Number System Notes – Quantitative Aptitude

The Number System is a crucial topic within the Quantitative Ability/Reasoning section of the General Science and Ability syllabus for the CSS written exams. The Federal Public Service Commission (FPSC) has consistently tested candidates on this topic in various ways in the General Recruitment tests and the CSS MCQs-Based Preliminary Test (MPT) test. Students should devote substantial time and effort to understanding and practicing this topic.

Even before there were numbers, people needed to count things. They used different methods, like making scratches on stones or storing pebbles. Each pebble represented one item. This was a simple way to keep track of their belongings, but it wasn’t very efficient. One of the most important inventions in human history was the creation of numbers. Numbers gave us a way to represent quantities in a more organized way. We could count things accurately and answer questions like “How many?” and “How much?”. A special number called zero was also invented. Zero represents nothing. It might seem strange, but it’s a very important number. It helps us understand the concept of emptiness and makes our number system complete.

Numbers and Digits:

In the realm of mathematics, numbers are the fundamental entities that quantify, measure, and represent quantities. These numbers are constructed using individual elements known as digits. In the decimal number system, the ten digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. A combination of these digits forms a numeral, which represents a specific number.

Number System:

A number system is a set of rules and symbols used to write and represent numbers. It’s like a language that allows us to communicate mathematical ideas. Just as we use letters to form words, we use digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to create numbers. Number system goes beyond simple counting. It provides a unique representation of every number and represents the arithmetic and algebraic structure of the figures. It helps us understand the relationships between numbers and perform operations like addition, subtraction, multiplication, and division. These operations are the foundation of arithmetic and algebra.

Different cultures and civilizations have developed their own unique number systems throughout history. The decimal system, which we use today, is based on ten digits. Other systems, like binary and hexadecimal, are used in computer science and technology.

Sub-topics covered in Number System Notes

Basics of Number System
- Face Value
- Place Value
Types of Numbers
- Natural Numbers (N)
- Whole Numbers (W)
- Integer Numbers (I)
- Even Numbers
- Odd Numbers
- Rational Numbers
- Irrational Numbers
- Prime Numbers
- Composite Numbers
- Co-Prime Numbers
- Triangular Numbers
Factors
- Prime factorisation of a number
- Number of factors
- Sum of all factors
- Number and Sum of even factors of a number
- Number and Sum of odd factors of a number
- Some Important Results of Factors
Recurring Decimal
Divisibility Test
Prime Number Test
Number of Zeros in an expression
Number of Zeros in n!
Remainder Theorem
Important Formulae