Mathematics

Conversion of Number Bases explained with examples

len Alfred Ajibola - Sat, 22nd February, 2020 @ 21:55: PM

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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Conversion of Number Bases:

In order to convert a base to another base; for instance, if we were to convert a base 10 to base 2, we will first need to know the powers of the base to which we are converting to.

Please read on the Introduction and Explanations of the Number Base System using Tables here.

The instances below shows the powers of various numbers:

The powers of 2 are:

  • 2 raised to power 0 = 1. (That is; 20 = 1)
  • 2 raised to power 1 = 2. (That is; 21 = 2) or (2 x 1 = 2)
  • 2 raised to power 2 = 4. (That is; 22 = 4) or (2 x 2 = 4)
  • 2 raised to power 3 = 8. (That is; 23 = 8) or (2 x 2 x 2 = 8)
  • 2 raised to power 4 = 16. (That is; 24 = 16) or (2 x 2 x 2 x 2 = 16)
  • 2 raised to power 5 = 32. (That is; 25 = 32) or (2 x 2 x 2 x 2 x 2 = 32)
  • And so on.

Any value raised to the power of zero will always equal to 1.

Simply put, the power of 2 can be written as:

  • 1, 2, 4, 8, 16, 32, 64, 128, 256 and so on.

Following the same steps as above, the power or 3 will be:

  • 1, 3, 9, 27, 81, 243, 729 and so on.

Still following the same steps as above, the powers of 4 are:

  • 1, 4, 16, 64, 256, 1024 and so on:

You can read on the Factorization of Quadratic Equation here.


Note: During the final step of our base conversion, the value "one" (1) divided by our base value of interest will always result in the answer "zero remainder one" (0 remainder 1). This is an important step to note as we shall see in our examples below.

 

Example 1

  • Convert the decimal 10 to base 2

Step 1: We need divide the decimal number by the base we want to convert to.

  • Decimal value = 10
  • We are converting to base 2
10/2 = 5 Remainder 0

Note: We must take into account the remainder from our division because it will be used as our answer.

Every other step will be similar to step 1 but we will divide our resultant answer from the subsequent steps.


Step 2: Our previous answer from the above division was 5

5/2 = 2 Remainder 1

Step 3: Our previous answer from the above division was 2

2/2 = 1 Remainder 0

Step 4: Our previous answer from the above division was 1

1 divided by 2 = 0 Remainder 1

Once our division equals 0, we are done.

Next; we will have to write the reminder from bottom - top; and that’s our answer.

Answer is 10102

OR

We can also solve this question by using a table; where we will divide the decimal number by the base we want to convert to:

Base 2

Decimal value

Remainder

2

10

-

2

5

0

2

2

1

2

1

0

2

0

1

Counting our remainder from below;

Answer is 10102

Please read on the Explanations and Worked Examples on Algebra here.

 

Note: I will use different expressions for the questions below but they will all mean the same thing. (We will be converting a number from base 10 to another base).

 

Example 2

  • Convert 15 to base 2

For simplicity, we will use a table to solve this question.

Base 2

Decimal value

Remainder

2

15

-

2

7

1

2

3

1

2

1

1

2

0

1

Counting our remainder from below;

Answer is 11112

You can read on Trigonometry explained with Worked Examples here.

 

Example 3

  • Convert 16 to 164

Base 4

Decimal value = 16

Remainder

4

16

-

4

4

0

4

1

0

4

0

1

Counting our remainder from below;

Answer is 1004

 

Example 4

  • Convert 1610 to base 1616

Base 16

Decimal value = 16

Remainder

16

16

-

16

1

0

16

0

1

Counting our remainder from below;

Answer is 1016

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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 sounds like 'hahaha'. This is because the number '5' means 'ha' in Thailand

In mathematics, 10! means 10 factorial. 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

Interestingly, 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. Below are some points to note:

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 of a Circle - Len Academy

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

Circumference is to circle or any other curved surface

Perimeter of a Rectangle - Len Academy

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

Perimeter is to square or rectangle or polygon