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JSS1: MATHEMATICS - 1ST TERM

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  1. Whole Numbers I | Week 1
    3Topics
    |
    1 Quiz
  2. Whole Numbers II | Week 2
    1Topic
    |
    1 Quiz
  3. Counting in Base Two | Week 3
    4Topics
    |
    1 Quiz
  4. Arithmetic Operations | Week 4
    3Topics
    |
    1 Quiz
  5. Lowest Common Multiple (LCM) | Week 5
    1Topic
    |
    1 Quiz
  6. Highest Common Factor | Week 6
    1Topic
    |
    1 Quiz
  7. Fraction | Week 7
    7Topics
    |
    1 Quiz
  8. Basic Operations with Fractions I | Week 8
    3Topics
    |
    1 Quiz
  9. Basic Operations with Fractions II | Week 9
    1Topic
    |
    1 Quiz
  10. Directed Numbers | Week 10
    2Topics
    |
    1 Quiz
  11. Estimation and Approximation I | Week 11
    3Topics
    |
    1 Quiz
  12. Estimation and Approximation II | Week 12
    6Topics
    |
    1 Quiz
Lesson 3, Topic 1
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Number Base

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Counting in Base 10: (Decimal)

The usual system of counting is called the decimal or denary system.

“dec “means ten which means our usual decimal system is in Base 10.

In Base 10 we have digits for the numbers 0 – 9. We do not have a single-digit for ten.

We saw in the previous lesson that the Romans had a single character for 10 which is X.

In Base 10, we write 10 for number ten, but this stands for 1 ten and 0 ones. This is two digits; we have no single solitary digit that stands for “ten”.

We count in Base 10 like this.

 0 Start at 0
1 Then 1
••2 Then 2
   
•••••••••9 Up to 9
••••••••••10 Start back at 0 again, but add 1 on the left
••••••••••
11  
••••••••••
••
12  
   
••••••••••
•••••••••
19  
••••••••••
••••••••••
20 Start back at 0 again, but add 1 on the left
••••••••••
••••••••••
21 And so on!

This system enables us to write small or large numbers using a combination of digits.

Numbers in base 10 are usually written without the subscript ten or 10

431 ten is simply written as 431.

Apart from base 10, numbers are counted in other bases such as base two, base five, base seven, base eight, etc.

For example, 64eight means 64 in base 8.

Counting in Groups of Twos: (Binary)

Binary numbers are numbers written using only 0s and 1s.

Numbers 2, 3, 4, 5, 6, 7, 8, 9 do not exist in binary.

A major difference between decimal numbers are binary numbers is that decimal numbers are in base 10 and binary numbers are in base 2.

To show that a number is a binary number, follow it with a little 2 like this: 1012. This way people won’t think it is the decimal number “101” (one hundred and one).

As discussed in base 10 there are ten numbers: we count 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9

In base 2 we have two numbers: we count 0, 1

How do we Count in Base 2?

In the base 2 number system, we also count in groups of 2

When counting we go to a new group each time we reach a number that is a power of 2.

We, therefore, count as follows:

\(\scriptsize \circledast\) 1 unit (1)
\(\scriptsize \color{green}{\circledast \, \circledast}\) 1 group of 2 and 0 units (10)
\(\scriptsize \color{green}{\circledast \, \circledast} \, \color{black}{\circledast}\) 1 group of 2 and 1 unit (11)

If we add another object, we have 2 groups of two, which is 4. We continue counting as follows:

\(\scriptsize \color{blue}{\circledast \, \circledast \, \circledast \, \circledast}\) 1 group of four, 0 groups of two, and 0 units (100)
\(\scriptsize \color{blue}{\circledast \, \circledast \, \circledast \, \circledast}\, \color{black}{\circledast}\) 1 group of four, 0 groups of two, and 1 unit (101)
\(\scriptsize \color{blue}{\circledast \, \circledast \, \circledast \, \circledast} \, \color{green}{\circledast \, \circledast}\) 1 group of four, 1 group of two, and 0 units (110)
\(\scriptsize \color{blue}{\circledast \, \circledast \, \circledast \, \circledast} \, \color{green}{\circledast \, \circledast} \, \color{black}{\circledast}\) 1 group of four, 1 group of two, and 1 unit (111)

If we add another object, we have 3 groups of two, which is 8. We continue counting as follows:

\(\scriptsize \color{red}{\circledast \, \circledast \, \circledast \, \circledast \, \circledast \, \circledast \, \circledast \, \circledast}\) 1 group of eight, 0 groups of four, 0 groups of two, and 0 unit (1000)
\(\scriptsize \color{red}{\circledast \, \circledast \, \circledast \, \circledast \, \circledast \, \circledast \, \circledast \, \circledast} \, \color{black}{\circledast}\) 1 group of eight, 0 groups of four, 0 groups of two, and 1 unit (1001)
\(\scriptsize \color{red}{\circledast \, \circledast \, \circledast \, \circledast \, \circledast \, \circledast \, \circledast \, \circledast}\, \color{green}{\circledast\, \circledast}\) 1 group of eight, 0 groups of four, 1 group of two, and 0 units (1010)
\(\scriptsize \color{red}{\circledast \, \circledast \, \circledast \, \circledast \, \circledast \, \circledast \, \circledast \, \circledast}\, \color{green}{\circledast\, \circledast}\, \color{black}{\circledast}\) 1 group of eight, 0 group of four, 1 group of two, and 1 unit (1011)
\(\scriptsize \color{red}{\circledast \, \circledast \, \circledast \, \circledast \, \circledast \, \circledast \, \circledast \, \circledast}\, \color{blue}{\circledast\, \circledast\, \circledast\, \circledast}\) 1 group of eight, 1 group of four, 0 groups of two, and 0 units (1100)

Decimal vs. Binary

Binary Decimal
00
11
102
113
1004
1015
1106
1117
10008
10019
101010
101111
110012

10 as a decimal number is 1010 as a binary number

5 as a decimal number is 101 as a binary number

The four most commonly used number systems are;

  1. Decimal Number System
  2. Binary Number System
  3. Octal Number System
  4. Hexadecimal Number System
Types of Number Systems 1
Number SystemBaseDigits Used
Decimal Number System100, 1, 2, 3, 4, 5, 6, 7, 8, 9(Total 10 digits)
Binary Number System20, 1(Total 2 digits)
Octal Number System80, 1, 2, 3, 4, 5, 6, 7(Total 8 digits)
Hexadecimal Number System160, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F(Total 16 digits)
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