Decimals
Tenths:-
·
Means 1 part
out of 10 parts of a whole.
·
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In decimals, 7 cm 5mm can
be expressed as:
Since, 10 mm = 1 cm
Therefore, 1 mm = 
cm or one-tenth cm = 0.1 cm
7cm 5mm = 7 
cm i.e. 7cm and
5 tenths of a cm = 7.5cm.
Representing
Decimals on number line:-
Since, 0.6 is more than zero but less than
one. There are 6 tenths in it. Divide the unit length between 0 and 1 into 10
equal parts and take 6 parts
Example 1: Write the
following numbers in the place value table: (a) 20.5 (b) 4.2
Solution:
Let us make a common place value table, assigning appropriate
place value to the digits in the given numbers. We have,
|
|
Tens(10) |
Ones(1) |
Tenths( |
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20.5 |
2 |
0 |
5 |
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4.2 |
0 |
4 |
2 |
Fractions as decimals:-
·
Make the
denominator equal to ten by multiplying numerator and denominator by a number.
Example: Find decimal representation of (a) 
(b) 
Solution:-
Thus, 
is 2.2 in decimal notation.
Thus, is 0.5 in decimal notation.
Decimals as fractions:-
·
Express
digits after decimal in fractions according to decimal value chart.
Example: - Express 1.2 in
fractions.
Solution:-
Hundredths:-
·
Means 1 part out of 100 parts of a whole.
·
In
decimal notation, = 0.01 and is read as zero point zero one.
Pictorially:-
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Each small square is 
or
one-hundredth of the whole square.
In decimals, 4 m and 25 cm
can be expressed as:-
1 cm = m
25 cm = 
m
Example: Given the place value table, write the number in
decimal form.
|
Hundreds (100) |
Tens (10) |
Ones (1) |
Tenths
|
Hundredths
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2 |
4 |
3 |
2 |
5 |
|
Solution:
The number is 2 × 100 + 4 × 10 + 3 × 1 + 2 ×
+ 5 × 
= 200 +
40 + 3 + 2 10 + 5 100 = 243.25
Example: Write as
fractions in lowest terms. (a) 0.04 (b) 2.34 (c) 0.342
Solution:
(a) 0.04 = 
= 
(b) 2.34 = 2 + 
(c) 0.342= 
Comparing Decimals:-
Which is greater, 0.07 or 0.1?
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Thus, 0.1>0.07
Example: compare the numbers 32.55 and 32.5.
Solution: -
In this case, first compare the whole part. Since, the whole
part for both the numbers is 32 and, hence, equal. So, we now compare the tenth
part. We find that for 32.55 and 32.5, the tenth part is also equal, the5n we
compare the hundredth part.
32.55 = 32 + + 
and 32.5 = 32
+ + 
Therefore, 32.55 > 32.5 as the hundredth part of 32.55 is more.
Addition of Numbers with
Decimals:-
·
Addition
of decimals can be done by adding hundredths with hundredths, tenths with tenths,
ones with ones.
Example: - add 0.32 + 0.45
Solution:-
|
Ones |
Tenths
|
Hundredths
|
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0 |
3 4 |
2 5 |
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7 |
7 |
Using Decimals:-
·
Money:-
100 paisa = Rs. 1
Therefore,
1 paisa
= Rs.
= Rs 0.01
So, 65 paisa = Rs. 
= Rs.0.65
105
paisa = Rs. 1 and 5 paisa = Rs. 1.05
Example: - Lata spent Rs. 9.50 for buying a pen and Rs. 2.50 for
one pencil. How much money did she spend?
Solution:
Money
spent for pen = Rs. 9.50
Money spent for
pencil = Rs. 2.50
Total money spent = Rs. 9.50 + Rs. 2.50
Total money spent =
Rs. 12.00
·
Length:-
1
cm = m = 0.01 m
25
cm = m = 0.25 m
Example: - Samson travelled 5 km 52 m by bus, 2 km 265 m by car
and the rest 1km 30 m he walked. How much distance did he travel in all?
Solution:
Distance travelled by bus = 5 km 52 m =
5.052 km
Distance travelled by car = 2 km 265 m =
2.265 km
Distance travelled on foot = 1 km 30 m =
1.030 km
Therefore, total distance travelled is
5.052
km
2.265
km
+ 1.030 km
8.347
km
Therefore, total distance travelled = 8.347 km
·
Weight:-
1000
g = 1 kg
Therefore,
1kg = 
kg = 0.001 kg
Example: - Rahul bought 4
kg 90 g of apples, 2 kg 60 g of grapes and 5 kg 300 g of mangoes. Find the
total weight of all the fruits he bought.
Solution:
Weight
of apples = 4 kg 90 g = 4.090 kg
Weight of grapes = 2 kg 60 g = 2.060 kg
Weight of mangoes = 5 kg 300 g = 5.300 kg
Therefore,
the total weight of the fruits bought is
4.090
kg
2.060 kg
+
5.300 kg
11.450 kg
Total
weight of the fruits bought = 11.450 kg
Subtraction of Decimals:-
·
Subtraction
of decimals can be done by subtracting hundredths from hundredths, tenths from
tenths, ones from ones.
Example: - Subtract 1.74 from 3.5.
Solution:-
. 
1. 7 4
1. 7 6
Example 1: Abhishek had
Rs. 7.45. He bought toffees for Rs. 5.30. Find the balance amount left with
Abhishek.
Solution:
Total
amount of money = Rs. 7.45
Amount spent on toffees = Rs. 5.30
Balance amount of money = Rs. 7.45 – Rs. 5.30 =
Rs. 2.15
Example 2: Urmila’s school is at a distance of 5 km 350 m from
her house. She travels 1 km 70 m on foot and the rest by bus. How much distance
does she travel by bus?
Solution:
Total
distance of school from the house = 5.350 km
Distance travelled on
foot = 1.070 km
Therefore, distance travelled by bus = 5.350 km –
1.070 km = 4.280 km or 4 km 280 m
Example 3: Kanchan bought a watermelon weighing 5 kg 200
g. Out of this she gave 2 kg 750 g to her neighbour. What is the weight of the
watermelon left with Kanchan?
Solution:
Total
weight of the watermelon = 5.200 kg
Watermelon given to the neighbour = 2.750 kg
Therefore, weight of
the remaining watermelon = 5.200 kg – 2.750 kg
= 2.450 kg