The way we define places in a whole number digit, like ones, tens, hundreds and so on is similar to how we define places for decimal numbers, as tenths, hundredths, thousandths, ten-thousandths and so on.

• • Tenths place

The first place after the decimal point  is called the tenths place. It is 1 unit divided into 10 parts i.e. 1/10= 0.1

• • Hundredths place

The second place after the decimal point  is called the hundredths place. It is 1 unit divided into 100 parts i.e. 1/100= 0.01

• • Thousandths place 

The third place after the decimal point  is called the thousandths  place. It is 1 unit divided into 1000 parts, i.e. 1/1000= 0.001

To represent decimal numbers on the number line, divide the gap between two integers into 10 equal parts for tenths. If you want to show the hundredths place on a number line, then divide the gap between two tenths into 10 equal parts and so on for the thousandths and ten-thousands places. 

For example: here 2.1 is represented on the number line.

To locate 2.1, first divide the gap between 2 and 3 into 10 equal parts. Then starting from 2, take 1 part to the right.

As discussed above, we now know how to convert fractions with 10, 100, 1000…as denominators. For eg: 1/100=0.01.

To convert fractions with denominators other than powers of ten, we first make equivalent fractions. 

Equivalent fractions: divide both the numerator and the denominator by the same number such that the denominator becomes a power of ten. 

For eg: 1/2 = 1x5/ 2x 5= 5 /10 = 0.5

Q1: 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

Solutions:

(a)Seven-tenths will be written as  7 / 10 = 0.7 in decimal form.

(b) Two tens and nine tenths is 20 + 9 / 10 = 20.9

(c) Fourteen point six is 14.6

(d) One hundred and two ones is 100 + 2 = 102.0

(e) Six hundred point eight is 600.8

Q2: Write each of the following as decimals:

(a) 5 / 10

(b) 3 + 7 / 10

(c) 200 + 60 + 5 + 1 / 10

(d) 70 + 8 / 10

Solutions:

(a) 5 / 10 = 0.5

(b) 3 + 7 / 10 = 3 + 0.7

= 3.7

(c) 200 + 60 + 5 + 1 / 10 = 265 + 0.1

= 265.1

(d) 70 + 8 / 10 = 70 + 0.8

= 70.8

The conversion of decimals to fractions is exactly opposite to converting fractions into decimals. 

Let us write 2.1 into fractions.

Step1: Separately write the whole number and the decimal part as 2+1/10.

Step2: Now divide both the terms by the same power of ten in order to add the numerator. 

2/10+1/10=21/10.

So 2.1=21/10

 

Q1: Write the following decimals as fractions. Reduce the fraction to the lowest form.

(a) 0.6

(b) 2.5

(c) 1.0

(d) 3.8

(e) 13.7

(f) 21.2

(g) 6.4

Solutions:

(a) 0.6 = 6 / 10

= 3 / 5

(b) 2.5 = 25 / 10

= 5 / 2

(c) 1.0 = 1

= 1

(d) 3.8 = 38 / 10

= 19 / 5

(e) 13. 7 = 137 / 10

(f) 21.2 = 212 / 10

= 106 / 5

(g) 6.4 = 64 / 10

= 32 / 5

Length

a. 1 metre = 100 centimetre

              1 centimetre=1/100 =0.01metre

               For example: 25cm=25/100=0.25metre

b. 1cm=10mm

              1mm=1/10= 0.1cm

              For ex: 20mm=20/10=2cm

Money

1 rupee=100 paisa

1paisa=1/100= Re 0.01

For eg: 65 paise = 65 /100 = Re 0.65

 

When comparing decimals, first the whole part is compared followed by the decimal places: tenths, hundredths, thousandths and so on, respectively. 

Only when the whole part is equal, decimal parts are compared. 

For ex: Compare 25.3 and 25.5
Here, the whole part, i.e 25, is equal. Therefore, we will compare the tenths part.
25.3=25 + 3/10
25.5 = 25 + 5/10
3/10<5/10
∴ 22.3 < 22.5.

Q1: Which one is greater?

(a) 0.3 or 0.4

(b) 0.07 or 0.02

(c) 3 or 0.8

(a) 0.3 or 0.4

Solutions:

Whole parts are equal, so comparison will be made between decimal points.since, tenth part of 0.4 is greater than that of 0.3

∴ 0.4 > 0.3

(b) 0.07 or 0.02

Whole part and tenths place are equal, therefore, hundredths place will be compared.since, hundredth part of 0.07 is greater than that of 0.02

∴ 0.07 > 0.02

(c) 3 or 0.8

The whole part of 3 is greater than the whole part of 0.8

∴ 3 > 0.8

The process of subtracting two decimal numbers is exactly the same as the standard subtraction rule. 

Subtraction of 6.25 from 9.28

 

Thus,  9.28-6.25 = 3.03

 

1. How will these chapter-wise solutions help me score more in NCERT Solutions for Class 6 Decimals?

It helps you understand the topics in a much better and clearer way. The solutions are well-structured to teach students how to write answers in the exam.

 

2. Can I access this chapter for free?

Yes, you can get this chapter for free on the NCERT website or on the MSVGo app.

 

3. Which is the best book for studying NCERT Solutions Class 6 decimals?

The Class 6 NCERT textbook has all the solutions to the NCERT questions. The NCERT class 6 maths textbook provides solutions in a detailed and straightforward manner to help students build a strong subject base. The solutions are well-structured to teach students how to write answers in the exam. You can also access them through the MSVGo app.

 

4. How can I practice essential questions for all chapters in NCERT Solutions class 6 maths?

You can get practice questions for each chapter on the MSVGo app. The MSGVo app has many practice questions related to every topic of all chapters. They also provide precise and easily understandable notes for each chapter on their app.