Decimals

We can write the numbers observing from the figure as below:

The given numbers can be written in the form of place value table as follows:

(a) Here,

We can write the given number into fraction as follows:

Seven-tenths =

Now,

According to the question,

This fraction can be converted in the form of decimal as follows:

(b) Here,

We can write the given numbers into fraction as follows:

Two tens = 20

And,

Nime-tenths =

It can together be written as

20 +

Now,

According to the question,

This fraction can be converted in the form of decimal as follows:

(c) We know that,

The given number cannot be written in the fraction form

But,

It is already written into decimal form.

Hence,

The given number can be directly written into the decimal format as below:

Fourteen point six = 14.6

(d) Here,

We know that,

The given number cannot be written in the fraction format

We can write the given numbers as follows:

On hundred = 100

And,

Two ones = 2

It can together be written as

100 + 2

= 102

Now,

According to the question,

This number can be converted in the form of decimal as follows:

102 = 102.0

(e) We know that,

The given number cannot be written in the fraction form

But,

It is already written into decimal form.

Hence,

The given number can be directly written into the decimal format as below:

Six hundred point eight = 600.8

(a)

Here,

According to the question,

We have to convert the given fraction into decimal

Thus,

As per the question,

The given fraction can be converted in the form of decimal as follows:

(b)

Here,

According to the question,

We have to convert the given fraction into decimal

Thus,

As per the question,

The given fraction can be converted in the form of decimal as follows:

= 3.7

(c)

Here,

According to the question,

We have to convert the given fraction into decimal

Thus,

As per the question,

The given fraction can be converted in the form of decimal as follows:

= 265.1

(d)

Here,

According to the question,

We have to convert the given fraction into decimal

Thus,

As per the question,

The given fraction can be converted in the form of decimal as follows:

= 70.8

(e)

Here,

According to the question,

We have to convert the given fraction into decimal

Thus,

As per the question,

The given fraction can be converted in the form of decimal as follows:

= 8.8

(f)

Here,

According to the question,

We have to convert the given fraction into decimal

Thus,

At first,

We will convert the mixed fraction into improper fraction

=

=

As per the question,

The given fraction can be converted in the form of decimal as follows:

(g)

Here,

According to the question,

We have to convert the given fraction into decimal

Thus,

As per the question,

The given fraction can be converted in the form of decimal as follows:

=

= 1 + 0.5

= 1.5

(h)

Here,

According to the question,

We have to convert the given fraction into decimal

Thus,

As per the question,

The given fraction can be converted in the form of decimal as follows:

(i)

Here,

According to the question,

We have to convert the given fraction into decimal

Thus,

As per the question,

The given fraction can be converted in the form of decimal as follows:

=

= 2 + 0.4

= 2.4

(j)

Here,

According to the question,

We have to convert the given fraction into decimal

Thus,

At first,

We will convert the mixed fraction into improper fraction

=

=

As per the question,

The given fraction can be converted in the form of decimal as follows:

(k)

Here,

According to the question,

We have to convert the given fraction into decimal

Thus,

At first,

We will convert the mixed fraction into improper fraction

=

=

As per the question,

The given fraction can be converted in the form of decimal as follows:

(a) Here,

According to the question,

At first,

We have to convert the given decimals into fractions

Thus,

0.6 =

Now,

According to the question,

We have to reduce the fractions to their lowest form as follows:

(b) Here,

According to the question,

At first,

We have to convert the given decimals into fractions

Thus,

2.5 =

Now,

According to the question,

We have to reduce the fractions to their lowest form as follows:

(c) Here,

According to the question,

At first,

We have to convert the given decimals into fractions

Thus,

1.0 =

Now,

According to the question,

We have to reduce the fractions to their lowest form

But,

We can observe that,

The fraction so obtained is already in its simplest form

(d) Here,

According to the question,

At first,

We have to convert the given decimals into fractions

Thus,

3.8 =

Now,

According to the question,

We have to reduce the fractions to their lowest form as follows:

(e) Here,

According to the question,

At first,

We have to convert the given decimals into fractions

Thus,

13.7 =

Now,

According to the question,

We have to reduce the fractions to their lowest form

But,

We can observe that,

The fraction so obtained is already in its simplest form

(f) Here,

According to the question,

At first,

We have to convert the given decimals into fractions

Thus,

21.2 =

Now,

According to the question,

We have to reduce the fractions to their lowest form as follows:

(g) Here,

According to the question,

At first,

We have to convert the given decimals into fractions

Thus,

6.4 =

Now,

According to the question,

We have to reduce the fractions to their lowest form as follows:

(a) 2 mm

Here,

We have to convert the given quantity into cm

Now,

We know that,

1cm = 10mm

Hence,

We can convert the given quantity into cm as follows:

2mm =

= 0.2 cm

(b) 30 mm

Here,

We have to convert the given quantity into cm

Now,

We know that,

1cm = 10mm

Hence,

We can convert the given quantity into cm as follows:

30mm =

= 3.0 cm

(c) 116 mm

Here,

We have to convert the given quantity into cm

Now,

We know that,

1cm = 10mm

Hence,

We can convert the given quantity into cm as follows:

116mm =

= 11.6 cm

(d) 4 cm 2 mm

Here,

We have to convert the given quantity into cm

Now,

We know that,

1cm = 10mm

Hence,

We can convert the given quantity into cm as follows:

4cm 2mm =

= 4.2 cm

(e) 162 mm

Here,

We have to convert the given quantity into cm

Now,

We know that,

1cm = 10mm

Hence,

We can convert the given quantity into cm as follows:

162mm =

= 16.2 cm

(f) 83 mm

Here,

We have to convert the given quantity into cm

Now,

We know that,

1cm = 10mm

Hence,

We can convert the given quantity into cm as follows:

83mm =

= 8.3 cm

(a) Here,

We can clearly see that,

0.8 lie between 0 and 1.

And,

It is nearer to 1

(b) Here,

We can clearly see that,

5.1 lie between 5 and 6

And,

It is nearer to 5

(c) Here,

We can clearly see that,

2.6 lie between 2 and 3

And,

It is nearer to 3

(d) Here,

We can clearly see that,

6.4 lie between 6 and 7

And,

It is nearer to 6

(e) Here,

We can clearly see that,

9.1 lie between 9 and 10

And,

It is nearer to 9

(f) Here,

We can clearly see that,

4.9 lie between 4 and 5

And,

It is nearer to 5

(a) 0.2

Here,

We can see that,

On a number line 0.2 lies between 0 and 1

In such a way that the space between 0 and 1 is divided into 10 equal parts.

Hence,

We can obseve that each part will be equal to one-tenth.

Now,

0.2 is the second point between 0 and 1.

(b) 1.9

Here,

We can see that,

On a number line 1.9 lie between 1 and 2

In such a way that the space between 1 and 2 is divided into 10 equal parts.

Hence,

We can obseve that each part will be equal to one-tenth.

Now,

1.9 is the ninth point between 1 and 2.

(c) 1.1

Here,

We can see that,

On a number line 1.1 lies between 1 and 2

In such a way that the space between 1 and 2 is divided into 10 equal parts.

Hence,

We can obseve that each part will be equal to one-tenth.

Now,

1.1 is the second point between 1 and 2.

(d) 2.5

Here,

We can see that,

On a number line 2.5 lies between 2 and 3

In such a way that the space between 2 and 3 is divided into 10 equal parts.

Hence,

We can obseve that each part will be equal to one-tenth.

Now,

2.5 is the second point between 2 and 3.

Here,

We can observe that,

Point A on the number line represents 0.8

Point B on the number line represents 1.3

Point C on the number line represents 2.2

Point D on the number line represents 2.9

From the question, we have:

Length of the Ramesh’s notebook = 9cm 5mm

According to the question,

We have to convert the length into cm

Now,

We know that,

1cm = 10mm

Hence,

We can convert the length of notebook into cm as follows:

9cm 5mm =

= 9.5 cm

Therefore,

Length of Ramesh’s notebook in cm = 9.5 cm

From the question, we have:

Length of the young gram plant = 65mm

According to the question,

We have to convert the length into cm

Now,

We know that,

1cm = 10mm

Hence,

We can convert the length of young gram plant into cm as follows:

65mm =

= 6.5 cm

Therefore,

Length of young gram plant in cm = 6.5cm

Here,

We can complete the table as follows:

(a) Using the place value table,

We can write in decimal form as follows:

³

=

= 3.25

(b) Using the place value table,

We can write in decimal form as follows:

100

=

= 102.63

(c) Using the place value table,

We can write in decimal form as follows:

3

=

= 30.025

(d) Using the place value table,

We can write in decimal form as follows:

200

=

= 211.902

(e) Using the place value table,

We can write in decimal form as follows:

10

=

= 12.241

(a) 0.29

Here,

We can write the decimal number in the form of place value table as follows:

0.29 = 0.2 + 0.09

=

(b) 2.08

Here,

We can write the decimal number in the form of place value table as follows:

2.08 = 2 + 0.08

=

(c) 19.60

Here,

We can write the decimal number in the form of place value table as follows:

19.60 = 10 + 9 + 0.60

=

(d) 148.32

Here,

We can write the decimal number in the form of place value table as follows:

148.32 = 148 + 0.32

=

(e) 200.812

Here,

We can write the decimal number in the form of place value table as follows:

200.812 = 200 + 0.8 + 0.01 + 0.002

=

Now,

We can write them in the place value table as follows:

(a) Here,

We can write them in the form of decimals as follows:

20

=

= 29.41

(b) Here,

We can write them in the form of decimals as follows:

137

=

= 137.05

(c) Here,

We can write them in the form of decimals as follows:

=

= 0.764

(d) Here

We can write them in the form of decimals as follows:

23

=

= 23.206

(e) Here,

We can write them in the form of decimals as follows:

700

=

= 725.09

(a) Zero point zero three

(b) One point two zero

(c) One hundred eight point-five six

(d) Ten point zero seven

(e) Zero point zero three two

(f) Five point zero zero eight

(a) Here for 0.06

We can observe that,

The given decimal number lies between the following consecutive numbers up to ten place:

0.06 = 0 and 0.1

(b) Here for 0.45

We can observe that,

The given decimal number lies between the following consecutive numbers:

0.45 = 0.4 and 0.5

(c) Here for 0.19

We can observe that,

The given decimal number lies between the following consecutive numbers:

0.19 = 0.1 and 0.2

(d) Here for 0.66,

We can observe that,

The given decimal number lies between the following consecutive numbers:

0.66 = 0.6 and 0.7

(e) Here for 0.92

We can observe that,

The given decimal number lies between the following consecutive numbers:

0.92 = 0.9 and 1.0

(f) Here for 0.57,

We can observe that,

The given decimal number lies between the following consecutive numbers:

0.57 = 0.5 and 0.6

(a) 0.60

Here,

The given fractions can be converted into their lowest fractions as follows:

0.60 =

=

=

(b) 0.05

Here,

The given fractions can be converted into their lowest fractions as follows:

0.05 =

=

(c) 0.75

Here,

The given fractions can be converted into their lowest fractions as follows:

0.75 =

=

(d) 0.18

Here,

The given fractions can be converted into their lowest fractions as follows:

0.18 =

=

(e) 0.25

Here,

The given fractions can be converted into their lowest fractions as follows:

0.25 =

=

(f) 0.125

Here,

The given fractions can be converted into their lowest fractions as follows:

0.125 =

=

(g) 0.066

Here,

The given fractions can be converted into their lowest fractions as follows:

0.066 =

=

(a) In the above question,

The whole parts of both the numbers are same and the tenth part of 0.4 is greater than tenth part of 0.3

Hence,

0.4 > 0.3

(b) In the above question,

Both numbers have same parts upto the tenth place. Also, hundredth part of 0.07 is greater than that of hundredth part that of 0.02

Hence,

0.07 > 0.02

(c) In the above question,

It is clearly seen that whole part of 3 is greater than that of 0.8

Therefore,

3 > 0.8

(d) In the above question,

It is clearly seen that whole parts of these numbers are same. Also, tenth part of 0.5 is greater than that of 0.05

Therefore,

0.5 > 0.05

(e) In the above question,

Both the numbers have same parts upto tenth place but the hundredth part of 1.23 is greater than that of 1.20

Therefore,

1.23 > 1.20

(f) In the above question,

Both the numbers have same whole parts but the tenth part of 0.19 is greater than 0.099

Therefore,

0.099 < 0.19

(g) In the above question,

Both the numbers have same parts upto tenth place but there is no digit in the hundredth part of 1.5 which implies that the hundredth digit will be zero

Therefore,

1.5 = 1.50

(h) In the above question,

Both the numbers have same parts upto tenth place but the hundredth part of 1.490 is greater than that of 1.431

Therefore,

1.431 < 1.490

(i) In the above question,

Both the numbershave same parts upto tenth place but there is no digit in the hundredth and thousandth place of 3.3 which implies that these digits are 0 which are as same as that of 3.300

Therefore,

3.3 = 3.300

(j) In the above question,

Both the numbers have same parts up to the tenth place but the hundredth part of 5.64 is greater than that of 5.603

Therefore,

5.64 > 5.603

(i) 0.5 or 0.8

In the above question,

The whole parts of both the numbers are same and the tenth part of 0.8 is greater than tenth part of 0.5

Hence,

0.5 < 0.8

(ii) 2.0 or 0.9

In the above question,

It is clearly seen that whole part of 2.0 is greater than that of 0.9

Therefore,

2.0 > 0.9

(iii) 0.042 or 0.22

In the above question,

Both the numbers have same whole parts but the tenth part of 0.22 is greater than 0.042

Therefore,

0.042 < 0.22

(iv) 3.012 or 2.99

In the above question,

It is clearly seen that whole part of 3.012 is greater than that of 2.99

Therefore,

3.012 > 2.99

(v) 0.055 or 0.15

In the above question,

Both the numbers have same whole parts but the tenth part of 0.15 is greater than 0.055

Therefore,

0.055 < 0.15

(a) We know that,

100 Paise = 1 Rupee

Therefore,

5 Paise = Rupee

= 0.05 Rupee

(b) We know that,

100 Paise = 1 Rupee

Therefore,

75 Paise = Rupee

= 0.75 Rupee

(c) We know that,

100 Paise = 1 Rupee

Therefore,

20 Paise = Rupee

= 0.20 Rupee

(d) We know that,

100 Paise = 1 Rupee

Therefore,

50 Rupees 90 Paise = (50 + ) Rupees

= 50 + 0.90 Rupees

= 50.90 Rupees

(e) We know that,

100 Paise = 1 Rupee

Therefore,

725 Paise = Rupees

= 7.25 Rupees

(a) We know that,

100 cm = 1 m

Therefore,

15 cm = m

= 0.15 m

(b) We know that,

100 cm = 1 m

Therefore,

6 cm = m

= 0.06 m

(c) We know that,

100 cm = 1 m

Therefore,

2 m 45 cm = (2 + ) m

= 2 + 0.45 m

= 2.45 m

(d) We know that,

100 cm = 1 m

Therefore,

9 m 7 cm = (9 + ) m

= 9 + 0.07 m

= 9.07 m

(e) We know that,

100 cm = 1 m

Therefore,

419 cm = m

= 4.19 m

(a) We know that,

10 mm = 1 cm

Therefore,

5 mm = cm

= 0.5 cm

(b) We know that,

10 mm = 1 cm

Therefore,

60 mm = cm

= 6 cm

(c) We know that,

10 mm = 1 cm

Therefore,

164 mm = cm

= 16.4 cm

(d) We know that,

10 mm = 1 cm

Therefore,

9 cm 8 mm = (9 + ) cm

= 9 + 0.8 cm

= 9.8 cm

(e) We know that,

10 mm = 1 cm

Therefore,

93 mm = cm

= 9.3 cm

(a) We know that,

1000 m = 1 km

Therefore,

8 m = km

= 0.008 km

(b) We know that,

1000 m = 1 km

Therefore,

88 m = km

= 0.088 km

(c) We know that,

1000 m = 1 km

Therefore,

8888 m = km

= 8.888 km

(d) We know that,

1000 m = 1 km

Therefore,

70 km 5 m = (70 + ) km

= 70 + 0.005 km

= 70.005 km

(a) We know that,

1000 g = 1 kg
1 g =

Therefore,

2 g = kg

= 0.002 kg

(b) We know that,

1000 g = 1 kg

Therefore,

100 g = kg

= 0.1 kg

(c) We know that,

1000 g = 1 kg

Therefore,

3750 g = kg

= 3.750 kg

(d) We know that,

1000 g = 1 kg

Therefore,

5 kg 8 g = (5 + ) kg

= 5 + 0.008 kg

= 5.008 kg

(e) We know that,

1000 g = 1 kg

Therefore,

26 kg 50 g = (26 + ) kg

= 26 + 0.050 kg

= 26.050 kg

(a) We have to find out the sum for the following:

0.07 + 8.5 + 30.08

Therefore, sum is 38.587

(b) We have to find out the sum for the following:

15 + 0.632 + 13.8

Therefore, sum is 29.432

(c) We have to find out the sum for the following:

27.076 + 0.55 + 0.004

Therefore, sum is 27.630

(d) We have to find out the sum for the following:

25.65 + 9.005 + 3.7

Therefore, sum is 38.355

(e) We have to find out the sum for the following:

0.75 + 10.425 + 2

Therefore, sum is 13.175

(f) We have to find out the sum for the following:

280.69 + 25.2 + 38

Therefore, sum is 343.89

Given that,

Cost of Maths book = Rs. 35.75

Also,

Cost of Science book = Rs. 32.60

Therefore,

Total amount = 35.75 + 32.60

Hence, total amount spent by Rashid is Rs. 68.35

Money gave by Mother = Rs. 10.50

Also,

Money Gave by Father = Rs. 15.80

Therefore,

Total money = 10.50 + 15.80

Hence, total money given by her parents = Rs. 26.30

Given that,

Cloth for shirt = 3 m 20 cm = 3.20 m

Also,

Cloth for trouser = 2 m 5 cm = 2.05 m

Therefore,

Total length of cloth = 3.20 + 2.05

Hence, total length of cloth = 5.25 m

It is given in the question that,

Distance walked in the morning = 2 km 35 m

= (2 + ) km

= 2 + 0.035 km

= 2.035 km

Also,

Distance walked in the evening = 1 km 7 m

= (1 + ) km

= 1 + 0.007 km

= 1.007 km

Therefore,

Total Distance = 2.035 + 1.007

Hence, total distance walked by him = 3.042 km

It is given in the question that,

Distance travelled by bus = 15 km 268 m

= (15 + ) km

= 15 + 0.268 km

= 15.268 km

Distance walked in the evening = 7 km 7 m

= (7 + ) km

= 7 + 0.007 km

= 7.007 km

Also,

Distance travelled by foot = 500 m

= km

= 0.500 km

Therefore,

Total Distance = 15.268 + 7.007 + 0.500

Hence, total distance of school from her residence = 22.775 km

Given in the question that,

Weight of rice = 5 kg 400 g

= (5 + ) kg

= 5 + 0.400 kg

= 5.400 kg

Weight of Sugar = 2 kg 20 g

= (2 + ) kg

= 2 + 0.020 kg

= 2.020 kg

Also,

Weight of flour = 10 kg 850 g

= (10 + ) kg

= 10 + 0.850

= 10.850 kg

Therefore,

Total weight = 5.400 + 2.020 + 10.850

Hence, total weight of purchases = 18.270 kg

(a) We have to find out the difference for the following:

20.75 - 18.25

Therefore, difference is 2.50

(b) We have to find out the difference for the following:

250 - 202.54

Therefore, difference is 47.46

(c) We have to find out the difference for the following:

8.40 - 5.36

Therefore, difference is 3.04

(d) We have to find out the difference for the following:

5.206 - 2.051

Therefore, difference is 3.155

(e) We have to find out the difference for the following:

2.107 – 0.314

Therefore, difference is 1.793 kg

(a) Difference is as follows:

9.756 – 6.28

Therefore, difference is 3.476

(b) Difference is as follows:

21.05 – 15.27

Therefore, difference is 5.78

(c) Difference is as follows:

18.5 – 6.79

Therefore, difference is 11.71

(ds) Difference is as follows:

11.6 – 9.847

Therefore, difference is 1.753

It is given in the question that,

Cost of book = Rs. 35.65

Money given to seller = Rs. 50

Therefore,

Money that Raju will get back = Rs. 50 – Rs. 35.65

Therefore, he will get back Rs. 14.35

It is given in the question that.

Money spent by Rani on ice-cream = Rs. 11.75

Total money that Rani has = Rs. 18.50

Money left with Rani after buying an ice-cream = Rs. 18.50 – Rs. 11.75

Therefore, Rs. 6.75 left with Rani

Total length of cloth = 20 m 5 cm = 20.05 m

Length if cloth cut to make curtain = 4 m 50 cm = 4.50 m

Therefore,

Length of cloth left with her = 20.05 – 4.50

Hence, 15.55 m length of cloth left with her

It is given in the question that,

Total distance travelled by Namita = 20 km 50 m = 20.050 km

Distance travelled by bus = 10 km 200 m = 10.200 km

Therefore,

Distance travelled by auto = Total distance – Distance travelled by bus

= 20.050 – 10.200

Hence, distance travelled by auto = 9.850 km

It is given in the question that,

Total weight of vegetables = 10 kg

Weight of onions = 3 kg 500 g

As 1 g = 1/1000 kg

500 g = 500/1000 kg

= 0.500 kg


3 kg 500 g = 3 + 0.500

= 3.500 kg

Weight of tomatoes = 2 kg 75 g

Therefore,

Weight of potatoes = Total weight – (Weight of onions + weight of tomatoes)

= 10.000 – (3.500 + 2.075)

= 10.000 – 5.575

Hence, weight of potatoes = 4.425 kg