Solved Examples on Numbers System

Example 1: Identify natural numbers among the following given numbers.

a) -34  b) 113  c) 0

Solution:

a) -34 is a negative number, so it is not a natural number.

b) 113 is a natural number.

c) 0 is not a natural number.

Example 2: Is √17 a rational number?

Solution:

No, √17 is not a rational number. The value of √17 is 4.123105625617661… It is a non-terminating and non-recurring decimal. So, √17 is not a rational number.

Example 3: What is the value of √-49?

Solution:

√(-49) = √(49)(-1) 

= √(49) × √(-1)

We know that √(-1) = i

So, √(-49) = 7i.

Example 4: What is the decimal value of 3/5?

Solution:

To convert 3/5 into a decimal multiply the numerator and the denominator with 2, such that we obtain 10 in the denominator.

(3/5) × (2/2) = 6/10.

Now, convert this fraction with a denominator of 10 to a decimal by shifting the decimal point to one place towards the left.

6/10 = 0.6.

Hence, the decimal value of 3/5 is 0.6.

Example 5: Identify integers among the following given numbers.

a) √18/√2 b) -54.09 c) 12 d) 3/7

Solution:

a) √18/√2 = √(18/2)

                  = √9

                  = 3

3 is an integer, so, √18/√2 is an integer.

b) -54.09 is a decimal number. So, it is not an integer.

c) 12 is an integer

d) 3/7 is a fraction. So, it is not an integer.

In mathematics, a number system is a system of expressing numbers in various forms through writing. It is also often called the numeral system, which represents numbers by consistently using digits or other symbols. We have different types of number systems, such as a binary number system, an octal number system, a decimal number system, and a hexadecimal number system. Digits from 0 to 9 are used to represent the number systems. For example, a binary number system is represented by using the digits 0 and 1. A number is defined as a mathematical value that is used to count, measure, and also aid in performing various arithmetical calculations. There are different types of numbers, such as natural numbers, whole numbers, integers, rational and irrational numbers, etc.