Number Systems Questions with Answers for MBA Preparation: Download PDFs

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

To further understand this topic of Mathematics, understand various concepts related to it:

• Numeral System: It is defined as the way in which numbers are written and represented using digits or symbols.
• Natural Numbers: It refers to positive whole numbers used for counting (example: 1, 2, 3, ...).
• Whole Numbers: It refers tonatural numbers and zero (example: 0, 1, 2, 3, ...).
• Integers: It refers to hole numbers and their negative counterparts (example: -4 -3 -2, -1, 0, 1, 2, 3, 4...).
• Rational Numbers: When numbers are expressed as a fraction p/q, where p and q are integers and q is not zero, then it is called Rational Numbers.
• Real Numbers: It refers to all rational and irrational numbers.
• Complex Numbers: It refers to those numbers that are expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit (√-1).

These concepts are taught in school so one would have basic understanding of the same. To prepare for competitive exams, one needs to however, study in further detail and practice advance level questions. 

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 2025: 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. 

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