CLASS: JSS 1
TERM: 1st TERM
TOPIC: WHOLE NUMBERS
It is likely that mathematics began when people started to count and measure. Counting and measuring are part of everyday life.
Ancient people used fingers and toes to help them count or group numbers in different number bases. This led them to collect numbers in groups: sometimes 5s (fingers of one hand), sometimes 10s (both hands) and even in 20s (hands and feet). When people group numbers in 5s, we say they use a base five method. The most common bases used were five, ten and twenty. For example, a person with thirty two cows would say ‘I have six fives and two cows’ when counting in base ten. The most widely used base is base ten also called the denary system.
Other bases of counting: seven and sixty
7 days = 1 week
60 seconds = 1 minute
60 minutes = 1 hour
In English, ‘dozen’ means 12, ‘score’ means 20 and ‘gross’ means 144
System of Counting
Tally marks were probably the first numerals.
The ancient people employed tally marks to count large numbers. The tally marks were scratched on stones or sometimes cut on sticks but today we use tally marks to count or record large data, especially in statistics.
A tally mark of 5 is written by putting a line across a tally count of 4.
i.e = 4 and = 5
Draw the tally marks for each of the following numbers:
The Romans used capital letters of the alphabets to represent numbers. Many people believe that the Romans used the fingers to represent numbers as follows:
I for one finger, II for two fingers, III for three fingers, V for five fingers and X for the combination of two hands ( or two V’s) .
The Roman also used L for fifty, C for hundred, D for five hundred and M for one thousand as shown below.
The Roman used the subtraction and addition method to obtain other numerals. For example
Change the following numbers to Roman numerals: (a) 2459 (b) 3282
400 = CD
50 = L
9 = IX
2459 = MMCDLIX
= MMM CC LXXX II
i.e 3282 = MMMCCLXXXII
A counting board is a block of stone or wood ruled in columns. Loose counters, pebbles, stones or seeds in the columns show the value of the numbers in the columns.
Counters in the right-hand column (U) represent units, counters in the next column (T) represent tens, and so on.
2 7 5
The diagram below is a counting board showing the number 275.
An abacus is a frame consisting of beads or disks that can be moved up or down (i.e. slide) on a series of wires or strings. Each wire has its own value. Both abacus and counting board work in the same way when carrying out calculations.
M HTH TH H T U
An Abacus showing 2703
Numbers of units, tens, hundreds,…….., are each represented by a single numeral.
(a).For a whole number:
- the units place is at the right-hand end of the number.
- the tens place is next to the units place on the left, and so on
For example: 5834 means ↓
5 thousands, 8 hundreds, 3 tens, and 4 units.
See the illustration below:
5 8 3 4
(b) for decimal fraction, we count the places to the right from the decimal point as tenths, hundredths, thousandths, etc.
See the illustration below:
↓ ↓ ↓ ↓ ↓
6 . 7 9 8
6 → units
. → decimal
7 → tenths
9 → hundredths
8 → thousandths
What is the place value of each of the following?
What is the value of each of the following?
What is the value of each digit in 3 865 742
3 000 000
Eight hundred thousand
1 (a) The place value of 5 in 5763 is ……………
(b)What is the place value 1 in 5.691?
Counting and Writing in millions, billions and trillions
The figures 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are called digits or units.
The table below gives the names and values of some large numbers.
One hundred thousand
1 000 000
10 000 000
One hundred million
100 000 000
1 000 000 000
1 000 000 000 000
Large numbers can be read easily by grouping the digits in threes starting from the right hand side as shown below.
Billion Million TH H T U
25 800 074 4 3 0
The 1st gap separates hundreds from thousands and the second gap separates thousands from millions and the third gap separates million from billion.
Thus 25 800 074 430 reads twenty five billion, eight hundred million, seventy four thousand, eight hundred and ninety.
Write the following in figures:
= 12 000 000 000
Three hundred and nine million
= 309 000 000
Ninety five thousand
= 95 000
Six hundred and sixty three
= 12 309 095 663
= 6 000 000 000 000
Four hundred and thirty billion
= 430 000 000 000
One hundred and five million
= 105 000 000
Two hundred and one thousand
= 201 000
= 6 430 105 201 054
Nine hundred and four billion
= 904 000 000 000
Five hundred and forty million
= 540 000 000
Three hundred and seventy thousand
= 370 000
Seven hundred and fifty
= 904 540 370 750
(i) MMCDLXXI (ii) MMMCLIV
(a) fifteen trillion, six hundred and seventy one billion, three hundred and ninety one million, eighty eight thousand, five hundred and fifty five.
(b) three hundred and twenty-nine billion, five hundred and sixty two million, eight hundred and one thousand, four hundred and thirty three.
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