without fractions or decimals)

Entire numbers equal 0,1,2,3, etc.

As a result, we can claim that integers include both positive and negative numbers.

All rational numbers are whole numbers, however not all rational numbers are whole numbers.