10
WHOLE NUMBERS (Chapter 1)
Opening problem
The scorecard alongside shows the number of runs
scored by each batsman in an innings of cricket.
F. JONES
C. WILLIAMS
T. CHURCH
A. THOMSON
G. MULLNER
S. STONE
W. HIGGINS
L. SPENCER
T. HILL
P. SPIERS
M. HAINES
EXTRAS
Things to think about:
a How many batsmen scored:
i less than 10 runs
ii 100 runs or more?
b We sometimes say that batsmen who have scored
100 runs or more have “reached triple figures”.
Can you explain what this means?
c How many runs did Jones and Williams score in
total?
d How many more runs did Stone score than
Mullner?
48
87
3
205
19
137
26
4
8
13
1
12
TOTAL 563
In our number system, we can write any number using a combination of the digits 0, 1, 2, 3,
4, 5, 6, 7, 8, and 9.
For example, the number ‘fifty seven’ can be written using the digits 5 and 7 as 57.
The numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, .... and so on are known as
the whole numbers.
In this chapter, we will learn about writing, rounding, adding, and subtracting whole numbers.
A
PLACE VALUE
units
tens
hundreds
thousands
ten thousands
hundred thousands
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The place or position of a digit in a number determines
its value.
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100
1000
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WHOLE NUMBERS (Chapter 1)
11
The number 5382 is a short way of writing 5 thousands + 3 hundreds + 8 tens + 2 units
5000 + 300 + 80 + 2
thousands
hundreds
tens
units
5
3
8
2
We write 5382 in words as five thousand, three hundred, and eighty two.
In some numbers, we use the digit zero or 0 to show an empty place value.
For example:
² 5206 is 5000 + 200 + 6 or five thousand, two hundred, and six.
0 shows there are no ‘tens’
² 7640 is 7000 + 600 + 40 or seven thousand, six hundred, and forty.
0 shows there are no ‘units’
Historical note
An abacus or counting frame is a tool used to
perform operations with numbers. It was invented
over 4300 years ago in Mesopotamia, which is in
modern-day Iraq.
The abacus is still used by traders in Asia and
Africa.
EXERCISE 1A
1 Write each of the following numbers in short form:
a 60 + 3
b 400 + 20 + 9
c 700 + 10 + 2
d 500 + 6
e 3000 + 600 + 30 + 7
f 8000 + 700 + 6
g 9000 + 400 + 60
h 2000 + 5
i 10 000 + 6000 + 500 + 10 + 1
j 30 000 + 8000 + 70 + 7
2 Write each of the numbers in 1 in words.
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3 Write as a number in short form:
a five thousand, seven hundred, and forty four
b two thousand, nine hundred, and eleven
c eight thousand and eight
d fifteen thousand, two hundred, and thirty seven
e twenty four thousand, six hundred, and one
f eighty eight thousand, eight hundred
g four hundred and seventy two thousand, six hundred, and seventeen
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WHOLE NUMBERS (Chapter 1)
4 Match each number with its value:
a 527
b 28
e 5207
f 373
c 3073
g 5027
d 208
h 3730
A
200 + 8
B
3000 + 70 + 3
C
300 + 70 + 3
D
3000 + 700 + 30
E
5000 + 20 + 7
F
5000 + 200 + 7
G
500 + 20 + 7
H
20 + 8
Example 1
Self Tutor
What number does this abacus
show?
The number of
disks on each spike
represents the digit
for that position.
2
We count the number of disks
on each spike.
6
3
0
8
hu
nd
re
d
th
ten ous
th and
ou s
s
th and
ou s
sa
hu nds
nd
re
ds
ten
s
un
its
The abacus shows the number
26 308.
DEMO
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5 What number does each abacus show?
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WHOLE NUMBERS (Chapter 1)
g
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6 Draw an abacus to show each of the following numbers:
a 3617
b 5088
c 13 621
d 527 013
Example 2
Self Tutor
What number is represented by the digit 5 in:
a 251
b 4205
c 53 891?
a In 251, the 5 represents 5 tens, or 50.
b In 4205, the 5 represents 5 units, or 5.
c In 53 891, the 5 represents 5 ten thousands, or 50 000.
7 What number is represented by the digit 6 in:
a 657
b 8617
c 168
e 3076
f 6294
g 37 465
d 4962
h 61 098?
8 What number is represented by the digit 3 in:
a 903
e 7030
b 1302
f 39 814
c 238
g 20 309
d 3888
h 137 208?
9 For the number 76 813, write down the value of the:
a 6
b 1
c 3
d 7
e 8
10 For the number 451 792, write down the value of the:
a 9
b 1
c 4
d 7
e 5
Example 3
Self Tutor
Arrange in order from smallest to largest: 24, 42, 27, 72, 47
All of the numbers have two digits. In each number we look first at the number of tens,
and then at the number of units.
24 and 27 have the smallest number of tens, and 24 has less units so it is smallest.
42 and 47 have the same number of tens, and 42 has less units than 47.
72 has the most number of tens, so it is the largest number.
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So, in order from smallest to largest, we have: 24, 27, 42, 47, 72.
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WHOLE NUMBERS (Chapter 1)
11 Arrange each set of numbers in order from smallest to largest:
It may be helpful
a 39, 93, 19, 31, 91
to use a place
value table.
b 308, 301, 207, 109, 208
c 2710, 2071, 2701, 2017, 2170
d 47 913, 31 749, 91 347, 17 394, 47 193
e sixty four, forty, sixteen, forty six, sixty, fourteen
f seventeen, seventy, fifty seven, seventy five, fifteen
g one thousand and fifty three, 1503, one thousand and fifty, 1305
h two thousand and forty seven, 2407, 247, seven hundred and twenty four.
12 Write down the largest and smallest numbers we can make using the digits:
a 4, 2, 9, and 3
b 8, 3, 5, 2, and 9
c 3, 8, 6, 7, and 4.
B
ROUNDING NUMBERS
When a quantity is being described, we often do not need to know the exact number.
For example:
² You may look at a handful of marbles and say,
“There are about thirty there.”
² A fishing report might read
“About 600 kg of crayfish were caught last week.”
² A commentator might estimate the crowd at a
sporting event as 85 000.
When we estimate a number of objects, we usually
round to the nearest 10, 100, 1000, and so on. There
are rules for doing this.
ROUNDING TO THE NEAREST TEN
This number line shows the whole numbers from 20 to 30.
nearer to 20
20
21
22
23
nearer to 30
24
25
26
27
28
29
30
21, 22, 23, and 24 are nearer to 20 than to 30, so we
round them down to 20.
26, 27, 28, and 29 are nearer to 30 than to 20, so we
round them up to 30.
25 is midway between 20 and 30 on the number line.
We make the choice that numbers ending in 5 will be
rounded up to the next 10.
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So, 25 is rounded up to 30.
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