Mathematics

Number Base System - Table showing the Number Bases with explanations

len Alfred Ajibola - Tue, 21st May, 2019 @ 15:42

Topics in Mathematics

Angles: Type of angles based on degree measurement Angle Pairs: Types of angle pairs Conversion of Number Bases explained with examples Angles: What are Angles? Categories of Angles Lines and Types in Mathematics Number Base System - Table showing the Number Bases with explanations Mathematics Scheme of Work, SS1, 3rd Term Mathematics Scheme of Work, SS1, 2nd Term Mathematics Scheme of Work, SS1, 1st Term Trigonometry - Sine, Cosine and Tangent explained with worked examples Quadratic Equation - Factorization of Quadratic Equation Algebra - Explanation and Worked Examples on Algebra


Academic Questions in Mathematics

Please check out our Test Your Knowledge page to see all Questions and Answers

Factorize 12a2 - 20a + 3

  • A. (6a - 1)(2a - 3)

  • B. (6a - 1)(2a + 3)

  • C. (6a + 1)(2a - 3)

  • D. (6a + 1)(2a + 3)

  • E. (-6a + 1)(2a - 3)

  • F. (-6a + 1)(2a + 3)

Simplify 10ab + 7ab

  • A. 17ab2

  • B. 17a2b2

  • C. 3ab2

  • D. 3a2b2

  • E. 17ab

  • F 3ab

Which of the following is not a type of angle?

  • A. Right angle

  • B. Left Angle

  • C. Acute Angle

  • D. Complete Angle

  • E. Straight Angle

  • F. Reflex angle

Two lines that can never meet each other are best considered as _____ lines.

  • A. straight
  • B. vertical
  • C. horizontal
  • D. parallel
  • E. oblique
  • F. perpendicular

An angle at exactly 90o is a/an _____ angle.

  • A. acute
  • B. obtuse
  • C. reflex
  • D. right
  • E. complete
  • F. straight

Slanted or tilted lines that will finally meet at some point but NOT at a right angle are referred to as _____.

  • A. Oblique
  • B. Curved
  • C. Vertical
  • D. Perpendicular
  • E. Parallel
  • F. Horizontal

The two sides that forms an angle are referred to as the _____.

  • A. Arms
  • B. Vertexes
  • C. Bays
  • D. Zones
  • E. Limbs
  • F. Dune

The point where the two sides of an angle meet is termed the _____.

  • A. Arms
  • B. Vertex
  • C. Bays
  • D. Zones
  • E. Limbs
  • F. Dune

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Introduction to Number Bases:

Numbering begins with 0 (zero). Also, numbers are expressed in bases (sometimes called radix). A base 10 number for instance will comprise of 10 digits ranging from 0 – 9.

Note: We generally use base 10 in our numbering system.

Base 10 digits will comprise of: 0 1 2 3 4 5 6 7 8 9

Since the above numbers are composed of 10 digits, Base 10 may be referred to as decimals or denary digits.

The table below illustrates base 10 digits:

Unary or Base 1

Base 10

Sumary

 

0

All base digits starts at 0

1

1

Next digit is 1

11

2

Next digit is 2

111

3

Next digit is 3

1111

4

Next digit is 4

11111

5

Next digit is 5

111111

6

Next digit is 6

1111111

7

Next digit is 7

11111111

8

Next digit is 8

111111111

9

Next digit is 9. Base 10 digit ends with 9

1111111111

10

After the last digit which is 9 above, we will start at zero again, but add 1 to the left

11111111111

11

We will add 1 digit to the right

111111111111

12

We will add 1 digit to the right

1111111111111

13

We will add 1 digit to the right

11111111111111

14

We will add 1 digit to the right

111111111111111

15

We will add 1 digit to the right

1111111111111111

16

We will add 1 digit to the right

11111111111111111

17

We will add 1 digit to the right

111111111111111111

18

We will add 1 digit to the right

1111111111111111111

19

We will add 1 digit to the right

11111111111111111111

20

After the last digit which is 9 above, we will start at zero again, but add 1 to the left

111111111111111111111

21

We follow the same procedure all through

 

Apart from base 10 (Decimal), we also have other bases like:

  • Base 2 also called Binary: consists of 2 digits which are 0 and 1
  • Base 3 also called Ternary: consists of 3 digits which are 0, 1 and 2
  • Base 4 also called Quaternary: consists of 4 digits which are 0, 1, 2 and 3
  • Base 5 also called Quinary: consists of 5 digits which are 0, 1, 2, 3 and 4
  • Base 6 also called Senary: consists of 6 digits which are 0, 1, 2, 3, 4, 5 and 6
  • Base 7 also called Septenary: consists of 7 digits which are 0, 1, 2, 3, 4, 5, 6 and 7
  • Base 8 also called Octal: consists of 8 digits which are 0, 1, 2, 3, 4, 5, 6, 7 and 8
  • Base 9 also called Nonary: consists of 9 digits which are: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9

Note: When we have a base number greater than 10; for instance base 11 or base 12 or base 13 and so on, the next digit will be an alphabet in its ascending order.

Let's see the examples below:

  • Base 11 also called Undecimal: consists of 11 digits which are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A
  • Base 12 also called Duodecimal: consists of 12 digits which are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B

Note: Base 16 is also known as hexadecimal digits.

Hexadecimal digits prove useful in Internet Protocol Address (IP Address) and Media Access Control Address (MAC Address) in computer networking.

Please read on the OSI Model of Networking here.

The digits for base 16 (Hexadecimal digits) are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

 

With regards to base 2, it will comprise of only 2 digits which are 0 and 1.

Since we have just 2 digits here, base 2 is often referred to a binary digit.

Binary digits are fundamental to how computers work. This is why you may see stuffs like "01001100101011011" in a programming or computer language. Remember, we have just two digits in binary and that’s 0 and 1.

The table below shows what base 2 would look like:

Base 1

Base 2

Summary

 

0

All base digits starts at 0

1

1

Next digit is 1. Base 2 digit ends with 1

11

10

We start at zero again, but add 1 to the left

111

11

We will add 1 digit to the right

1111

100

Since the above digits is all 1’s and base 2 ends with digit 1, we will change all the 1’s to 0’s and add 1 to the left

11111

101

We will add one to the farthest 0 at the right

Note: Understanding base 2 is very vital for Internet Protocol address (IP Address) in computer networking.

Please read on Computer Networks here.

 

Ternary or Base 3 comprise of 3 digits which are 0, 1 and 2.

The table below shows what base 3 would look like:

Unary/Base 1

Base 3

Summary

 

0

All base digits starts at 0

1

1

Next digit is 1.

11

2

Next digit is 2. Base 3 digit ends with 2

111

10

We will start back at 0 and add 1 to the left

1111

11

Next digit is 1 from the right

11111

12

Next digit is 2 from the right

111111

20

We will start back at zero and add one to the left

1111111

21

We will add 1 to the right

11111111

22

We will add 1 to the right

111111111

100

Since the above digits is all 2’s, we will change all  the 2’s to 0’s and add 1 to the left

1111111111

101

We will add 1 to the farthest right

 

The table below shows a summary of base 10, base 2, base 6, base 11 and base 16 respectively.

Unary

Base 10

Base 2

Base 6

 Base 11

Base 16

1

1

1

1

1

1

11

2

10

2

2

2

111

3

11

3

3

3

1111

4

100

4

4

4

11111

5

101

5

5

5

111111

6

110

10

6

6

1111111

7

111

11

7

7

11111111

8

1000

12

8

8

111111111

9

1001

13

9

9

1111111111

10

1010

14

A

A

11111111111

11

1011

15

10

B

111111111111

12

1100

20

11

C

1111111111111

13

1101

21

12

D

11111111111111

14

1110

22

13

E

111111111111111

15

1111

23

14

F

1111111111111111

16

10000

24

15

10

Notice that we skipped the zero (0) value in the above table.

Please read on the Conversion of Number Bases explained with worked examples here.

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Alfred Ajibola is a Medical Biochemist, a passionate Academician with over 7 years of experience, a Versatile Writer, a Web Developer, a Cisco Certified Network Associate and a Cisco CyberOps Associate.


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Amazing facts in Mathematics

The opposite sides of a 🎲 dice 🎲 will always give a sum of seven

31,556,926 seconds makes one year

From 0 through 1000, the only number that has the letter 'a' in it is 'one thousand'

÷

The division symbol '÷' is actually called an obelus

Four is the only number in the English language that is spelt with the same number of letters as the number (4) itself

40 is spelt as FORTY and not FOURTY. It is the only number that is spelt with letters arranged in alphabetical order 🙄

An odd number is a number that cannot be divisible by 2.

Every odd number has an 'e' in its spelling. They include:

  • One
  • Three
  • Five
  • Seven
  • Nine

555 in Thailand should sound like 'hahaha'. This is because the word '5' means 'ha' in Thailand

10! Actually means 10 factorial in mathematics. Below is its calculation:

10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3628800

3628800 seconds is the same as 42 days

42 days is the same as 6 weeks

We can therefore say that 10! equals 6 weeks or 3628800 seconds in mathematics

When you multiply 111,111,111 by 111,111,111; the result equals 12,345,678,987,654,321


NOTABLE POINTS IN Mathematics

Sides of a right angle triangle - Len Academy

 

The image above shows a right angled triangle. The angle of the above right triangle is denoted as θ

 

Hypotenuse is always the longest side of the triangle.

Opposite is the side opposite the angle (θ)

Adjacent is the shorter side next to the angle (θ)

Each of Sin θ, cos θ and tan θ are the ratio of sides of the right triangle. They are calculated by using the formula (margic word) sohcahtoa:

Sohcahtoa - Len Academy

soh

Sin θ = Opposite/Hypotenuse

cah

Cos θ = Adjacent/Hypotenuse

toa

Tan θ = Opposite/Adjacent

Please read more on sine, cosine and tangent here

Circumference in mathematics means the distance around the edge of a circle (or a another curverd surface).

Perimeter means the distance around a square or rectangle or polygon.

Circumference is to circle or any other curved surface

Circumference of a Circle - Len Academy

Perimeter is to square or rectangle or polygon

Perimeter of a Rectangle - Len Academy