Number System Introduction With Tips & Tricks

Safalta Expert Published by: Saksham Chauhan Updated Wed, 18 May 2022 12:04 AM IST

Highlights

A number system is a representational system for numbers. It's also known as the numeration system, and it specifies a set of values to represent a quantity. These numbers are used as digits, with the most popular ones being 0 and 1, which represent binary numbers. Other sorts of number systems are represented by digits ranging from 0 to 9.  Check here at safalta.com

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A number system is a representational system for numbers. It's also known as the numeration system, and it specifies a set of values to represent a quantity. These numbers are used as digits, with the most popular ones being 0 and 1, which represent binary numbers. Other sorts of number systems are represented by digits ranging from 0 to 9.

Number System Types

In mathematics, there are several different types of number systems. The following are the four most popular number systems:

System of decimal numbers (Base- 10)
System of binary numbers (Base- 2)
System of octal numbers (Base-8)
System of hexadecimal numbers (Base- 16)
Let us now look at some instances of different sorts of number systems.

System of decimal numbers

Because it employs ten digits from 0 to 9, the decimal number system has a base of ten.

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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 represent itself. Every position demonstrates the base's unique power (10).

The following is an example of a decimal number system:

The decimal number 1457 has seven digits in the units place, five in the tens place, four in the hundreds place, and one in the thousands place, and its value may be represented as
(1×103) + (4×102) + (5×101) + (7×100)

(1×1000) + (4×100) + (5×10) + (7×1)

1000 + 400 + 50 + 7

1457

System of binary numbers

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, which are a mix of 0 and 1, are the figures specified by this system. 110101, for example, is a binary number.

Any system may be converted to binary and vice versa.

System of octal numbers

The octal number system has an eight-digit basis and employs digits ranging from 0 to seven to denote numbers. In computer applications, octal numerals are often employed. The process of converting an octal number to decimal is the same as decimal conversion and is demonstrated with an example below.

Example: Convert 2158 into decimal.

Solution:

2158 = 2 × 82 + 1 × 81 + 5 × 80

= 2 × 64 + 1 × 8 + 5 × 1

= 128 + 8 + 5

= 14110

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 as they are in the decimal system, i.e. from 0 to 9. The numerals are then represented using the alphabets A through F. The table below demonstrates how numbers are represented in the hexadecimal number system.

Question 1:
Find the sum of place and face values of 8 in 43836

Option 1: 88

Option 2: 808

Option 3: 880

Option 4: 888

2: 808

Explanation: Place value of 8 = 800 Face value of 8=8 A required sum=800+8=808

Question 2:
Of the 3 numbers whose average is 112, the first is 3/13 times the sum of other 2. The first number is _____.

Option 1: 63

Option 2: 95

Option 3: 42

Option 4: 126

1: 63

Explanation:

Let the three numbers be z, y, z

Sum of three numbers = x+y+z=112 × 3 = 336

According to ques,=>x = 3/13  × (y + 2)

Question 3:
If 5 - x > 1 + 3x and 5 + 5x ≥ 2 + 2x; then x can take which of the following values?

Option 1: 2

Option 2: -2

Option 3: 3

Option 4:0

4:0

Explanation:
Expression (i) : 5 - x > 1 + 3x3x + x < 5 - 1, = > 4x < 4x < 1Expression (ii) : 5 + 5x ≥ 2 + 2x5x - 2x ≥

Question 4:
If 5x - 1 < 3x + 2 and 5x + 5 > 6 - 2x; then x can take which of the following values?

Option 1: 0

Option 2: 1

Option 3: -1

Option 4: 2

Explanation:
Expression 1 : 5x - 1 < 3x + 25x − 3x 2 + 1 = 2x < 3x < 3 2 - - - i Expression 2 : 5x + 5 > 6 - 2x5x + 2x

Question 5:
In an arithmetic progression, if 9 is the 5th term, -26 is the 12th term, then -6 is which term?

Option 1: 11

Option 2: 8

Option 3: 10

Option 4: 7

Question 6:
The sum of two numbers is 7 and the sum their squares is 23, their product is equal to

Option 1: 10

Option 2: 11 Option 3: 12

Option 4: 13

4: 13

Explanation:
Let the numbers be x and yIt is given that x 2 + y 2 = 23 - - - i Also, x + y = 7Squaring both sides, we get : x 2 + y

Question 7:
The difference between two numbers is 1146. When we divide the larger number by smaller we get 4 as quotient and 6 as remainder. Find the larger number.

Option 1: 1526

Option 2: 1431

Option 3: 1485

Option 4: 1234

1: 1526

Explanation:
Let the smaller number be and the larger number = (x + 1146)According to ques, on dividing the larger term by smaller

Question 8:
If 2x + 3y/ 3x - 4y = 11/7 , then the value of x y is _______

Option 1: 65 19

Option 2: 68 = 19

Option 3: 67

Option 4: 64 19

1: 65/19

Question 9:
Find the value of√(2x + 5) 2 − 2 √(x − 1) 2

Option 1: 1

Option 2: 6

Option 3: 3

Option 4: 0

2: 6

Question 10:
The pair of equations are 7x+8ky-16=0 and 14x+112y-21=0. Find the value of ‘k’ for which the system is in consistent.

Option 1: 2

Option 2: 3

Option 3: 5

Option 4: 7

4: 7

Explanation:
Equations : 7x+8ky-16=0 and 14x+112y-21=0 For two equations to be inconsistent (no solution), the ratio of coefficients of both equations must be of the form = a1/b1 = a2/b2 ≈
c1/c2

Question 11:
The value of 40 + √9√81 is

Option 1: 9

Option 2 7:

Option 3: 11

Option 4:√111

2: 7

Explanation:

Question 12:
How many two digit numbers are divisible by 3 but not by 7 ?

Option 1: 13

Option 2: 26

Option 3: 30

Option 4: 8

2: 26

Explanation:
Two digit numbers divisible by 3 are : 12, 15, 18, ......., 96, 99
The above series follows an A.P. with first term a= 12 , common difference d = 3 and last term l=99. Let number of terms be n

l=a+(n−1)d
12+(n−1)(3)=99
(n−1)×3=99−12=87
n−1=87/3 = 29
n=29+1=30
Similarly, two digit numbers divisible by L.C.M. (3,7) = 21 are : 21, 42, 63, 84 = 4 numbers Two digit numbers are divisible by 3 but not by 7 = 30−4=26

Question 13:
If a number 6573547x45 is divisible by 9, then find the value of x.

Option 1: 7

Option 2: 0

Option 3: 8

Option 4: 6

3: 8

Explanation:
For a number to be divisible by 9, sum of digits of the number must be divisible be 9. = > Sum of digits of number = 6

Question 14:
Calculate the value of 59881 × 59881 − 49681 × 49681/10200

Option 1: 110956

Option 2: 109562

Option 3: 109652

Option 4: 109662

2: 109562

Explanation:

Question 15:
If 169 is subtracted from the square of a number, then the result obtained is 7056. What is the number?

Option 1: 75

Option 2: 78

Option 3: 85

Option 4: 87

3: 85

Explanation:

Question 16:
The number 334 x 545 x 7 p is divisible by 3340 if p is at least

Option 1: 2

Option 2: 4

Option 3: 3

Option 4: 1

1: 2

Explanation:
334 x 545 x 7 p is divisible by 3340 334×(5×109)×7×p is divisible by 334×5×2 Clearly, p=2

Question 17:
The last digit of the number obtained by multiplying the numbers 41 x 42 x 43 x 44 x 45 x 46 x 47 x 48 x 49 will be ?

Option 1: 0

Option 2: 1

Option 3: 4

Option 4: 5

1: 0

Explanation:
Last digit will be multiplication of 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9. It includes 5 & 2. So, 5 x 2=10, 0 will be the last digit.

Question 18:
The sum of the digits of a two digit number is 10, when the number is reversed, the number increases by 72.Find the number.

Option 1: 19

Option 2: 20

Option 3: 21

Option 4: 22

1: 19

Explanation:
By checking options 91-19=72 Or Let the number be xy So 10x + y = 10 ..... (i) When the number is reversed the new number is yx So (10y + 10 ) - ( 10x +y ) = 72 ....(ii) From Eqs. (i) & (ii) x = 1 and y =9 ∴number = 19

Question 19:
The units digit in the product ( 784 x 618 x 917 x 463 ) is

Option 1: 2

Option 2: 3

Option 3: 4

Option 4: 5

1: 2

Explanation:
Units digit in the given product = Units digit of 4 x 8 x 7 x 3
= Units digit of 672
= 2

Question 20:
If 1x5x01 is divisible by 11, then the value of x is

Option 1: 6

Option 2: 4

Option 3: 8

Option 4: 9

3: 8

Explanation:
When a number is divisible by 11, then sum of numbers at even place - sum of numbers at odd place = 0 or
divisible by 11.
( x + x + 1 ) - ( 1+ 5 + 0 ) = 11
⇒ 2x - 5 = 11
∴ x = 8

What are the different types of number system ?

The following are the four most popular number systems:

System of decimal numbers (Base- 10)
System of binary numbers (Base- 2)
System of octal numbers (Base-8)
System of hexadecimal numbers (Base- 16)

How do you explain number system?

A number system is defined as the representation of numbers by using digits or other symbols in a consistent manner. The value of any digit in a number can be determined by a digit, its position in the number, and the base of the number system

Who created the number system?

The Babylonians got their number system from the Sumerians, the first people in the world to develop a counting system

Who used numbers first?

Numbers, and counting, began about 4,000 BC in Sumeria, one of the earliest civilizations. With so many people, livestock, crops and artisan goods located in the same place, cities needed a way to organize and keep track of it all, as it was used up, added to or traded.

Who discovered zero as a number?

The first recorded zero appeared in Mesopotamia around 3 B.C. The Mayans invented it independently circa 4 A.D. It was later devised in India in the mid-fifth century, spread to Cambodia near the end of the seventh century, and into China and the Islamic countries at the end of the eighth

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