Number Systems: Definition, Rules, Sample Questions, Tips and FAQs

The Number System is the method by which we formulate numbers. There are several forms of number systems including binary, decimal, etc. It is a system wherein numbers are expressed. It is the mathematical notation for describing numbers with a consistent sequence of digits or symbols. It proceeds to represent any number and the arrangement of the figures.

Number System Concepts

Under Number Systems, we need to learn about:

• Natural Numbers

• Whole Numbers

• Integers

• Rational Numbers

• Irrational Numbers

• Real Numbers
  

A rational number either has a finite expansion into rational numbers, or it continues forever. 

The decimal expansion of an irrational number is not terminating or recurring. 

1. Demonstrate that 0.3333 … = 0.3, may be represented in rational form; i.e, p/q. 

Let x = 0.33333. 

10 x = 10 × (0.333….) = 3.333.... 

3.3333... = 3 + x. 

10x = 3 + x. 

9/x = 3. 

x = ⅓.

2. Write the following in decimal form and name expansions.   

1. 36/100.  

2. 1/11. 

Solution: 

1. 36/100 = 0.36. 

It is terminating. 

2. 1/11 = 0.09090909…

The solution is non-terminating and repeating.

Illustrated Examples:

1. Multiply 5√3 by 4√3.

Solution: 5√3 x 4√3

5 x 4 x √3 x √3

= 20 x 3

= 60

2. Rationalise the denominator of √3/(√2-√7).

Solution: Multiply both numerator and denominator by √2+√7

[√3/(√2-√7)] x [(√2+√7)/(√2+√7)]

Numerator = √3(√2+√7)

Denominator = (√2-√7)(√2+√7) = (√2)^2-(√7)^2 = 2-7 = -5

Therefore,

[√3(√2+√7)]/-5

= -√3/5(√2+√7)

3. Rationalise the denominator of 1/√5.

Solution: To rationalise the denominator of 1/√5, we need to multiply the numerator and denominator by √5

1/√5 x (√5/√5)

= √5/5

Also Read: MBA Preparation 2024: Tips to Prepare for MBA Entrance Exams

1. What are the five numbers between one and two? 

There are 5 rational numbers between one and two. 

Solution: We need to find 5 rational numbers between 1 and 2

Divide and multiple both the numbers by (5+1)

Hence,

6/6 and 12/6 are rational numbers now.

Therefore, 6/6, 7/6, 8/6, 9/6, 10/6, 11/6, 12/6.

Irrational numbers cannot be represented as either a fraction or a decimal. 

2. Is there a number √3 on the number line? 

Solution:

To locate √3 on the number line, we need to:

Build BD that passes via point OB perpendicular to it. 

Using Pythagora's theorem, we notice that OD = √((√2)^2+1^2) = √3. 

Draw an arc with centre O and radius OD to cut the number line at Q. 

Also Read:

Get here free PDFs of DILR practice questions with solutions. Practice these DILR questions to improve your performance in CAT and other MBA entrance exams:

Q: What is the significance of number systems?

Q: Describe the various groups of numbers.

Q: Why are the numbers used?

Q: What are the four different types of number systems?

Q: What are the uses of number systems?