4 Decimals Form 1

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68
3
4
0
0.0
0
5
.
4
3
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0
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Topic 4
DECIMALS
23.9
12.6
0.7789
Decimals
We use decimals
everyday. For example,
the prices of things we
buy are written in the
form of decimals.
5.67 km
To school
1.75 liter
My home
Sale!
RM4.99
59.8 m
1.5A
39.5C
Look at the prices of the things

in the pictures below. How
much the prices of the things?
RM1,820.99
RM19.95
RM30.55
Can you write the mass of

verges as a decimal using the
unit kilogram (kg). Can you
see the mass of this verges
from the scale below?
2
3
3.5kg
Decimals are used

when we need to
give more accurate
readings that whole
numbers cannot
give.
Decimal is a number that represents a

fraction in which the denominator is
in the form of 10, 100, 1 000.
0.32 = 32
100
3.89 = 389
100
0.4 = 4
10
0.067 = 67
1000
Representing Fractions 1 and 1 as Decimals

10 100
and vise versa.
Decimals are numbers which represent

fractions with denominators such as 10,
100 or 1000.
3
10
Reading & Writing Decimals

a) 0.3
Zero point three.
b) 79.86
Seventy-nine point eight six.
c) 4.0012
Four point zero zero one two.
d) 387.605
Three hundred eighty-seven point

six zero five.
e) RM34.25 Ringgit Malaysia thirty-four and

twenty-five cents.
f) RM0.45
Forty five cents or Ringgit Malaysia

zero point four five.
Changing Fractions Into Decimals

To change fractions into decimals, divide
the numerator by the denominator
a) 1
= 5
= 1 2 = 0.5
2
10
b) 8
13
= 8 13 = 0.615
= 615
1000
c) 11
20
= 11 20 = 0.55
= 55
100
d) 3 2
5
= 17 5 = 3.4
= 34
10
= 11 8 = 1.375
= 1375
1000
e) 1 3
8
Changing Decimals into Fraction

To change decimal into fraction, look
at the number of decimals given. If
there is only one decimal place, the
denominator will have only one zero.
Then write the decimal as a fraction
with a denominator of 10, 100 or 1000.
Simplify the fraction if possible.
Change the following decimals into

fractions
a) 0.9
b) 0.87
c) 0.403
d) 2.574
e) 76.45
f) 0.0038
0.9
=9
10
1 decimal place therefore,

1 zero
Place Value
Units
Decimal
Point
Tenths
Hundredths
Thousandths
Digit
Tens
Place
Value
Hundreds
1) As with whole numbers, a digit in a decimal

has a place value. The table below shows
the place values for decimals.
789.163 means 7 hundreds, 8 tens, 9 units, 1 tenths, 6

hundredths and 3 thousandths.
A decimal point is placed to separate the whole
number from the fraction.
Value Of Digit
Each digit in a decimal has its own value.
The value of a digit is determined by its
place value. In decimal 789.163, the place
value of the digit 6 is hundredths.
Therefore, the value of digit 6 is 6 or 0.06
100
State the number of the places in the
following.
(a) 89.431
(b) 16.56
(c) 307.25
Comparing and Ordering

Decimals
0.68
3
4
0
-0.0
9
0
1.
23.9
Addition, Subtraction, Multiplication

and Division on Decimals
-12.6
-0.7789
0
5
.
4
3
M
R
Comparing Decimals
Which of these decimals has a greater value,
45.0976 or 45.0915? How do you compare
these two decimals?
45.0976
45.0915
Thus, 45.0976
is greater than
45.0915
In order to compare these two decimals,

arrange them according to their place
value. Then start comparing from the
left.
Identify the larger number of the
following pairs:
(a) 0.8 and 0.188
(b) 3.095 and 3.099
(c) 56.28 and 56.286
Any decimal with a

value less than
zero is a negative
decimal.
-0.25 -0.20 -0.15 -0.10 -0.5
Negative decimals
0.50
1.00
1.50
2.00
2.50
positive decimals
zero
Good
job!!!
Any decimal with

a value greater
than zero is a
positive decimal.
Look at the numbers on the line number below.

-20 -18 -16 -14 -12 -10
-8 -6 -4 -2
Compare the numbers given and determine which number is greater.
a) -20 and 12
b) -7 and -6
c) 0 and -5
d) -9 and -3
e) -17 and -14
-12
-6
0
-3
-14
The negative
sign makes
the decimal
number
smaller than
the greater
numerical
value.
Arranging Decimals
Decimals can be arranged in order using a
number line or by comparing their values.
Rearrange the following numbers in increasing order
(a) 0.32, 0.34,0.39, 0.37, 0.31 = 0.31, 0.32, 0.34, 0.37, 0.39
Method 1: Draw
a number line
with ten equal
intervals. Mark
off each interval
in hundredths,
from 0.30 to 0.40
Method 2:
Arrange the
numbers
according to
their place value
0.30
0.31
0.32
0.33
0.34
0.35
0.36
0.37
0.38
0.39
0.40
0.32
0.31
0.34
0.32
0.39
Compare the hundredths

and rearrange the order
0.34
0.37
0.37
0.31
0.39
Rounding Off Decimals
Decimals can be rounded off to a given

number of decimal places.
Lets say, we
want to round
the number
3.6489 to 2
decimal places.
A number
written to 2
decimal places
has two digits
after the decimal
point.
Step 1:
Identify the second decimal place and
mark it with a slash.
3.64 / 89
2nd decimal places
3rd decimal places
1st decimal places
Step 2:
Look at the number in the third decimal
place. Since 8 is greater than 5, round
up by adding 1 to the digit 4. Therefore,
3.6489 = 3.65 (to decimal places).
Addition and Subtraction of Decimals

To add or subtract decimals, line up the decimal points
and then follow the rules for adding and subtracting
whole numbers.
Example: Find the sum of the following.
(a) 7.45 + 99.2 + 23.79 (b) 67.305- 25.29 + 13.84
Step 1: Line up the
decimal points.
Step 1
7.45
+99.2
+23.79
Step 2: Add the

numbers. Therefore,
7.45+ 99.20 23.79
= 130.44
Can you find the answer
for question (b) ?
Step 2
7.45
+99.20
+23.79
130.44
Multiplication Of Decimals
Find the product of:
(a) 3.71 X 6.4
(b) 3.56 x 4.2 x 6.2
(a) 3.71
X 6.4
1484
2226
23744
2 decimal places
1 decimal places
2 decimal places +
1 decimal place
= 3 decimal
places
So the answer is 23.744
(b) 3.56
X 4.2
712
1424
14952
x
6.2
29904
89712
927024
2 decimal places
1 decimal places
1 decimal places
2d.p+1d.p+1d.p
=3 decimal points
So the answer is 927.024
Multiplying Decimals
Multiplying decimals is just like multiplying
whole numbers. Put in the decimal point after
multiplying. The number of decimal places in the
answer must be the same as the total number of
decimal places in the decimals being multiplied.
When we multiply a
decimal by 0.1, 0.01
or 0.001, we move
the decimal point
one, two, or three
places to the left to
find the answer.
Multiply 85.34 by 0.1 and 0.001

Solution:
85.34 X 0.1 = 8. 534 = 8.534
85.34 X 0.001 = 0. 08534 =0.08534
We add 0 after the decimal point
to show another place value. In
this case the 0 is the place
holder for the value of tenths
Dividing
Dividing Decimals
Decimals
By
By 10,100,1
10,100,1 000,
000, 10
10 000
000
Division
Answer
a) 24.56 10
24.56 = 2.456
b) 24.56 100
24.56 = 0.2456
c) 24.56 1000
0 24.56 = 0.02456
0 0 24.56 = 0.002456
d) 24.56 10000
We can mentally divide decimals by 10, 100,

1 000, 10 000 by moving the decimal point
one, two or three decimal places to the left.
Dividing Decimals By Decimals

To divide a decimal by another decimal, the divisor should
be changed to a whole number.
Example: 42.6 1.2
426 12
35.5
= 35.5
Division
a) 0.165 0.1
b) 29.376 0.01
12 426
36
66
Answer
60
60
1.65 60
..
2937.6
c) 5.98 0.32 = 598 32 18.6875
d) 93.5 2.5 = 935 25
37.4
Combined Operations
Calculate each of the following. Give your
answer correct to 3 decimal places.
1) 47.56 X 12.45 2.5

2) (2.62 1.3) - 2.3 X 0.1 + 4.4
3) 20.50 3.024 0.52 + 1.4(3.59)
4) 3 + 15 + 6 + 85
10 100
1000 10000
236.849
6.185
18.063
0.465
Solving Problem Involving of Decimals

Aisyah bought 8
kg of coffee
powder for
RM133.60. How
much does 1 kg of
coffee powder
cost?
Thus, 1 kg of
coffee powder
costs RM16.70
Solution:
Step 1
Understand
Given : 8 kg of coffee powder cost RM133.60

Find : Cost of 1 kg of coffee powder
Step 2
Plan
Step 3
Solve
133.60 8 = 16.70
Therefore, 1 kg of
coffee powder costs
RM16.70
Step 3
Check
Use division
16.70
133.60
-8
53
-48
56
-56
0
Check your answer by using the

calculator.

Simon takes 13.5
Solution:
minutes to jog a
lake. If Simon jogs
=
13.5
x
3.5
at the same speed,
how long does it
= 47.25 minutes
take him to jog 3.5
times around the
lake?

Puan Azizah wants
to buy 88 pens and
distributes them to
needy students in
her school. If each
pen is RM0.43 ,
how does she has
to pay for all the
pens?
Solution:
= 88 x 0.43
= RM37.84

The fence of Sekolah
Cantik is 4,247.9 cm
long. Its principal wants
to hang yellow and red
flags around the fence
for the school Sports
Day. Each yellow flag is
21.4cm long and each
red flag is 18.3 long.
How many yellow flags
and red are needed.
Solution:
=4247(21.4+18.3)
= 4247.9 39.7
= 107
= 107 yellow flags
and 107 red flags.

Mary had RM50 to
spend for 3 days.
She spent
RM12.25 on the
first day and
RM18.65 on the
second day. How
much did she has
left to spend on
the third day?
Solution:
= 50-12.25-18.65
= RM19.10

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0.

Look at the prices of the things

Can you write the mass of

Decimals are used

Decimal is a number that represents a

Representing Fractions 1 and 1 as Decimals

Decimals are numbers which represent

Reading & Writing Decimals

Zero point three.

Seventy-nine point eight six.

Four point zero zero one two.

Three hundred eighty-seven point

e) RM34.25 Ringgit Malaysia thirty-four and

Forty five cents or Ringgit Malaysia

Changing Fractions Into Decimals

Changing Decimals into Fraction

Change the following decimals into

1 decimal place therefore,

1) As with whole numbers, a digit in a decimal

789.163 means 7 hundreds, 8 tens, 9 units, 1 tenths, 6

Comparing and Ordering

Addition, Subtraction, Multiplication

In order to compare these two decimals,

Any decimal with a

Any decimal with

Look at the numbers on the line number below.

Compare the numbers given and determine which number is greater.

Compare the hundredths

Rounding Off Decimals

Decimals can be rounded off to a given

Addition and Subtraction of Decimals

Step 2: Add the

So the answer is 23.744

So the answer is 927.024

Multiply 85.34 by 0.1 and 0.001

We can mentally divide decimals by 10, 100,

Dividing Decimals By Decimals

1) 47.56 X 12.45 2.5

Solving Problem Involving of Decimals

Given : 8 kg of coffee powder cost RM133.60

Check your answer by using the

Solving Problem Involving of Decimals

Solving Problem Involving of Decimals

Solving Problem Involving of Decimals

Solving Problem Involving of Decimals

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