MAIP 211
Non-decimal place value in
numeration systems (1/2) /
Nie-desimale plekwaarde in
getalsisteme (1/2)
Ms. Reinhard Selowa
56139446@nwu.ac.za /
Rey.Selowa@nwu.ac.za
Outcomes / Uitkomstes
Section outcomes
After completing this study unit, you should be
able to:
Represent numbers in other bases than the
decimal (base 10) number system, for example
base 5
Addition in base 5
Subtraction in base 5
Multiplication in base 5
Preparation / Voorbereiding
Meaning of non-decimal place value
• In place value, "non-decimal" refers to a number
that does not have any fractional parts, meaning it
is a whole number with no digits to the right of the
decimal point; essentially, an integer, like 5.
Non-decimals in the number system / Nie-
desimale in die getallestelsel
To understand how base 10 works, we will be
looking at other base systems (like base 5 and 6) /
Om te verstaan hoe basis 10 werk, gaan ons kyk
na ander basis sisteme (soos basis 5 en 6).
Remember base10 number system works with 10
digits {0, 1,2,3,4,5,6,7,8 and 9 }
Base 5 / Basis 5
Here are some basics / Hier is so ‘n paar “basics”
When you work with bases, write down the base you are referring
to as a subscript E.g. 43215
You cannot read the number as “four thousand, three
hundred and twenty-one”, because the values Units,
Tens, Hundreds and Thousands only refer to base 10.
Therefore, you read 43215 as “four, Three, two, one
base five”
How does place values work here? / Hoe werk
plekwaardes hier?
In base 10 you multiplied with 10 each time/ In basis 10, het jy elke
keer gemaal met 10, byvoorbeeld…
In base 5 you with…… each time? /In basis 5, het jy elke keer
gemaal met 5, byvoorbeeld…
Base 5 / Basis 5
If base 10 look as follows,
then… / As basis 10 so lyk,
dan……
Base 5 looks like…? / lyk basis 5 soos…?
Base 5 / Basis 5
Why is the digits used in column two, from zero up to four? /
Hoekom is die getalle wat gebruik word in kolom twee, van nul
tot by vier?
Remember, you are working with base 5 / Onthou, jy werk met
basis 5
Converting Base 5 to base 10 /omskakeling Basis 5 na
basis 10
Convert 43215 into base 10
Step 1: Write your base 5 positional values
underneath your number e.g. / Jou basis 5
posisionele waardes onder jou getal bv.
4 2 3 1
5
54 53 52 51 50
625 125 25 5 0
Base 5 to base 10 / Basis 5 na basis 10
• Step 2: Multiply the corresponding base 5 digit
with the positional value e.g. / Vermenigvuldig
nou die ooreenstemmende basis 5 getal met
die posisionele waarde bv.
4 2 3 1 5
125 25 5 1
(4 x125) (2 x 25) (3 x 5) (1 x 1)
Base 5 to base 10 / Basis 5 na basis 10
Step 3: Complete the multiplication and add the answers of
every base 5 positional value together – it equals to your
base 10 number / Voltooi die vermenigvuldiging en tel die
antwoorde van elke basis vyf posisionele waarde bymekaar –
dit gee vir jou, jou basis 10 getal
500+50+15+1=566
TRY THIS ONE
Convert 𝟒𝟏𝟐𝟎𝟒𝟓 into a base 10 number
Adding base 5
How do we add in base 5 / Hoe tel ons op in basis
5?
• E.g. 1 2 3 𝟑𝟓
1 1 1 𝟏𝟓
2 3 4 𝟒𝟓
How do we add in base 5 / Hoe tel ons op in basis
5?
• E.g. 1 2 3 𝟑𝟓
1 1 4 𝟐𝟓
2 4 3 𝟎𝟓
Try this
𝟏𝟐𝟏𝟑𝟓 + 𝟐𝟑𝟏𝟒𝟓
Substraction in base 5
𝟑𝟐𝟏𝟓 - 𝟐𝟑𝟎𝟓
• ²3
• 5+2
• 𝟏𝟓
• ²3
• 5+2
• 𝟏𝟓
How do we subtract in base 5? / Hoe trek ons af in
basis 5?
1 𝟒𝟓 1 𝟐𝟓
𝟑𝟓 𝟒𝟓
1 𝟏𝟓 0 𝟑𝟓
Multiplication in base 5
How do we multiply in base 5? / Hoe vermenigvuldig
ons in basis 5?
• Two ways to conduct multiplication in base 5:
• Number 1: Traditional column method
1 group of 5
3 2 𝟏𝟓
2 𝟒𝟓
1 group of 5 1 group of 5
2 3 3 𝟒𝟓
1 1 4 2 𝟎𝟓
1 4 3 0 𝟒𝟓
How do we multiply in base 5? / Hoe
vermenigvuldig ons in basis 5?
• Two ways to conduct multiplication in base 5:
• Number 2: Table method
• 3x2=6
• 6 is how much more
than 5?..... 1
• How many fives in
6?..... 1
• Hence 115
STOP…….. REFLECT!!!!!!
• At the end of this presentation navigate to the
following videos…..
• Base 5 Number System – Basics
• Convert base 5 to base 10
• Convert Base 10 to Base 5
• Adding Base 5 Numbers
• Subtracting in base 5
• Base 5 Multiplication
• It is located on eFundi >>> Resources >>> More
study material >>> Supplementary Videos
CONGRATULATIONS – You mastered Base 5!!! /
GELUK – Jyt Basis 5 bemeester!!!
How does non-decimal numeration systems link to
the intermediate phase? / Hoe sluit nie-desimale
getalsisteme aan by die intermediêre fase?
Please take note:
Reminder
Complete the Complete Revise and
Please refer to homework efundi prepare for our
module guide activity tasks/reflections next class
Preparation / Voorbereiding
© North-West University (2012)
