NCERT Textbook: Decimals

``` Page 1

Savita and Shama were going to market to buy some stationary items. Savita
said, “I have 5 rupees and 75 paise”. Shama said, “I have 7 rupees and 50
paise”.
They knew how to write rupees and paise using decimals.
So Savita said, I have ` 5.75 and Shama said,
“I have ` 7.50”.
Have they written correctly?
We know that the dot represents a decimal point.
with decimals.
8.2 Comparing Decimals
Can you tell which is greater, 0.07 or 0.1?
Take two pieces of square papers of the same size. Divide them into 100
equal parts. For 0.07 we have to shade 7 parts out of 100.
Now, 0.1 =
1
10
=
10
100
, so, for 0.1, shade 10 parts out 100.
8.1 Introduction
Chapter 8 Chapter 8 Chapter 8 Chapter 8 Chapter 8
Decimals Decimals
Decimals Decimals Decimals
0.07 =
7
100
0 1
1
10
. =
=
10
100
Rationalised 2023-24
Page 2

Savita and Shama were going to market to buy some stationary items. Savita
said, “I have 5 rupees and 75 paise”. Shama said, “I have 7 rupees and 50
paise”.
They knew how to write rupees and paise using decimals.
So Savita said, I have ` 5.75 and Shama said,
“I have ` 7.50”.
Have they written correctly?
We know that the dot represents a decimal point.
with decimals.
8.2 Comparing Decimals
Can you tell which is greater, 0.07 or 0.1?
Take two pieces of square papers of the same size. Divide them into 100
equal parts. For 0.07 we have to shade 7 parts out of 100.
Now, 0.1 =
1
10
=
10
100
, so, for 0.1, shade 10 parts out 100.
8.1 Introduction
Chapter 8 Chapter 8 Chapter 8 Chapter 8 Chapter 8
Decimals Decimals
Decimals Decimals Decimals
0.07 =
7
100
0 1
1
10
. =
=
10
100
Rationalised 2023-24
MATHEMATICS
134
This means 0.1>0.07
Let us now compare the numbers 32.55 and 32.5. In this case , we first
compare the whole part. We see that the whole part for both the nunbers is 32
and, hence, equal.
W e, however, know that the two numbers are not equal. So, we now compare
the tenth part. We find that for 32.55 and 32.5, the tenth part is also equal, then
we compare the hundredth part.
W e find,
32.55 = 32 +
5
10
+
5
100
and 32.5 = 32 +
5
10
+
0
100
, therefore, 32.55>32.5 as
the hundredth part of 32.55 is more.
Example 1 : Which is greater?
(a) 1 or 0.99 (b) 1.09 or 1.093
Solution : (a)
1 1
0
10
0
100
= + +
;
0 99 0
9
10
9
100
. = + +
The whole part of 1 is greater than that of 0.99.
Therefore, 1 > 0.99
(b)
1 09 1
0
10
9
100
0
1000
. = + + +
;
1 093 1
0
10
9
100
3
1000
. = + + +
In this case, the two numbers have same parts upto hundredth.
But the thousandths part of 1.093 is greater than that of 1.09.
Therefore, 1.093 > 1.09.
EXERCISE 8.1
1. Which is greater?
(a) 0.3 or 0.4 (b) 0.07 or 0.02 (c) 3 or 0.8 (d) 0.5 or 0.05
(e) 1.23 or 1.2 (f) 0.099 or 0.19 (g) 1.5 or 1.50 (h) 1.431 or 1.490
(i) 3.3 or 3.300 (j) 5.64 or 5.603
2.    Make five more examples and find the greater number from them.
8.3 Using Decimals
8.3.1 Money
We know that 100 paise = ` 1
Therefore,         1 paise = `
1
100
= ` 0.01
(i) Write 2 rupees 5 paise
and 2 rupees 50 paise
in decimals.
(ii) Write 20 rupees
7 paise and 21 rupees
75 paise in decimals?
Rationalised 2023-24
Page 3

Savita and Shama were going to market to buy some stationary items. Savita
said, “I have 5 rupees and 75 paise”. Shama said, “I have 7 rupees and 50
paise”.
They knew how to write rupees and paise using decimals.
So Savita said, I have ` 5.75 and Shama said,
“I have ` 7.50”.
Have they written correctly?
We know that the dot represents a decimal point.
with decimals.
8.2 Comparing Decimals
Can you tell which is greater, 0.07 or 0.1?
Take two pieces of square papers of the same size. Divide them into 100
equal parts. For 0.07 we have to shade 7 parts out of 100.
Now, 0.1 =
1
10
=
10
100
, so, for 0.1, shade 10 parts out 100.
8.1 Introduction
Chapter 8 Chapter 8 Chapter 8 Chapter 8 Chapter 8
Decimals Decimals
Decimals Decimals Decimals
0.07 =
7
100
0 1
1
10
. =
=
10
100
Rationalised 2023-24
MATHEMATICS
134
This means 0.1>0.07
Let us now compare the numbers 32.55 and 32.5. In this case , we first
compare the whole part. We see that the whole part for both the nunbers is 32
and, hence, equal.
W e, however, know that the two numbers are not equal. So, we now compare
the tenth part. We find that for 32.55 and 32.5, the tenth part is also equal, then
we compare the hundredth part.
W e find,
32.55 = 32 +
5
10
+
5
100
and 32.5 = 32 +
5
10
+
0
100
, therefore, 32.55>32.5 as
the hundredth part of 32.55 is more.
Example 1 : Which is greater?
(a) 1 or 0.99 (b) 1.09 or 1.093
Solution : (a)
1 1
0
10
0
100
= + +
;
0 99 0
9
10
9
100
. = + +
The whole part of 1 is greater than that of 0.99.
Therefore, 1 > 0.99
(b)
1 09 1
0
10
9
100
0
1000
. = + + +
;
1 093 1
0
10
9
100
3
1000
. = + + +
In this case, the two numbers have same parts upto hundredth.
But the thousandths part of 1.093 is greater than that of 1.09.
Therefore, 1.093 > 1.09.
EXERCISE 8.1
1. Which is greater?
(a) 0.3 or 0.4 (b) 0.07 or 0.02 (c) 3 or 0.8 (d) 0.5 or 0.05
(e) 1.23 or 1.2 (f) 0.099 or 0.19 (g) 1.5 or 1.50 (h) 1.431 or 1.490
(i) 3.3 or 3.300 (j) 5.64 or 5.603
2.    Make five more examples and find the greater number from them.
8.3 Using Decimals
8.3.1 Money
We know that 100 paise = ` 1
Therefore,         1 paise = `
1
100
= ` 0.01
(i) Write 2 rupees 5 paise
and 2 rupees 50 paise
in decimals.
(ii) Write 20 rupees
7 paise and 21 rupees
75 paise in decimals?
Rationalised 2023-24
DECIMALS
135
So, 65 paise = `
65
100
= ` 0.65
and 5 paise = `
5
100
= ` 0.05
What is 105 paise? It is ` 1 and 5 paise = ` 1.05
8.3.2 Length
Mahesh wanted to measure the length of his
table top in metres. He had a 50 cm scale.
He found that the length of the table top was
156 cm. What will be its length in metres?
Mahesh knew that
1 cm  =
1
100
m   or   0.01 m
Therefore, 56 cm =
56
100
m = 0.56 m
Thus, the length of the table top is
156 cm = 100 cm + 56 cm
= 1 m +
56
100
m = 1.56 m.
Mahesh also wants to represent this length pictorially. He took squared
papers of equal size and divided them into 100 equal parts. He considered
each small square as one cm.
8.3.3 Weight
Nandu bought 500g potatoes, 250g capsicum,
700g onions, 500g tomatoes, 100g ginger and
300g  radish. What is the total weight of the
vegetables in the bag? Let us add the weight of all
the vegetables in the bag.
500 g + 250 g + 700 g + 500 g + 100 g + 300 g
= 2350 g
100 cm 56 cm
1. Can you write 4 mm in ‘cm’ using
decimals?
2. How will you write 7cm 5 mm in ‘cm’
using decimals?
3. Can you now write 52 m as ‘km’
using decimals? How will you
write 340 m as ‘km’ using decimals?
How will you write 2008 m in ‘km’?
1. Can you now write
456g as ‘kg’ using
decimals?
2. How will you write
2kg 9g in ‘kg’ using
decimals?
Rationalised 2023-24
Page 4

Savita and Shama were going to market to buy some stationary items. Savita
said, “I have 5 rupees and 75 paise”. Shama said, “I have 7 rupees and 50
paise”.
They knew how to write rupees and paise using decimals.
So Savita said, I have ` 5.75 and Shama said,
“I have ` 7.50”.
Have they written correctly?
We know that the dot represents a decimal point.
with decimals.
8.2 Comparing Decimals
Can you tell which is greater, 0.07 or 0.1?
Take two pieces of square papers of the same size. Divide them into 100
equal parts. For 0.07 we have to shade 7 parts out of 100.
Now, 0.1 =
1
10
=
10
100
, so, for 0.1, shade 10 parts out 100.
8.1 Introduction
Chapter 8 Chapter 8 Chapter 8 Chapter 8 Chapter 8
Decimals Decimals
Decimals Decimals Decimals
0.07 =
7
100
0 1
1
10
. =
=
10
100
Rationalised 2023-24
MATHEMATICS
134
This means 0.1>0.07
Let us now compare the numbers 32.55 and 32.5. In this case , we first
compare the whole part. We see that the whole part for both the nunbers is 32
and, hence, equal.
W e, however, know that the two numbers are not equal. So, we now compare
the tenth part. We find that for 32.55 and 32.5, the tenth part is also equal, then
we compare the hundredth part.
W e find,
32.55 = 32 +
5
10
+
5
100
and 32.5 = 32 +
5
10
+
0
100
, therefore, 32.55>32.5 as
the hundredth part of 32.55 is more.
Example 1 : Which is greater?
(a) 1 or 0.99 (b) 1.09 or 1.093
Solution : (a)
1 1
0
10
0
100
= + +
;
0 99 0
9
10
9
100
. = + +
The whole part of 1 is greater than that of 0.99.
Therefore, 1 > 0.99
(b)
1 09 1
0
10
9
100
0
1000
. = + + +
;
1 093 1
0
10
9
100
3
1000
. = + + +
In this case, the two numbers have same parts upto hundredth.
But the thousandths part of 1.093 is greater than that of 1.09.
Therefore, 1.093 > 1.09.
EXERCISE 8.1
1. Which is greater?
(a) 0.3 or 0.4 (b) 0.07 or 0.02 (c) 3 or 0.8 (d) 0.5 or 0.05
(e) 1.23 or 1.2 (f) 0.099 or 0.19 (g) 1.5 or 1.50 (h) 1.431 or 1.490
(i) 3.3 or 3.300 (j) 5.64 or 5.603
2.    Make five more examples and find the greater number from them.
8.3 Using Decimals
8.3.1 Money
We know that 100 paise = ` 1
Therefore,         1 paise = `
1
100
= ` 0.01
(i) Write 2 rupees 5 paise
and 2 rupees 50 paise
in decimals.
(ii) Write 20 rupees
7 paise and 21 rupees
75 paise in decimals?
Rationalised 2023-24
DECIMALS
135
So, 65 paise = `
65
100
= ` 0.65
and 5 paise = `
5
100
= ` 0.05
What is 105 paise? It is ` 1 and 5 paise = ` 1.05
8.3.2 Length
Mahesh wanted to measure the length of his
table top in metres. He had a 50 cm scale.
He found that the length of the table top was
156 cm. What will be its length in metres?
Mahesh knew that
1 cm  =
1
100
m   or   0.01 m
Therefore, 56 cm =
56
100
m = 0.56 m
Thus, the length of the table top is
156 cm = 100 cm + 56 cm
= 1 m +
56
100
m = 1.56 m.
Mahesh also wants to represent this length pictorially. He took squared
papers of equal size and divided them into 100 equal parts. He considered
each small square as one cm.
8.3.3 Weight
Nandu bought 500g potatoes, 250g capsicum,
700g onions, 500g tomatoes, 100g ginger and
300g  radish. What is the total weight of the
vegetables in the bag? Let us add the weight of all
the vegetables in the bag.
500 g + 250 g + 700 g + 500 g + 100 g + 300 g
= 2350 g
100 cm 56 cm
1. Can you write 4 mm in ‘cm’ using
decimals?
2. How will you write 7cm 5 mm in ‘cm’
using decimals?
3. Can you now write 52 m as ‘km’
using decimals? How will you
write 340 m as ‘km’ using decimals?
How will you write 2008 m in ‘km’?
1. Can you now write
456g as ‘kg’ using
decimals?
2. How will you write
2kg 9g in ‘kg’ using
decimals?
Rationalised 2023-24
MATHEMATICS
136
W e know that 1000 g = 1 kg
Therefore, 1 g =
1
1000
kg
= 0.001 kg
Thus, 2350 g = 2000 g + 350 g
=
2000
1000
350
1000
kg kg +
= 2 kg + 0.350 kg = 2.350 kg
i.e. 2350 g = 2 kg 350 g = 2.350 kg
Thus, the weight of vegetables in Nandu’s bag is 2.350 kg.
EXERCISE 8.2
1. Express as rupees using decimals.
(a) 5 paise (b) 75 paise (c) 20 paise
(d) 50 rupees 90 paise (e) 725 paise
2. Express as metres using decimals.
(a) 15 cm (b) 6 cm (c) 2 m 45 cm
(d) 9 m 7 cm (e) 419 cm
3. Express as cm using decimals.
(a) 5 mm (b) 60 mm (c) 164 mm
(d) 9 cm 8 mm (e) 93 mm
4. Express as km using decimals.
(a) 8 m (b) 88 m (c) 8888 m
(d) 70 km 5 m
5. Express as kg using decimals.
(a) 2 g (b) 100 g (c) 3750 g
(d) 5 kg 8 g (e) 26 kg 50 g
8.4 Addition of Numbers with Decimals
Take a square and divide it into 100 equal parts.
Do This
Rationalised 2023-24
Page 5

Savita and Shama were going to market to buy some stationary items. Savita
said, “I have 5 rupees and 75 paise”. Shama said, “I have 7 rupees and 50
paise”.
They knew how to write rupees and paise using decimals.
So Savita said, I have ` 5.75 and Shama said,
“I have ` 7.50”.
Have they written correctly?
We know that the dot represents a decimal point.
with decimals.
8.2 Comparing Decimals
Can you tell which is greater, 0.07 or 0.1?
Take two pieces of square papers of the same size. Divide them into 100
equal parts. For 0.07 we have to shade 7 parts out of 100.
Now, 0.1 =
1
10
=
10
100
, so, for 0.1, shade 10 parts out 100.
8.1 Introduction
Chapter 8 Chapter 8 Chapter 8 Chapter 8 Chapter 8
Decimals Decimals
Decimals Decimals Decimals
0.07 =
7
100
0 1
1
10
. =
=
10
100
Rationalised 2023-24
MATHEMATICS
134
This means 0.1>0.07
Let us now compare the numbers 32.55 and 32.5. In this case , we first
compare the whole part. We see that the whole part for both the nunbers is 32
and, hence, equal.
W e, however, know that the two numbers are not equal. So, we now compare
the tenth part. We find that for 32.55 and 32.5, the tenth part is also equal, then
we compare the hundredth part.
W e find,
32.55 = 32 +
5
10
+
5
100
and 32.5 = 32 +
5
10
+
0
100
, therefore, 32.55>32.5 as
the hundredth part of 32.55 is more.
Example 1 : Which is greater?
(a) 1 or 0.99 (b) 1.09 or 1.093
Solution : (a)
1 1
0
10
0
100
= + +
;
0 99 0
9
10
9
100
. = + +
The whole part of 1 is greater than that of 0.99.
Therefore, 1 > 0.99
(b)
1 09 1
0
10
9
100
0
1000
. = + + +
;
1 093 1
0
10
9
100
3
1000
. = + + +
In this case, the two numbers have same parts upto hundredth.
But the thousandths part of 1.093 is greater than that of 1.09.
Therefore, 1.093 > 1.09.
EXERCISE 8.1
1. Which is greater?
(a) 0.3 or 0.4 (b) 0.07 or 0.02 (c) 3 or 0.8 (d) 0.5 or 0.05
(e) 1.23 or 1.2 (f) 0.099 or 0.19 (g) 1.5 or 1.50 (h) 1.431 or 1.490
(i) 3.3 or 3.300 (j) 5.64 or 5.603
2.    Make five more examples and find the greater number from them.
8.3 Using Decimals
8.3.1 Money
We know that 100 paise = ` 1
Therefore,         1 paise = `
1
100
= ` 0.01
(i) Write 2 rupees 5 paise
and 2 rupees 50 paise
in decimals.
(ii) Write 20 rupees
7 paise and 21 rupees
75 paise in decimals?
Rationalised 2023-24
DECIMALS
135
So, 65 paise = `
65
100
= ` 0.65
and 5 paise = `
5
100
= ` 0.05
What is 105 paise? It is ` 1 and 5 paise = ` 1.05
8.3.2 Length
Mahesh wanted to measure the length of his
table top in metres. He had a 50 cm scale.
He found that the length of the table top was
156 cm. What will be its length in metres?
Mahesh knew that
1 cm  =
1
100
m   or   0.01 m
Therefore, 56 cm =
56
100
m = 0.56 m
Thus, the length of the table top is
156 cm = 100 cm + 56 cm
= 1 m +
56
100
m = 1.56 m.
Mahesh also wants to represent this length pictorially. He took squared
papers of equal size and divided them into 100 equal parts. He considered
each small square as one cm.
8.3.3 Weight
Nandu bought 500g potatoes, 250g capsicum,
700g onions, 500g tomatoes, 100g ginger and
300g  radish. What is the total weight of the
vegetables in the bag? Let us add the weight of all
the vegetables in the bag.
500 g + 250 g + 700 g + 500 g + 100 g + 300 g
= 2350 g
100 cm 56 cm
1. Can you write 4 mm in ‘cm’ using
decimals?
2. How will you write 7cm 5 mm in ‘cm’
using decimals?
3. Can you now write 52 m as ‘km’
using decimals? How will you
write 340 m as ‘km’ using decimals?
How will you write 2008 m in ‘km’?
1. Can you now write
456g as ‘kg’ using
decimals?
2. How will you write
2kg 9g in ‘kg’ using
decimals?
Rationalised 2023-24
MATHEMATICS
136
W e know that 1000 g = 1 kg
Therefore, 1 g =
1
1000
kg
= 0.001 kg
Thus, 2350 g = 2000 g + 350 g
=
2000
1000
350
1000
kg kg +
= 2 kg + 0.350 kg = 2.350 kg
i.e. 2350 g = 2 kg 350 g = 2.350 kg
Thus, the weight of vegetables in Nandu’s bag is 2.350 kg.
EXERCISE 8.2
1. Express as rupees using decimals.
(a) 5 paise (b) 75 paise (c) 20 paise
(d) 50 rupees 90 paise (e) 725 paise
2. Express as metres using decimals.
(a) 15 cm (b) 6 cm (c) 2 m 45 cm
(d) 9 m 7 cm (e) 419 cm
3. Express as cm using decimals.
(a) 5 mm (b) 60 mm (c) 164 mm
(d) 9 cm 8 mm (e) 93 mm
4. Express as km using decimals.
(a) 8 m (b) 88 m (c) 8888 m
(d) 70 km 5 m
5. Express as kg using decimals.
(a) 2 g (b) 100 g (c) 3750 g
(d) 5 kg 8 g (e) 26 kg 50 g
8.4 Addition of Numbers with Decimals
Take a square and divide it into 100 equal parts.
Do This
Rationalised 2023-24
DECIMALS
137
Mark 0.35 in this square by shading
3 tenths and colouring 5 hundredths.
Mark 0.42 in this square by shading
4 tenths and colouring 2 hundredths.
Now count the total number of tenths in the square and
the total number of hundredths in the square.
Therefore, 0.35 + 0.42 = 0.77
Thus, we can add decimals in the same
way as whole numbers.
Can you now add 0.68 and 0.54?
Thus, 0.68 + 0.54 = 1.22
Example 2 : Lata spent ` 9.50 for buying a pen and ` 2.50 for one pencil. How
much money did she spend?
Solution : Money spent for pen = ` 9.50
Money spent for pencil = ` 2.50
Total money spent = ` 9.50  + ` 2.50
Total money spent = ` 12.00
Example 3 : 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
Ones Tenths Hundredths
0 6 8
+ 0 5 4
1 2 2
Find
(i)   0.29 + 0.36   (ii)  0.7 + 0.08
(iii) 1.54 + 1.80   (iv)  2.66 + 1.85
Ones Tenths Hundredths
0 3 5
+ 0 4 2
0 7 7
Rationalised 2023-24
```

## Mathematics (Maths) Class 6

94 videos|347 docs|54 tests

## FAQs on NCERT Textbook: Decimals - Mathematics (Maths) Class 6

 1. What is a decimal number?
Ans. A decimal number is a number that contains a decimal point, separating the whole number part from the fractional part. It is based on the powers of 10, where each digit to the right of the decimal point represents a power of 10 raised to a negative exponent.
 2. How to convert a fraction into a decimal?
Ans. To convert a fraction into a decimal, divide the numerator (top number) of the fraction by the denominator (bottom number). The quotient obtained is the decimal representation of the fraction.
 3. What is the significance of the place value in decimal numbers?
Ans. Place value plays a crucial role in decimal numbers. Each digit in a decimal number has a specific place value based on its position from the decimal point. The place value determines the magnitude of the digit and helps in comparing and ordering decimal numbers.
 4. How can decimals be used in real-life situations?
Ans. Decimals are extensively used in various real-life scenarios. They are used in measuring lengths, weights, and quantities, such as in cooking recipes, financial transactions, and scientific calculations. Decimals also help in representing probabilities, percentages, and monetary values.
 5. What are terminating and non-terminating decimals?
Ans. Terminating decimals are decimals that have a finite number of digits after the decimal point. For example, 0.25 is a terminating decimal. Non-terminating decimals, on the other hand, have an infinite number of digits after the decimal point. For example, 0.333... is a non-terminating decimal.

## Mathematics (Maths) Class 6

94 videos|347 docs|54 tests

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