NCERT Class 6 Mathematics Textbook 2018 - made Screen Readable for Blind Students by Professor T K Bansal.

Table of Symbols Used in This Chapter:

Symbol	Known As	Used For	Description	Autocorrect in word
−	Minus	Subtraction	The normal dash sign
₹	Indian Rupee Sign	Indian Rupee	Looks like hindi letter r

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8.1 Introduction

NCERT Class 6 Mathematics Textbook made Screen Readable for Blind Students by Professor T K Bansal.

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 the values correctly?

We know that the dot represents a decimal point. In this chapter, we will learn more about working with decimals.

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8.2 Tenths

NCERT Class 6 Mathematics Textbook made Screen Readable for Blind Students by Professor T K Bansal.

Ravi and Rajeev measured the lengths of their pencils. Ravi’s pencil was 7 cm & 5mm long and Rajeev’s pencil was 8 cm & 3 mm long. Can you express these lengths in centimetre using decimals?

We know that 10 mm = 1 cm
Therefore, 1 mm = 1/10 cm or one-tenth of a cm = 0.1 cm

Now, length of Ravi’s pencil= 7cm & 5mm
= [7 + (5/10)] cm,
i.e., 7cm and 5 tenths of a cm = 7.5cm

The length of Rajeev’s pencil = 8 cm & 3 mm
= [8 + (3/10)] cm,
i.e., 8 cm and 3 tenths of a cm = 8.3 cm

Let us recall what we have learnt in our earlier classes.

Fig

If we show units by blocks then one unit is one block, two units are two blocks and so on. One block divided into 10 equal parts means each part is 1/10 (one-tenth) of a unit, 2 parts show 2 tenths and 5 parts show 5 tenths and so on.

A combination of 2 blocks and 3 parts (tenths) (as shown in the above figure) will be recorded as :

Ones	Tenths
(1)	(1/10)
2	3

Fig

It can be written as 2.3 and read as two point three.

Let us look at another example where we have more than ‘ones. Each tower represents 10 units. So, the number shown here is :

Fig

Tens	Ones	Tenths
(10)	(1)	(1/10)
2	3	5

i.e., 20 + 3 + 5/10 =23.5

This is read in words as ‘twenty-three point five’.

Try These

Q1. Can you now write the following as decimals?

Hundreds (100)	Tens (10)	Ones (1)	Tenths (1/10)
5	3	8	1
2	7	3	4
3	5	4	6

Q2. Write the lengths of Ravi’s and Rajeev’s pencils in ‘cm’ using decimals.

Q3. Make three more examples similar to the one given in question 1 and solve them.

8.2.1 Representing Decimals on number line :

We have been representing fractions on a number line.

Let us now learn to represent decimals too on a number line.

Let us now try to represent 0.6 on a number line.

We know that 0.6 is more than zero but less than one. There are 6 tenths in between 0 and 1. Divide the unit length between 0 and 1 into 10 equal parts and take 6 parts as shown below:

Fig

 

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Write five numbers between 0 and 1 and show them on the number line.

Can you now represent 2.3 on a number line? Check, how many ones and tenths are there in 2.3. Where will it lie on the number line?

Likewise, show 1.4 on the number line.

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 values to the digits in the given numbers. We have,

Number	Tens (10)	Ones (1)	Tenths ( 1/10 )
20.5	2	0	5
4.2	0	4	2

Example 2

Write each of the following as decimals:
(a) Two ones and five-tenths
(b) Thirty and one-tenth

Solution:

(a) Two ones and five-tenths = 2 + 5/10 = 2.5

(b) Thirty and one-tenth = 30 + 1/10 = 30.1

Example 3

Write each of the following numbers as decimals :
(a) 30 + 6 + 2/10
(b) 600 + 2 + 8/10

Solution :

(a) 30 + 6 + 2/10
How many tens, ones and tenths are there in this number?
We have 3 tens, 6 ones and 2 tenths.
Therefore, the decimal representation is 36.2.

(b) 600 + 2+ 8/10
Note that it has 6 hundreds, no tens, 2 ones and 8 tenths.
Therefore, the decimal representation is 602.8

8.2.2 Fractions as decimals

We have already seen how a fraction with denominator 10 can be represented using decimals.

Let us now try to find decimal representation of
(a) 11/5
(b) 1/2

(a)We know that 11/5 = 22/10 = (20 + 2) / 10 = 20/10 + 2/10 = 2+2/10 = 2.2

Therefore, 22/10 = 2.2 (in decimal notation.)

(b) In ½, the denominator is 2. For writing it in decimal notation, the denominator should be 10. We already know how to make an equivalent fraction. So,
(1/2) = (1×5) ÷ (2×5) = 5/10 = 0.5

Therefore, 1/2 is 0.5 in decimal notation.

Try These

Q1. Write 3/2, 4/5, 8/5 in decimal notation.

8.2.3 Decimals as fractions

Till now we have learnt how to write fractions with denominators 10,2 or 5 as decimals. Can we write a decimal number like 1.2 as a fraction?

Let us see 1.2= 1 + 2/10 = 10/10 + 2/10 = 12/10

Exercise 8.1

Q1. Write the following as numbers in the given table.

Fig

 

Fig

 

Hundreds (100)	Tens (10)	Ones (1)	Tenths (1/10)
-	-	-	-
-	-	-	-

Q2. Write the following decimals in the place value table,
(a) 19.4
(b) 0.3
(c) 10.6
(d) 205.9

Q3. Write each of the following as decimals:
(a) Seven-tenths
(b) Two tens and nine-tenths
(c) Fourteen point six
(d) One hundred and two ones
(e) Six hundred point eight

Q4. Write each of the following as decimals:
(a) 5/10
(b) 3 + 7/10
(c) 200 + 60 + 5 +1/10
(d) 70 + 8/10
(e) 88/10
(f) 4(2/10)
(g) 3/2
(h) 2/5
(i) 12/5
(j) 3(3/5)
(k) 4(1/2)

Q5. Write the following decimals as fractions. Reduce the fractions to lowest form.
(a) 0.6
(b) 2.5
(c) 1.0
(d) 3.8
(e) 13.7
(f) 21.2
(g) 6.4

Q6. Express the following as cm using decimals.
(a) 2mm
(b) 30mm
(c) 116mm
(d) 4cm 2mm
(e) 162mm
(f) 83 mm

Q7. Between which two whole numbers on the number line do the given numbers lie ? Which of these whole numbers is nearer to the number?
(a) 0.8
(b) 5.1
(c) 2.6
(d) 6.4
(e) 9.1
(f) 4.9

Figure of number line

 

Q8. Show the following numbers on the number line.
(a) 0.2
(b) 1.9
(c) 1.1
(d) 2.5

Q9. Write the decimal number represented by the points A, B, C, D on the given number line.

Figure of number line

 

Q10.
(a) The length of Ramesh’s notebook is 9 cm 5 mm. What will be its length in cm?
(b) The length of a young gram plant is 65 mm. Express its length in cm.

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8.3. Hundredths

NCERT Class 6 Mathematics Textbook made Screen Readable for Blind Students by Professor T K Bansal.

Fig

 

David was measuring the length of his room. He found that the length of his room is 4 m and 25 cm.

He wanted to write the length in metres. Can you help him?

What part of a metre will be one centimetre?

1 cm = (1/100) m or one-hundredth of a metre.

This means 25 cm = 25/100 m

Now (1/100) means 1 part out of 100 parts of a whole. As we have done for 1/10, let us try to show this pictorially.

Fig (i)

Fig (ii)

 

Take a square and divide it into ten equal parts.

What part is the shaded rectangle of this square?

It is 1/10 or one-tenth or 0.1, see Fig (i).

Now divide each such rectangle into ten equal parts.

We get 100 small squares as shown in Fig (ii). Then what fraction is each small square of the whole square?

Each small square is (1/100) or one-hundredth of the whole square. In decimal notation, we write (1/100) = 0.01 and read it in words as zero point zero one.

What part of the whole square is the shaded portion, if we shade 8 squares, 15 squares, 50 squares, 92 squares of the whole square?

Take the help of following figures to answer

Figure

 

Table

Shaded portions	Ordinary fraction	Decimal number
8 squares	8/100	0.08
15 squares	15/100	0.15
50 squares	-	-
92 squares	-	-

Let us look at some more place value tables.

Table

Ones (1)	Tenths (1/10)	Hundredths (1/100)
2	4	3

The number shown in the table above is 2 + 4/10 + 3/100. In decimals, it is written as 2.43, which is read as ‘two point four three’.

Example 4

Fill the blanks in the following table using ‘block’ information given below and write the corresponding number in decimal form.

Figure

 

Solution:

Table

Hundreds (100)	Tens (10)	Ones (1)	Tenths (1/10)	Hundredths (1/100)
1	3	2	1	5

The number is

\[100\ +\ 30\ +\ 2\ +\ \frac{1}{10}\ +\ \frac{5}{100}\ =\ 132.15\]

Example 5

Fill the blanks in the following table and write the corresponding number in decimal form using ‘block’ information given below.

Block (presented in the form of two tables)

■	■	■	■	■	■	■	■	■	■
■	■	■	■	■	■	■	■	■	■
■	■	■	■	■	■	■	■	■	■
■	■	■	■	■	■	■	■	■	■
■	■	■	■	■	■	■	■	■	■
■	■	■	■	■	■	■	■	■	■
■	■	■	■	■	■	■	■	■	■
■	■	■	■	■	■	■	■	■	■
■	■	■	■	■	■	■	■	■	■
■	■	■	■	■	■	■	■	■	■

 

■	■	■	■	■	■	■	■	■	■
■	■	■	■	■	■	■	■	■	■
■	■	■	■	■	■	■	■	■	■
■	■	■	■	■	■	■	■	■	■
■	■	-	-	-	-	-	-	-	-
-	-	-	-	-	-	-	-	-	-
-	-	-	-	-	-	-	-	-	-
-	-	-	-	-	-	-	-	-	-
-	-	-	-	-	-	-	-	-	-
-	-	-	-	-	-	-	-	-	-

Table

Ones (1)	Tenths (1/10)	Hundredths (1/100)
-	-	-

Solution:

Table

Ones (1)	Tenths (1/10)	Hundredths (1/100)
1	4	2

Therefore, the number is 1.42.

Example 6

Given the place value table, write the number in decimal form.

Table

Hundreds (100)	Tens (10)	Ones (1)	Tenths (1/10)	Hundredths (1/100)
2	4	3	2	5

Solution :

The number is 2 × 100 + 4 × 10 + 3 × 1 + 2 × 1/10 + 5 × (1/100)
= 200 + 40 + 3 + 2/10 + 5/100
=243.25

The first digit 2 is multiplied by 100; the next digit 4 is multiplied by 10, i.e., (1/10 of 100); the next digit 3 is multiplied by 1. After this, the next multiplying factor is 1/10; and then it is 1/100 i.e. (1/10 of 1/10).

The decimal point comes between one’s place and tenths place in a decimal number.

It is now natural to extend the place value table further, from hundredths to 1/10 of hundredths, i.e., thousandths.

Let us now solve some examples.

Example 7

Write the following numbers as decimals,
(a) 4/5
(b) 3/4
(c) 7/1000

Solution :

(a) We have to find a fraction equivalent to 4/5 whose denominator is 10.

\[\frac{4}{5}\ =\ \frac{(4×2)}{(5×2)}\ =\ \frac{8}{10}\ =\ 0.8\]

(b) Here, we have to find a fraction equivalent to 3/4, with denominator 10 or 100. There is no whole number that gives 10 on multiplying by 4, therefore, we make the denominator 100 and we have,

\[\frac{3}{4}\ =\ \frac{(3×25)}{(4×25)}\ =\ \frac{75}{100}\ =\ 0.75\]

(c) For 7/1000, We find that, the tenth and the hundredth place is zero.

Therefore, we write 7/1000 = 0.007

Example 8

Write as fractions in lowest terms.
(a) 0.04
(b) 2.34
(c) 0.342

Solution :

(a) 0.04 = 4/100 = 1/25

(b) 2.34 = 2 + 34/100 = 2 + (34/2) ÷ (100/2) = 2 + 17/50 = 2(17/50)

(c) 0.342 = 342/1000 = (342/2) ÷ (1000/2) = 171/500

Example 9

Write each of the following numbers as a decimal.
(a) 200 + 30 + 5 + 2/10 + 9/100
(b) 50 + 1/10 + 6/100
(c) 16 + 3/10 + 5/1000

Solution:

(a) 200 + 30 + 5 + 2/10 + 9/100
= 235 + 2×1/10 + 9×1/100
= 235.29

(b) 50 + 1/10 + 6/100
= 50 + 1×1/10 + 6×1/100
= 50.16

(c) 16 + 3/10 + 5/1000
= 16 + 3/10 + 0/100 + 5/1000
= 16 + 3×1/10 + 0×1/100 + 5×1/1000
= 16.305

Example 10

Write each of the following as a decimal.
(a) Three hundred six and seven-hundredths
(b) Eleven point two three five
(c) Nine and twenty-five thousandths

Solution:

(a) Three hundred six and seven-hundredths
= 306 + 7/100
= 306 +0×1/10 + 7×1/100
= 306.07

(b) Eleven point two three five
= 11.235

(c) Nine and twenty-five thousandths
= 9 + 25/1000
= 9 + 0/10 + 2/100 + 5/1000
= 9.025
Since, 25 thousandths = 25/1000 = 20/1000 + 5/1000 = 2/100 + 5/1000

EXERCISE 8.2

Q1. Complete the table with the help of these boxes and use decimals to write the number.

Figure

 

Table

Ones	Tenths	Hundredths	Number
-	-	-	-

Q2. Write the numbers given in the following place value table in decimal form.

Hundreds 100	Tens 10	Ones 1	Tenths 1/10	Hundredths 1/100	Thousandths 1/1000
0	0	3	2	5	0
1	0	2	6	3	0
0	3	0	0	2	5
2	1	1	9	0		2
0		1	2	2	4	1

Q3. Write the following decimals in the place value table.
(a) 0.29
(b) 2.08
(c) 19.60
(d) 148.32
(e) 200.812

Q4. Write each of the following as decimals.
(a) 20+9+4/10+1/100
(b) 137+5/100
(c) 7/10+6/100+4/1000
(d) 23+2/10+6/1000
(e) 700+20+5+9/100

Q5. Write each of the following decimals in words.
(a) 0.03
(b) 1.20
(c) 108.56
(d) 10.07
(e) 0.032
(f) 5.008

Q6. Between which two numbers in tenths place on the number line does each of the given number lie?
(a) 0.06
(b) 0.45
(c) 0.19
(d) 0.66
(e) 0.92
(f) 0.57

Q7. Write as fractions in lowest terms.
(a) 0.60
(b) 0.05
(c) 0.75
(d) 0.18
(e) 0.25
(f) 0.125
(g) 0.066

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8.4 Comparing Decimals

NCERT Class 6 Mathematics Textbook made Screen Readable for Blind Students by Professor T K Bansal.

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 each. 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 of 100.

 

■	■	■	■	■	■	■	■	■	■
-	-	-	-	-	-	-	-	-	-
-	-	-	-	-	-	-	-	-	-
-	-	-	-	-	-	-	-	-	-
-	-	-	-	-	-	-	-	-	-
-	-	-	-	-	-	-	-	-	-
-	-	-	-	-	-	-	-	-	-
-	-	-	-	-	-	-	-	-	-
-	-	-	-	-	-	-	-	-	-

0.07=7/100

Figure

0.1=1/10=10/100

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 numbers is 32 and, hence, equal.

We, 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.

We 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 11

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 up to hundredth. But the thousandths part of 1.093 is greater than that of 1.09. Therefore, 1.093 >1.09.

EXERCISE 8.3

Q1. 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

Q2. Make five more examples and find the greater number from them.

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8.5 Using Decimals

NCERT Class 6 Mathematics Textbook made Screen Readable for Blind Students by Professor T K Bansal.

8.5.1 Money

We know that 100 paise = ₹ 1
Therefore, 1 paise = ₹ 1/100 = ₹ 0.01
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

Try these

(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?

8.5.2 Length

Mahesh wanted to measure the length of his tabletop in metres. He had a 50 cm scale. He found that the length of the tabletop 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 tabletop 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.

Figure

 

 

Try These

Q1. Can you write 4 mm in ‘cm’ using decimals?

Q2. How will you write 7cm 5 mm in ‘cm’ using decimals?

Q3. 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’?

8.5.3 Weight

Nandan bought 500g potatoes, 250g capsicum, 700g onions, 500g tomatoes, 100g ginger and 300g radish. What is the total weight of the vegetables in his bag?

Let us add the weights of all the vegetables in the bag.

500g + 250g + 700g + 500g + 100g + 300g = 2350g

We know that 1000g = 1 kg
Therefore, 1 g = 1/1000kg = 0.001 kg

Thus, 2350 g = 2000 g +350 g
=2000/1000kg +350/1000 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 Nandan’s bag is 2.350 kg.

Try These

Q1. Can you now write 456g as ‘kg’ using decimals?

Q2. How will you write 2kg 9g in ‘kg’ using decimals?

EXERCISE 8.4

Q1. Express as rupees using decimals,
(a) 5 paise
(b) 75paise
(c) 20 paise
(d) 50 rupees 90 paise
(e) 725 paise

Q2. Express as metres using decimals,
(a) 15 cm
(b) 6 cm
(c) 2 m 45 cm
(d) 9m 7cm
(e) 419 cm

Q3. Express as cm using decimals,
(a) 5 mm
(b) 60 mm
(c) 164 mm
(d) 9 cm 8 mm
(e) 93 mm

Q4. Express as km using decimals,
(a) 8 m
(b) 88 m
(c) 8888 m
(d) 70 km 5 m

Q5. Express as kg using decimals.
(a) 2 g
(b) 100 g
(c) 3750 g
(d) 5kg 8 g
(e) 26kg 50 g

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8.6 Addition of Numbers with Decimals

NCERT Class 6 Mathematics Textbook made Screen Readable for Blind Students by Professor T K Bansal.

Do This

Q1. Add 0.35 and 0.42.

Take a square and divide it into 100 equal parts. 
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.

Remarks	Ones	Tenths	Hundredths
First Number	0	3	5
+ Second Number	0	4	2
Sum	0	7	7

Therefore, 0.35 + 0.42 = 0.77

Thus, we can add decimal numbers in the same way as we add the whole numbers.

Q2. Can you now add 0.68 and 0.54?

Remarks	Ones	Tenths	Hundredths
First Number	0	6	8
+ Second Number	0	5	4
Sum	1	2	2

Thus, 0.68 + 0.54 = 1.22

Try These

Q1.
(a) 0.29 + 0.36
(b) 0.7 + 0.08
(c) 1.54 + 1.80
(d) 2.66 + 1.85

Example 12

Lata spent ₹ 9.50 for buying a pen and ₹ 2.50 for buying 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 13

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

Example 14

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

Hence the total weight of the fruits bought =11.450 kg.

EXERCISE 8.5

Q1. Find the sum in each of the following:
(a) 0.007 + 8.5 + 30.08
(b) 15 + 0.632 + 13.8
(c) 27.076 + 0.55 + 0.004
(d) 25.65 + 9.005 + 3.7
(e) 0.75 + 10.425 + 2
(f) 280.69 + 25.2 + 38

Q2. Rishabh spent ₹ 35.75 for Maths book and ₹ 32.60 for science book. Find the total amount spent by Rishabh.

Q3. Radhika’s mother gave her ₹ 10.50, and her father gave her ₹ 15.80, find the total amount given to Radhika by her parents.

Q4. Neelam bought 3 m 20 cm cloth for her shirt and 2 m 5 cm cloth for her trouser. Find the total length of cloth bought by her.

Q5. Naresh walked 2 km 35 m in the morning and 1 km 7 m in the evening. How much distance did he walk in all?

Q6. Sunita travelled 15 km 268 m by bus, 7 km 7 m by car and 500 m on foot in order to reach her school. How far is her school from her residence?

Q7. Ravi purchased 5 kg 400 g rice, 2 kg 20 g sugar and 10 kg 850g flour. Find the total weight of his purchases.

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8.7 Subtraction of Decimals

NCERT Class 6 Mathematics Textbook made Screen Readable for Blind Students by Professor T K Bansal.

Do This

Q1. Subtract 1.32 from 2.58

This can be shown by the table.

Table

-	Ones	Tenths	Hundredths
First Number	2	5	8
− Second Number	1	3	2
Difference	1	2	6

Thus, 2.58 − 1.32= 1.26

Therefore, we can say that subtraction of decimal numbers can be done by subtracting hundredths from hundredths, tenths from tenths, ones from ones and so on, just as we do in addition.

Sometimes while subtracting decimals, we may need to regroup like we do in addition.

Let us subtract 1.74 from 3.5.

	Ones	Tenths	Hundredths
First Number	3	5	0
Second Number	1	7	4
Difference	1	7	6

Subtract in the hundredth place.
Can’t subtract!
so, regroup

3.50 − 1.74 = 1.76

Thus, 3.5 − 1.74 = 1.76

Try These

Q1. Subtract 1.85 from 5.46 .

Q2. Subtract 5.25 from 8.28 .

Q3. Subtract 0.95 from 2.29 .

Q4. Subtract 2.25 from 5.68.

Example 15

Abhishek had ₹ 7.45. He bought toffees for ₹ 5.30. Find the balance amount left with Abhishek.

Solution :

Total amount of money = ₹ 7.45
Amount spent on toffees = ₹ 5.30
Balance amount of money = ₹ 7.45 − ₹ 5.30 = ₹ 2.15

Example 16

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

Thus, distance travelled by bus = 4.280 km or 4 km 280 m

Example 17

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 = 5.200kg − 2.750 kg = 2.450 kg

EXERCISE 8.6

Q1. Subtract:
(a) ₹ 18.25 from ₹ 20.75
(b) 202.54 m from 250 m
(c) ₹ 5.36 from ₹ 8.40
(d) 2.051 km from 5.206 km
(e) 0.314 kg from 2.107 kg

Q2. Find the value of :
(a) 9.756 − 6.28
(b) 21.05 − 15.27
(c) 18.5 − 6.79
(d) 11.6 − 9.847

Q3. Rajeev bought a book for ₹ 35.65. He gave ₹ 50 to the shopkeeper. How much money did he get back from the shopkeeper?

Q4. Rani had ₹ 18.50. She bought one ice-cream for ₹ 11.75. How much money does she have now?

Q5. Tina had 20 m 5 cm long cloth. She cuts 4 m 50 cm length of cloth from this, for making a curtain. How much cloth is left with her?

Q6. Namita travels 20 km 50 m every day. Out of this she travels 10 km 200 m by bus and the rest by auto. How much distance does she travel by auto?

Q7. Aakash bought vegetables weighing 10 kg. Out of this, 3 kg 500 g is onions, 2 kg 75 g is tomatoes, and the rest is potatoes. What is the weight of the potatoes?

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What have we discussed?

NCERT Class 6 Mathematics Textbook Chapter 8 made screen readable for Blind Students by Professor T K Bansal.

1.
To understand the parts of one whole (i.e., a unit) we represent a unit by a block. One block divided into 10 equal parts means each part is 1/10 (one-tenth) of a unit. It can be written as 0.1 in decimal notation. The dot between 0 and 1, represents the decimal point and it comes between the units place and the tenths place.

2.
Every fraction with denominator 10 can be written in decimal notation and vice-versa.

3.
One block divided into 100 equal parts means each part is (1/100) (one-hundredth) of a unit. It can be written as 0.01 in decimal notation.

4.
Every fraction with denominator 100 can be written in decimal notation and vice-versa.

5.
In the place value table, as we go from the left to the right, the multiplying factor becomes 1/10 of the previous factor.

The place value table can be further extended from hundredths to 1/10 of hundredths, i.e., thousandths (1/1000), which is written as 0.001 in decimal notation.

6.
Every decimal number can be represented on a number line also.

7.
Every decimal number can be written as a fraction.

8.
Any two decimal numbers can be compared among themselves. The comparison is started with the whole part. If the whole parts are equal, then the tenth parts are compared and so on.

9.
Decimal notation is used in many ways in our lives. For example, in representing units of money, length and weight.

End of the chapter