There are several symbols and rules for numbers and how to use them to represent in the number system. They are used to express the number of different things present in a given set. Thus, the Roman numeral I, the Greek letter alpha, was the first letter used as a numerical.
The Hebrew letter aleph, the first letter used as a numeral, or the current number 1, is nothing but a Hindu-Arabic in origin. It can all be used to symbolize the concept of “oneness.”
You might not realize it, but mathematics is solely based on numbers. Without numbers, we would not have been able to learn trigonometry, calculus, and algebra, vectors, or indeed any area of life. As a result, we should feel grateful for discovering the number system which made our life simpler.
Thus, we must acknowledge that all integers are rational numbers. It is defined as numbers in the form p/q, where p and q are integers and q is not equal to 0. You can gain more knowledge by practising MCQ Questions for Class 9 Maths Chapter 1.
For example, 5 is an integer. However, it can be written as 5/1, the ratio of two integers of 5 and 1.
As some of you may believe, all decimal numbers are not rational numbers.
For example, two equals 1.414.
This includes infinite integers after the decimal; hence it cannot be stated as a ratio.
Decimal numbers that are also rational numbers include 1.5 = 3/2, 0.5 = 1/2, and so on.
What is the definition of a number?
Arithmetic calculations are performed with numbers. A number is a numerical value that is used to count, measure, or name items. Natural numbers, whole numbers, rational and irrational numbers, and so on are examples of numbers. A null value is also represented by the number 0.
There are many different types of numbers, such as even and odd numbers, prime and composite numbers. When a number is divisible by two, it is known as an even number. Whereas odd phrases are employed, prime and composite terminology is often referred to as devisors.
The locations to the left of the decimal point denote units, tens, hundreds, thousands, and so on in the decimal number system. This system uses decimal numbers to express itself. Every position demonstrates the base’s unique power (10).
Binary Number System
(BINARY NUMBER SYSTEM -Base 2 Number System)
Only two binary digits, 0 and 1, exist in the base 2 number system, often known as the Binary number system. A radix of 2 is the standard base-2 radix. Binary numbers, a mix of 0 and 1, are the figures specified by this system. For example, 110101 is a binary number.
Any system can be converted to binary, and a binary number can be converted to a system.
System of octal numbers (Base 8 Number System)
The octal number system has an eight-digit basis and employs digits ranging from zero to seven, denoting numbers. In computer applications, octal numerals are frequently employed. Decimal conversion is the same as converting an octal number to a decimal number.
The Hexadecimal Number System is a numerical system that uses hexadecimal (Base 16 Number System)
Base 16 is used to write or represent numbers in the hexadecimal format. The numbers in the hex system are first represented in the same way that they are in the decimal system, that is, from 0 to 9. The numerals are then represented using the alphabets A through F.
Hexadecimal numbers can be expressed as 0123456789ABCDEF
The decimal number can be expressed as 0123456789101112131415
Let us have a look at the diagram of the Number System
The base values and digits of many number systems can be found in the number system chart.
Unary Numeral System
When we hear the unary numeral system, it is a numerical system that uses only one (single) digit.
The unary numeral system is the simplest of the numeral systems. It consists of each natural number that is represented by an equal amount of symbols. For example, if they are marked by /, the number seven would be represented by //////, requiring us to type / seven times.
Tally marks are an example of a unary system that is still used today. On the other hand, the unary system can only be used for numbers that are of a smaller size. The number consists of a small value, even though this has a comparable role in theoretical computer science.
Do you know about Elias’s gamma coding? It is commonly employed in data compression that denotes arbitrary-sized integers by employing unary to signify binary number length.
Natural Numbers: The natural (or counting) numbers range from one to nine, including the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, etc. Natural numbers have an endless number of possibilities. The collection of natural numbers 1, 2, 3, 4, 5, 6, 7, 8, and so on is abbreviated as N.
The entire number ranges from zero to infinity, including natural integers.
Two natural numbers can be added to make a natural number (for example, 4 + 5000 will equal 5004). Any natural numbers can be combined to get a natural number (4 x 3500 = 14000).
However, the division and subtraction of any two or more natural numbers are not equal to natural numbers.
Rational Numbers: Rational numbers are numbers that can be expressed as a ratio between two integers. The fractions 13 and 11118, for example, are both rational numbers. Because each integer represented by z can be written as the ratio z1. Here, the rational number comprises all integers.
All decimal numbers that end with a zero are rational numbers (since 8.27 can be written as 827100.) A rational number is a decimal that is a recurring pattern in nature after a certain point.
Computer Numeral System
While using the computer, when we type any letter or word, the device translates those letters and digits into numbers. Computers are designed to understand only numbers and very few symbols like digits and symbols with different values. These values depend upon the position which presents the number.
MCQ Questions for Class 9 Maths Chapter 1
Problem 1
Between 3 to 4, find the value of six rational numbers.
Solution
Between 3 and 4, let qi be the rational number
Where j will be equal to 1 to 6.
Therefore, the 6 rational numbers will be as follows:
So here, the 6 rational numbers we have between 3 and 4 are as follows:
Conclusion
Hope you can now solve Number System MCQs without any issue. Thoroughly practice for grasping the concepts so that you can answer them easily.
