decimals.docx

8/10/2019 Decimals.docx

1/39

DECIMALS


2/39

DECIMAL AND FRACTION


3/39

1. A decimal is a fraction in which the denominator

is 10 or a power of 10.

For example :-

2. The decimal point ( the dot ) separates

the whole number from its fractional part.

A number written with a decimal point is

known as a decimal.

For example:-

3. The number of digits after the decimal point

is the same as the number of zeros in the

denominator.

For example:-


4/39

A) Representing Decimals with Diagrams

Decimals can be represented with diagrams.

For example :-

1 3 910 100 1 000

(1 out of 10 ) ( 3 out of 100 ) ( 7 out o f 1 000 )

B) Writing Decimals based on given Diagrams

Worked Example

Write a decimal to represent the shaded

area in the diagram above.

Solution

The shaded area is 3 .10

Therefore, the decimal is 0. 3.

C) Conversion of Fractions into Decimals

and vice versa

1. A fraction in which the denominator is

10 or a power if 10 can be converted to a


5/39

decimal mentally.

Worked Example

Express the following as decimals.

(a) 7 (c) 13810 1 000

(b) 52100

Solution

Worked Example

Change the following into fractions with

denominators of 10 or powers of 10.

(a) 0.6 (b) 0.55 (c) 0.374

Solution

2. A fraction can also be converted to a


6/39

decimal by dividing the numerator by

the denominator.

3. Mixed numbers can also be expressed

as decimals.

Worked Example

Express the following fractions as decimals.

(a) 3 (b) 7 24 5

Solution

Worked Example

Express the following as decimals.

(a) 1 14 (b) 4 5100 20

Solution


7/39

Worked Example

Express the following decimals as mixed

numbers.

(a) 3. 6 (b) 11. 025

Solution(a) 3. 6 = 3 + 0. 6

= 3 + 610

= 3 610

PLACE VALUE AND DIGIT VALUEIN DECIMALS

A) Place Value and Digit Value

1. Each digit in a decimal has its own

place value and digit value.

Look at the decimal 8.235 below.


8/39


9/39

(c) 3.152

3 decimal places

(d) 9.7420

4 decimal places

B) Representing Decimals on Number Lines

A decimal can be represented on a number line.

For example :-

Worked Example

State the decimal represented by each

of the letters on the number line above.

Solution

One part = 4.95 - 4.80


10/39

= 0.15

F = 4.95 + 0.15 + 0.15

= 5.25

G = 5.25 + 0.15

= 5.40

Therefore, F = 5.25 and G = 5.40.

C) Comparing Two Decimals

When comparing two decimals, arrange the

digits of the decimals according to their placevalues and then compare their digit values

from left to right.

Worked Example

Which is greater, 24.853 or 24.832

Solution

Arrange the decimals as shown below.

At the place value of hundredths, 5 is larger than 3.

Therefore, 24.853 is greater than 24.832.

Worked Example

Fill in each box with ' >' or '


11/39


12/39

Arrange 11 , 2.73 and 2.732 in increasing order.

4Solution

E) Rounding Off Decimals.

A Decimal can be rounded off to a whole number

or certain decimal places. The rules for rounding

off decimals are as follows.

(a) Look at the digit to the right of the digit that

is to be rounded off.

(b) If the digit is more than or equal to 5, add 1

to the digit that is to be rounded off and ignore

the rest of the digits after it.

(c) If the digit is less than 5, maintain the digit

that is to be rounded off and ignore the rest of

the digits after it.

Worked Example

Round off 8.3752 correct to


13/39

(a) 1 decimal place,

(b) 2 decimal places,

(c) 3 decimal places.

Solution

Worked Example

Round off the following decimals to the

nearest whole numbers.

(a) 8.6168 (c) 352.84

(b) 30.324

Solution


14/39

ADDITION AND SUBTRACTIONOF DECIMALS

1. Decimals are added and subtracted in

the same way as whole numbers.

2. When two decimals are added together

or subtracted from each other, the deci-

mal points must be placed directly one

below the other and the digits written in

the correct place value columns.

A) Addition of Decimals

Worked Example

Calculate

(a) 0.382 + 4.264 (b) 5 + 8.8

Solution


15/39

Worked Example

Calculate(a) 34.2 + 26.73 + 9.985

(b) 9.25 + 54 + 17.631

Solution

B) Problem Solving involvingAddition off Decimal

Worked Example

Salman is 1.75 m tall and Arjun is 0.19 m

taller than Salman. How tall is Arjun.

Solution

1. Understand the problem


16/39

Given information :

Salman's height = 1.75 m

Arjun is taller than Salman by 0.19 m

Find : Height of Arjun

2. Devise a plan

Use addition.

3. Carry out the plan

Arjun's height

= Salman's height + 0.19 m

1.75 m + 0.19 m = 1.94 m

1 . 7 5+ 0 . 1 9

1 . 9 4

Therefore, Arjun is 1.94 m tall.

4. Check1 . 9 4

- 1 . 7 50 . 1 9 ( The difference )

Worked Example

Dewi collected 21.10 litres of latex on

Monday, 26 litres on Tuesday and

23.906 litres on Wednesday. Find the

total amount of latex collected.

Solution


17/39

The total amount of latex collected was

69.906 litres.

C) Subtraction of Decimal

Worked Example

Calculate

(a) 0.85 - 0.35

(b) 83 - 26.421

Solution

Worked Example

Calculate

(a) 57.3 - 35.82 - 2.346

(b) 81 - 24.907 - 7.5

Solution


18/39


19/39

5 2 . 0 3+ 8 . 3 7

6 0 . 4 0

Worked Example

Zaiton bought 6.3 m of cloth. She used 2.15 m

to make a shirt and 3.28 m to make a pair of

pants. How much of the cloth remained ?

Solution

6.3 m - 2.15 m - 3.28 m = 0.87 m

Therefore, 0.87 m of the cloth remained.

MULTIPLICATION AND DIVISION OF DECIMALS

A) Multiplication of Decimals

i - Generel multiplication of decimals

1. To find the product of decimals, multiply the

numbers in the same way as for whole num-

bers first. Then, put in the decimal point.

2.The number of decimal places in the answer

must correspond to the total number of decimal

places in the decimals being multiplied.

Worked Example

Calculate


20/39

(a) 0.73 x 0.7

Solution

ii) Multiplying a decimal by a power of 10

When multiplying a decimal by 10, 100,

1 000, ect., we move the decimal point 1,

2, 3, ect. places respectively to the right.

Worked Example

Calculate

(a) 1.42 (c) 0.8

(b) 6.973 ( d) 0.0032

Solution


21/39

2. Similarly, when we multiply a decimal by

0.1, 0.01, 0.001, ect., we move the decimal

point 1, 2, 3, ect. Place respectively to the

left.

Worked Example

Calculate

(a) 24.8 x 0.1,

(b) 53.62 x 0.01,

(c) 21.73 x 0.001

Solution


22/39

Worked Example

Calculate 0.38 x 0.7 x 0.5.

Solution

B) Problem Solving involving Multiplication

of Decimals

Worked Example

Dalina needs 0.95 kg of flour to make a cake.


23/39

How much flour is needed to make 8 cakes ?

Solution


Given information :

Amount of flour to make 1 cake = 0.95

Find : Amount of flour to make 8 cakes

2. Devise a plan

Use multiplication.


8 x 0.95 kg = 7.60

0 . 9 5x 8

7 . 6 0

Therefore, 7. 60 kg of flour is needed to make

8 cakes.4. Check

Multiply again to verify the answer.

Worked Example

A apple costs RM0.70. The price of a jackfruit

is 4.8 times the price of the apple. What is the

cost of 5 jackfruits ?

Solution

Cost of a apple = RM0.70

Cost of a jackfruit = 4.8 x RM0.70


24/39

Cost of 6 jackfruits = 5 x 4.8 x 0.70

= RM16.80

0 . 7 0 3 . 3 6x 4 . 8 x 55 6 0 1 6 . 8 0

2 8 0__3 . 3 6 0

Therefore, the cost of 6 jackfruits is RM16.80.

C) Division of Decimals

i - Dividing a whole number or a decimal by

10 or a power of 10

When a whole number or a decimal is divided

by 10, 100, 1 000,... the decimal point is moved

1, 2, 3,,... places respectively to the left.

Worked Example

Calculate(a) 5 10, (b) 270 1 000.

Solution


25/39

Worked Example

Calculate

(a) 0.7 10, (c) 38.46 1 000.

(b) 231.4 100,

Solution

ii - Dividing a whole number by a whole number

Worked Example

Calculate 35 4

Solution

Therefore, 35 4 = 8.75


26/39


27/39

2. When dividing a whole number by a decimal,

convert the divisor to a whole number first by

moving its decimal point to the right.

Worked Example

Find the value of each of the following.

(a) 6 0.2

(b) 330.11

Solution


28/39

iv - Dividing a decimal by a decimal

When dividing a decimal by a decimal, use the

idea of equivalent fractions to convert the divisor

to a whole number. Shift the decimal points the

same number of places in the dividend and divi-

sor to make the divisor a whole number.

Worked Example


(a) 5.52 0.6

(b) 0.0720.8

Solution


29/39

v - Dividing a decimal by a fraction and vice versa When dividing a decximal by a fraction,

change the operation from division to

multiplication and invert the fraction at

the same time.

Worked Example


(a) 3.72 34

Solution


30/39

D) Problem Solving involvingDivision of Decimals

Worked Example

Akmal buys 6 tickets for a circus show

costing RM85.80. How much does each

ticket cost ?

Solution


Given information :

Number of tickets bought = 6

Cost of 6 tickets = RM 85.80

Find : Cost of 1 tickets

2. Devise a plan

Use division


RM85.80 6 = RM14.30


31/39

Therefore, the cost of 1 ticket is RM14.30.

4. Check

1 4 . 3 0x 6

8 5 . 8 0

COMBINED OPERATIONSOF +, -, x, OF DECIMALS

A) Combined Operations of Additionand Subtraction

Worked Example


(a) 7.41 + 6.35 - 10.02

(b) 8.41 - 31 + 2.074

Solution


32/39

B) Problem Solving involving Additionand Subtraction

Worked Example

A vessel weighing 0.98 kg contains 25.8

kg of rice. If 10.5 kg of the rice is used,

find the total mass of the vessel with the

remaining rice.

Solution



33/39

Given information :

Mass of vessel = 0.98 kg

Mass of rice = 25.8 kg

Mass of rice used = 10.5 kg

Find : Mass of the vessel and remaining rice

2. Devise a plan

Perform addition followed by subtraction.


0.98 + 25.8 - 10.5= 26.78 - 10.5

= 16. 28

0 . 9 6+ 2 5 . 8__

2 6 . 7 8- 1 0 . 5__

1 6 . 2 8

Therefore, the total mass of the vessel

and remaining rice is 16.28 kg.

C) Combined Operations ofMultiplication and Division

Worked Example

Calculate each of the following.

(a) 4.6 x 0.8 1.6

Solution


34/39

Worked Example


(a) 7 x 0 . 9 45

Solution

(a) 7 x 0 . 9 45

= 6. 3 4 ( Invert the f rac t ion . )5

= 6. 3 x 54

= 31. 5 4

= 7. 875

D) Problem Solving involvingMultiplication and Division

Worked Example

A shopkeeper buys 5 sacks of sugar

each weighing 64.2 kg. If he packs

the sugar into plastic bags of 11 kg2

each, how many bags are required ?

Solution



35/39

Given information :

Mass of a sack of sugar = 64.2 kg

5 sacks of sugar are packed into

plastic bags of 11 kg.

Find : Number of plastic bags required

2. Devise a plan

Perform multiplication followed by

division.

3. Carry out the plan5 x 64. 2 11

2

= 5 x 64. 2 32

= 192. 6 32

= 192. 6 x 2 3

= 385. 2 3

= 128. 4

4. Check

3 x 128. 4 = 192.62

192. 6 3

= 64. 2

Worked Example

Amy bought 20 eggs costing RM3. 80.


36/39

Lissa bought 35 of those eggs. How

much did Lissa pay ?

Solution

Cost of 20 eggs = RM3.80

Cost of 35 eggs

= 3.80 20 x 35

= 0.19 x 35

= 6.65

Therefore, Lissa paid RM6.65.

E) Combined Operations of Addition,Subtraction, Multiplication and Division

Worked Example


(a) 12. 5 - 0. 26 x 2. 6

(b) 3. 2 x 4 - 10. 4 4

(c) 5. 12 - 2. 8 14

Solution


37/39

F) Problem Solving involving CombinedOperations of Addition, Subtraction,Multiplication and Division

Worked Example

Amir bought 260 eggs costing RM0.15

each. He sold all the eggs at RM0.18

each. Find his profit.

Solution


38/39


39/39

Solution

Cost of 7 pencils = 7 x 0.80

Cost of 6 pens = 6 x 1.30

Total cost of pencils and pens

= 7 x 0.80 + 6 x 1.30

Change received by Haikal

= 30 - ( 7 x 0.80 + 6 x 1.30 )

= 30 - ( 5.60 + 7.80 )

= 30 - 13.40

= 16.60

0 . 8 0 1 . 3 0x 7 x 6

5 . 6 0 7 . 8 0

Therefore, the change was RM16.60

copyright 2005 Kenshido International Sdn Bhd

decimals.docx

Documents