DILR Preparation Tips for MBA Number Systems: Definition, Rules, Sample Questions, Tips and FAQs

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What is Number Systems?

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 learn about:

Natural Numbers
Whole Numbers
Integers
Rational Numbers
Irrational Numbers
Real Numbers

Questions on Number Systems with Solutions

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 Pythagoras 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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Terminating and Non-Terminating Decimal Expansion

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.

36/100.
1/11.

Solution:

36/100 = 0.36.

It is terminating.

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

FAQs Regarding Number Systems

Q: What is the significance of number systems?

A: In mathematics, a number system is characterised as a framework that allows all numbers to be represented. The number method offers a distinct means of communicating numbers and the logical basis for a math equation.

Q: Describe the various groups of numbers.

A: The various kinds of numbers are:

Natural numbers
Whole numbers
Real numbers
Rational numbers
Irrational numbers
Complex numbers

Q: Why are the numbers used?

A: The numbers define the spectrum of everything. Numbers are used to measuring anything from income to time. Without statistics, we cannot realise how useful items are.

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

A: The four major types of number system are:

Binary number system (base 2 number system)
Octal number system (base 8 number system)
Decimal number system (base 10 number system)
Hexadecimal number system (base 16 number system)

Q: What are the uses of number systems?

A: The most popular usage of the number system is in computers. The binary number system is used. Binary numbers are used in the encoding process of digital.

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