According to the waec syllabus, you are expected to know how to convert numbers from one base to another. You are also expected to understand Basic operations on number bases.

In the Video below, you will learn conversion from one base

to base 10 and vice versa. Conversion from one base to another base,

Addition, subtraction and multiplication of number bases.

**Note**: To ensure that you don’t get confused as a waec candidate, some convention were ignored. For example, saying 52, twelve instead of five two, one two and so on.

## Major Highlights From The Video

1. A number system is a way to **represent numbers**. Numeration is the action or process of calculating or assigning a number to something.

2. We are used to the **base-10 number system,** which is also called decimal. Other common number systems include base-16 (hexadecimal), base-8 (octal), and base-2 (binary).

3. **What is 5+5**? If you answered 10, you are thinking in base-10.

4. Let’s take a quick look at counting. First, you go through all the digits: 0, 1, 2… Once you hit 9, you have no more digits to represent the next number.

5. So, you change it back to 0, and add 1 to the tens digit, giving you 10. The process repeats over and over, and eventually, you get to 99, where you can’t make any larger numbers with two digits, so you add another, giving you 100.

6. Using 2347 as an example.

- As you saw, there are 2 groups of a thousand. Not coincidentally,
`1000 = 10*10*10`

which can also be written as`10`

.^{3} - There are 3 groups of a hundred. Again, not coincidentally,
`100 = 10*10`

or`10`

.^{2} - There are 4 groups of ten, and,
`10 = 10`

.^{1} - Finally, there are 7 groups of one, and.
`1 = 10`

(That may seem strange, but^{0}*any*number to the power of 0 equals 1, by definition.)

This is essentially the definition of base-10. To get a value of a number in base-10, we simply follow that pattern.

8. Base-8 is also called octal. Base-8 means just what is sounds like: the system is based on the number eight (as opposed to ten).

9. **Binary System**: Widely used in all forms of switching applications. The only symbols used are 0 and 1 and the place values are powers of 2, i.e the system has a base of 2.

10. **Converting From Base-8 to Base-10: **The pattern we saw before with base-10 holds true here also. We’ll look at 5238. There are five groups of 8^{2}, two groups of 8^{1} and three groups of 8^{0}(remember, 8^{0}=1). If we add these all up, `5*8`

, we get 33910 which is our final answer.^{2} + 2*8^{1} + 3*8^{0} = 5*64+2*8+3 = 339

11. We have also learnt multiplication, division, subtraction and addition on Number Bases.

Watch the video for everything you need to know as long as **Waec Mathematics Number and Numeration** is concerned.

**Reference:**

- Engineering mathematics
- Jamb past questions
- code.tutsplus.com

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