Decimal numbers
In mathematics various types of numbers are there. Decimal
numbers are among them. We come across whole (complete) parts as well as
fractional parts. But Decimals are the types of numbers which has a whole part as well as a fractional part.
For example :
When we measure the length of a pencil it may be 3 cm and 6
mm.
Which can be written as 3.6 cm.
Here 3 cm is the complete part but 6 mm is the fractional
part of a centimetre.
We know 1 cm = 10 mm
Or 1 mm = 1/10 cm or One – Tenth of a cm.
Similarly 6 mm = 6 / 10 cm or 6 tenth of a cm.
3.6 cm is read as ‘Three point six’ centimetre.
Tenths can be better understood as out of 10 equal parts.
Similarly, Hundredths can be understood as out of 100 equal parts
and Thousandths can be understood as out of thousand equal parts.
Hence we can say,
One part out of 10 parts = One tenth = 0.1
Two parts out of 10 parts = Two tenth = 0.2
Five parts out of 10 parts = Five tenth = 0.5
Parts of a decimal number
A decimal number has two parts. They are -
Whole number part and Decimal part
Both of the parts are separated with a point called decimal point.
For example:
563.25
Here 563 is the whole number part and 25 is the decimal
part. Both of the numbers have been separated with a decimal point.
Example: Underline the whole number part of the following numbers.
- 4230.005 Ans: 4230.005
- 58.268 Ans: 58.268
- 0.321 Ans: 0.321
Example : Underline the decimal part of the following numbers.
- 568.052 Ans: 568.052
- 100. 205 Ans: 100.205
- 0.03 Ans: 0.03
How to read Decimal numbers
Decimal numbers are not read as like counting numbers. They
are read as follows.
62.3 is read as Sixty two point three
21.583 is read as Twenty one point five eight three.
Example: Write the number names of the following numbers.
- 365.002
- 45085.245
- 0.568
- 2.308
- 1000.0001
Answer :
365.002 : Three hundred sixty five point zero zero two.
45085.245 : Forty five thousand eighty five point two four five.
0.568 : Zero point five six eight
2.308 : Two point three zero eight
1000.0001 : One thousand point zero zero zero one
Representing decimal numbers
The decimal numbers can be represented as follows.
For example
Represent 0.8
Represent 2.5
Represent 2.25
Conversion of Decimals into Fractions
Procedure to convert the decimal numbers into fractions:
For example:
Example: Convert 32.005
Conversion of fractions into decimals
Procedure to convert the fractions into decimal numbers:
For example:
Example: Convert 5632/100
Decimal Representation of Measurements
Facts to Remember
Example 1 : 35 mm = ? cm
Example 2 : 5630 cm = ? metre
Example 3 : 5745 m = ? km
Example 4 : 3800 ml = ? litre
Example 5 : 475 paise = ? Rupees
Example 6 : 7800 gm = ? Kg
Let's write the measurements in Decimal form
Now answer the following.
- 56 Kg. 30 gm = ? Kg.
- 36 litre 50 ml = ? litre
- 25 m 10 cm = ? m
- 19 cm 5 mm = ? cm
- 35 Rs. 5 paise = ? Rs.
- 12 kg 560 gm = ? kg
- 45 km 250 m = ? km
- 15 m 5 cm = ? m
- 125 km 50m = ? km
- 2500 Rs. 75 paise = ? Rs.
Decimal addition
Decimal addition is like the
addition of counting numbers. Let us see the following examples.
Example 1 Add 56.34 + 28.32
5 6 . 3 4
+ 2 8 . 3 2
----------------------
8 4 . 6 8
Example 2 Add 23.05 and 76.357
Step 1
2 3 . 0 5
+ 7 6 . 3 5 7
Step 2
2 3 . 0 5 0
+ 7 6 . 3 5 7
------------------------------
9 9 . 4 0 7
Now add the following.
- 5 m 34 cm + 24 m 5 cm + 18 m 85 cm
- 589.34 + 85.625 + 23.004
- Rs. 15.34 + Rs. 105.5 + Rs. 2005.80
- 56 kg 35 gm + 85 kg 250 gm + 102 kg 555 gm
- 54 km 358 m + 56 m + 320 km
Solve the following word problems.
1. Arun travelled a distance of 3
km and 50 m on Monday. He travelled 15 km and 350 m on Tuesday and 16 km 200 m
on Wednesday. Find out how far he travelled on all the three days.
2. Ramu’s father brought 3 kg 200
gm sugar, 5 kg 30 gm wheat, 15 kg 450 gm rice and 12 kg 75 gm dal. How much
weight did he carry?
3. Rahul’s father spent 345
rupees 50 paise for buying a cake, 420 Rupees 5 Paise on decoration, 1350
Rupees 75 Paise on food and 4330 Rupees 8 Paise on gift items. Now find out how
much money he spent on Rahul’s B’Day.
Decimal Subtraction
Decimal subtraction is also like the subtraction
of counting numbers. Let us see the following examples.
Example
1 Subtract 23.62 from 58.98
5 8 . 9 8
-
2 3 . 6 2
----------------------
3 5 . 3 6
Example
2 Subtract 23.058 from 76.35
Step 1
7 6 . 3 5
- 2 3 . 0 5 8
Step 2
7 6 . 3 5 0
- 2 3 . 0 5 8
------------------------------
5 3 . 2 9 2
( * For making the decimal part equal digits add zero to right )
Now solve the
following.
·
18 m 85 cm – 5 m 5 cm
·
589.34 - 23.004
·
Subtract Rs. 56.05 from Rs. 123
·
Subtract 56 Kg. 3 gm from 98 Kg. 450 gm
·
45 cm – 7 mm
Solve the
following word problems.
1. Sohan travelled a distance of 118
km and 50 m and Rahul travelled 415 km and 350 m. Who travelled more and how
much?
2. Anil’s father earns Rs. 8545 and
Sourav’s father earns 12456 rupees 8 paise. How much does Sourav’s father earn
more than Anil’s father?
3. Our school water tank holds 5045
litre of water. On Sunday the water tank was filled with 2865 litre and 45 ml
water. How much water could be filled to reach the capacity of
the tank ?
Textbook Word Problems
At the Market ( Page No. 138 and 139 )
Q. 6 The price of two pens is Rs ________. Can she buy two pens?
Sports Day ( Page No. 141 and 142 )
Teena jumped 3.50 m
which is 3 m and 50 cm.
Q. But how far did Anu jump?
Ans: Anu jumped 3.05 m = 3 m and 5 cm.
Q. Who is the winner in the long jump?
Ans: Rehana is the winner in the long jump.
Q. Write the names of the I, II and III winners on this stand.
Ans: First ( I ) Rehana
Second ( II ) Meena
Third ( III ) Teena
Q. Write in Metres
3 metre 45 centimetre = 3.45 metres
99 centimetre = 0.99 metre
1 metre and 5 centimetre = 1.05 metres
How Big Can You Get
Practice Time
1. Money from different countries
Have you seen any notes or coins used in any other country?
Shivam Bank has a chart to show us how many Indian rupees we can get when we change the money of different countries.
|
Country |
Money |
Changed
into Indian Rupees |
|
Korea |
Won |
0.04 |
|
Sri Lanka |
Rupee (SL) |
0.37 |
|
Nepal |
Rupee |
0.63 |
|
Hong Kong |
Dollar (HK) |
5.10 |
|
South Africa |
Rand |
5.18 |
|
China |
Yuan |
5.50 |
|
U.A.E |
Dirham |
10.80 |
|
U.S.A |
Dollar |
39.70 |
|
Germany |
Euro |
58.30 |
|
England |
Pound |
77.76 |
|
(This is the rate on 15.2.2008) |
||
Mithun spent for school trip = - Rs 350.00
-----------------------
Money left with Mithun = Rs 47.00
C ) Majeed's father is working in Saudi Arabia. He gets 1000 Saudi Riyal as salary. Arun's father who is working in Sri Lanka gets 2000 Sri Lankan Rupees. Who gets more Indian rupees as salary?
Ans:
We know 1 Dirham = Rs 10.80
1000 Dirham = Rs 10.80 X 1000 = Rs 10800.00
So Majeed's father's salary = Rs 10800.00
1 Sri Lankan rupee = Rs 0.37
2000 Sri Lankan rupees = Rs 0.37 X 2000 = Rs 740.00
So Arun's father's salary = Rs 740.00
It is clear that Majeed's father gets more Indian rupees as salary.
D ) Leena's aunty brought a present for her from China. It cost 30 Yuan. Find what it costs in Indian rupees.
Ans:
We know ,
1 Yuan = Rs 5.50
30 Yuan = Rs 5.50 X 30 = Rs 165.00
The present costs Rs 165 in Indian rupees.
E ) Astha wants some Hong Kong Dollars and Won.
1 ) How many Won can she change for Rs 4? For Rs 400?
2 ) How many Hong Kong Dollars can she change for Rs 508?
Ans:
1 ) 1 Won = Rs 0.04 = 4 paise
or we can say,
For Rs 0.04 we can change 1 Won
For Rs 4 we can change = 400 paise ➗ 4 paise ( Rs 4 = 400 paise )
= 100 Won
For Rs 400 she can change = 40000 paise ➗ 4 paise
= 10000 Won
2 ) We know ,
1 Hong Kong Dollar = Rs 5.10 = 510 paise
or For 510 paise she can change 1 HK Dollar
Then for 50800 paise ( Rs 508 ) she can change
50800 ➗ 510 = 99 HK Dollar
She can change 99 Hong Kong Dollars for Rs 508.
Q. 2 Kiran went shopping with Rs 200. Look at the bill. The shopkeeper forgot to put the point correctly in the prices. Put the point in the correct place and find out the total amount of the bill.
Item Quantity Price (Rupees)
Soap 1 1250
Green gram 1 kg 5025
Tea 250 gm 2725
Coconut Oil 1 Litre 6000
-------------------------------------------------------------------------------------
Total ______
Ans:
Item Quantity Price (Rupees)
Soap 1 12 . 50
Green gram 1 kg 50 . 25
Tea 250 gm 27 . 25
Coconut Oil 1 Litre 60 . 00
---------------------------------------------------------------------------------------
Total 150 . 00
3) Which city is cool?
The temperature in each city was noted at 3 pm on 16 January 2008.
1) Which place had the highest temperature at 3 pm? Which place is the coolest at that time?
Ans: Mumbai had the highest temperature t 3 pm.
Srinagar is the coolest at that time.
2) How much higher is the temperature in Mumbai from that in Srinagar?
Ans:
Temperature of Mumbai = 35.1︒C
Temperature of Srinagar= 8.1︒C
-------------------------
Temperature difference = 27.0 ︒C
3) How many degrees will the temperature need to rise for it to reach 40︒C in Thiruvananthapuram?
Ans:
Required temperature = 40 . 0︒C
Temperature of Thiruvananthapuram = 33 . 5 ︒C
------------------------
Temperature needs to rise = 6 . 5 ︒C
Hence 6.5 ︒C temperature will be needed to rise for it to reach 40 ︒C in Thiruvananthapuram.
4) How much lower is the temperature of Kolkata from that in Chennai?
Ans:
Temperature of Chennai = 29 . 9 ︒C
Temperature of Kolkata = 26 . 6 ︒C
---------------------
Temperature difference = 3 . 3 ︒C
5) The temperature in these cities was also noted at 3 am on the same day. Look at the table and answer the questions.
City Temperature at 3 am
Chennai 21.1
Mumbai 19.0
Th'puram 21.6
Kolkata 13.1
Bhopal 9.8
Srinagar 1.3
Guwahati 12.8
Jaipur 10.2
a) Which place had the lowest temperature at 3 am? imagine yourself to be there and describe how it would feel.
Ans: Srinagar had the lowest temperature at 3 am. It would be very cold at that time.
b) What is the difference between the temperature at 3 pm and 3 am in Chennai? In Bhopal?
Ans:
Chennai
Temperature at 3 pm = 29 . 9 ︒C
Temperature at 3 am = 21 . 1 ︒C
---------------------
Temperature difference = 08 . 8 ︒C
Bhopal
Temperature at 3 pm = 25 . 9 ︒C
Temperature at 3 am = 9 . 8 ︒C
---------------------
Temperature difference = 16 . 1︒C
Homework
Word problems
related to Decimal multiplication
1. A class has 23
students. Each student has to pay Rs 125.55 towards exam fees. Find out how
much fees will be collected for the whole class.
Solution:
The number of
students in the class = 23
Exam fees for
each student = Rs 125.55
Exam fees for
23 students = 125.55 X 23
Total exam fees
for the whole class will be = …….
2. A rectangular
figure is 15.23 m long and 7.06 m wide. What will be the area of the
rectangular figure?
Solution:
Length of the
rectangular figure = 15.23 m
Breadth of the
rectangular figure = 7.06 m
Area of the
rectangular figure = 15.23 X 7.06
Hence the
required area of the figure is ………….. sq. m
Thanks for the answering
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