In math, number systems are the means by which numbers are expressed mathematically with the help of a specific set of digits. There are basically four types of number systems.
Types of Number System
Binary number system:
A binary number contains only two digits, 0 and 1. They are mostly used in computer languages.
Decimal number system:
There are ten digits from 0-9 in this number.
Octal number system:
The number ranges from 0 to 7.
Hexadecimal number system:
There are digits ranging from 0 to 9 and alphabets ranging from 'A' to 'F' that make up the number. Here,
- A=10
- B=11
- C=12
- D=13
- E=14
- F=15
Natural numbers:
The number N contains all positive numbers from 1 to all possible positive numbers. This can also be written as N= [1, 2, 3... ].
Whole numbers:
The sets of numbers in this set are generally denoted by the letter W. They include 0 to all possible positive numbers. This can be written as W= {0,1,2,3….}
Integers:
This consists of every number from negative infinity to positive infinity, which can be represented by both the letters I and Z.
Number Systems Sample Questions for Class 11
Question 1
To write a complex number in standard form, the real number part proceeds the imaginary number part.
A. True
B. False
Question 2
If -a \ vec{v} = <<-9,12>> and a \ vec{v} = <<9,-12>>, and a can be any real number (positive or negative), which of the following are possible values of vec{v} ? Choose all that apply.
A. <<9,12>>
B. <<3,-4>>
C. <<-3,-4>>
D. <<-9,12>>
Question 3
For polynomials p(x) and q(x), where (p(x))/(x-1) = q(x) + b/(x-1), what value(s) of b ensure that p(1) = 0 ? There may be more than one correct answer.
A. x-1
B. 1
C. 0
D. Any real number
Question 4
For f(x)=3x-6 and g(x)=x-2, find (f//g)(x) and its domain.
A. 3; all real number except x = 2
B. 1; all real numbers
C. 3; all real numbers
D. -3; all real numbers except x = 3
Question 5
What is the missing reason in step 2?
A. Given
B. Division Property of Equality
C. Definition of rational numbers
D. Any number can be rewritten in another form