Back to: MATHEMATICS JSS3

**Welcome to JSS3!**

*We are eager to have you join us in class!!*

*In today’s class, We will be discussing Whole Numbers. We hope you enjoy the class!*

**NUMBER BASE CONVERSIONS**

People count in twos, fives, twenties etc. Also, the days of the week can be counted in 24 hours. Generally, people count in tens. The digits 0,1,2,3,4,5,6,7,8,9 are used to represent numbers. The place value of the digits is shown in the number example: 395:- 3 Hundred, 9 Tens and 5 Units. i.e. 3X10^{2} + 9 X 10^{1} +5 X 10^{0}.

Since the above number is based on the powers of tens it is called the base ten number system i.e. 300 + 90 + 5

Also 4075 = 4 Thousand 0 Hundred 7 Tens 5 Units i.e. 4 x 10^{3} + 0 X 10^{2} + 7 X 10^{1 }+ 5 X 10^{0} Other Number systems are sometimes used.

For Example: The base 8 system is based on the power of 8. For example: Expand 647_{8}, 26523_{7}, 1011012,

(a) 647_{8} = 6 x 8^{2} + 4 x 8^{1} + 7 X 8^{0} =6 x 64 + 4 x 8 + 7 x 1

(b) 26523_{7} =2 x 7^{4 }+ 6 x7^{3} + 5 x 7^{2} + 2x 7^{1} + 3 x 7^{0}

(c) 101101_{2}= 1 x 2^{5} + 0 x 2^{4} + 1 x 2^{3} + 1 x 2^{2} + 0 x2^{1} + 1 x 2^{0}

**SELF EVALUATION**

Expand The Following

- 434
_{3} - 101111
_{2}

**CONVERSION TO DENARY SCALE (BASE TEN)**

When converting from other bases to base ten the number must be raised to the base and added.

**Worked Examples:**

Convert the following to base 10

(a) 17_{8}

(b) 11011_{2}

Solutions:

(a) 17_{8} = 1 X 8^{1} + 7 X 8^{0} = 1 X 8 + 7 X 1 = 8 + 7 = 15

(b) 11011_{2} = 1 X 2^{4} + 1 X 2^{3} + 0 X 2^{2} + 1 X 2^{1} + 1 X 2^{0} = 1 X 16 + 1 X 8 + 0 X 4 + 1 X 2 + 1 X 1

= 16 + 8 + 0 + 2 + 1 = 27

**SELF EVALUATION**

Convert The Following To Base Ten:

(a) 10100_{2}

(b) 2120_{3}

**CONVERSION FROM BASE TEN TO OTHER BASES**

To change a number from base ten to another base

- Divide the base ten number by the new base number.
- Continue dividing until zero is reached
- Write down the remainder each time
- Start at the last remainder and read upwards to get the answer.

Worked Examples:

- Convert 68
_{10}to base 6 - Covert 129
_{10 }to base 2

Solutions:

$1.\phantom{\rule{0ex}{0ex}}6|68\phantom{\rule{0ex}{0ex}}6|11R2\phantom{\rule{0ex}{0ex}}6|1R5\phantom{\rule{0ex}{0ex}}0|1\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}={152}_{6}$$2.\phantom{\rule{0ex}{0ex}}2|129\phantom{\rule{0ex}{0ex}}2|64R1\phantom{\rule{0ex}{0ex}}2|32R0\phantom{\rule{0ex}{0ex}}2|16R0\phantom{\rule{0ex}{0ex}}2|8R0\phantom{\rule{0ex}{0ex}}2|4R0\phantom{\rule{0ex}{0ex}}2|2R0\phantom{\rule{0ex}{0ex}}2|1R0\phantom{\rule{0ex}{0ex}}2|0R1\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}={10000001}_{2}$

**SELF EVALUATION**

- Convert 569
_{10}to base 8 - Convert 100
_{10}to base 2

**GENERAL SELF EVALUATION**

Convert the following to base seven

- 405
_{10} - 876
_{10}

Evaluate the following

- 5 – 3 + 4

We have come to the end of this class. We do hope you enjoyed the class?

Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.

In our next class, we will be talking about **Whole Numbers II.** We are eager to meet you there.

**Pass WAEC, JAMB, POST-UTME & more in One Sitting for FREE!💃**

Funmi AfolarinThank you good class

sofiat Afolarinthanks such a good class

blessingremegius2Pls y is it dat in something like 7 × 8°it is =7×1