Decimals Class 6 Notes CBSE Maths Chapter 8 (Free PDF Download)

Decimal is mathematical notation to represent the fractions whose denominator is $10$ or the power of $10$.

For Example: 

$\dfrac{54}{10}$ can be written in decimal as $5.4$ 

$\dfrac{54}{100}$ can be written in decimal as $0.54$ 

Tenths: 

One out of $10$ equal parts are called tenths.

Decimal notation of tenths $\left( \dfrac{1}{10} \right)$  is $0.1$ 

For Example: A pencil is $8cm\text{ 3mm }$ long and can be represented in decimal using the concept of tenths. 

Since, $1mm=\dfrac{1}{10}cm=0.1cm$  

Therefore, $3mm=\dfrac{3}{10}cm=0.3cm$ 

Decimal notation of $8cm\text{ 3mm }=8.3cm$

Hundredths: 

One out of $100$ equal parts are called hundredths.

Decimal notation of tenths $\left( \dfrac{1}{100} \right)$  is $0.01$  

For Example: A pencil is $8m\text{ 3cm }$ long and can be represented in decimal using the concept of hundredths. 

Since, $1cm=\dfrac{1}{100}m=0.01m$  

Therefore, $3cm=\dfrac{3}{100}m=0.03m$ 

Decimal notation of $8m\text{ 3cm }=8.03m$

Representing Decimals on Number Line:

Let us suppose we have to represent $0.5$ on the number line.

$0.5$ is greater than $0$ and less than $1$ then it can be represented on number line by dividing unit length between $0$ and $1$ into ten equal parts and the fifth part will represent $0.5$ 

Fractions as Decimals:

Fraction can be represented in decimal by making the denominator of fraction $10$ 

For Example: The decimal notation of fraction $\dfrac{3}{2}$ is given by making denominator $10$ it can be done by multiplying denominator and numerator by $10$ 

Therefore, $\dfrac{3\times 5}{2\times 5}=\dfrac{15}{10}=1.5$ 

So, the decimal notation of fraction $\dfrac{3}{2}$ is $1.5$ 

Decimals as Fractions:

Decimal can be represented in fraction by representing the digits to the right of decimal as tenths or power of tenths according to the number of digits present and solving the improper fraction obtained.

For Example: The fraction form of decimal $8.9$ is given by 

$8.9$ can be written as $8\dfrac{9}{10}$ which is equal to $\dfrac{89}{10}$ 

$8.99$ can be written as $8\dfrac{99}{100}$ which is equal to \[\dfrac{899}{100}\] 

Place Value of Decimals:

The first digit to the right of the decimal is tenths place.

The second digit to the right of the decimal is hundredths place.

The third digit to the right of the decimal is thousandths place.

For Example: In $6.342$ the place value of $3$ is tenths place, $4$ is hundredths place and $2$ is thousandths place.

Comparing Decimals:

Compare the tenth part of the two decimals if the whole part is same 

For Example: Compare $32.5$ and $32.6$ 

Since, the whole part is same i.e., $32$ now on comparing tenth part we found that $32.6>32.5$ 

Similarly, compare the hundredth part of the two decimals if the whole part and tenth part are the same.

Using Decimals:

Money can be represented in decimal as 

$100paise=1Rs$

$\therefore 1paise=\dfrac{1}{100}Rs=0.01Rs$ 

Length can be represented in decimal as

$10mm=1cm$ 

$\therefore 1mm=\dfrac{1}{10}cm=0.1cm$ 

$100cm=1m$ 

$\therefore 1cm=\dfrac{1}{100}m=0.01m$ 

$1000m=1km$ 

$\therefore 1m=\dfrac{1}{1000}km=0.001km$

Weight can be represented in decimal as

$1000g=1kg$

$\therefore 1g=\dfrac{1}{1000}kg=0.001kg$ 

Addition of Number with Decimals:

Adding a number with decimals is the same as adding the whole number.

Decimals are aligned under one another.

Arrange the numbers according to their place value.

For Example: Add $63.52$ and $1.25$ 

\[\begin{align}  & 63.52 \\+& \text{ }1.25 \\  & \overline{64.77} \\ \end{align}\]

Subtraction of Number with Decimals:

Subtracting a number with decimals is the same as subtracting a whole number.

Decimals are aligned under one another.

Arrange the numbers according to their place value.

For Example: Subtract $1.25$ from $63.52$

\[\begin{align}  & 63.52 \\  -& 1.25 \\  & \overline{62.27} \\ \end{align}\]

Class 6 Maths Chapter 8 Revision Notes Free PDF

Vedantu provides Class 6 Maths Revision Notes Chapter 8 as well as keynotes chapter wise for the CBSE class exam in an easy-to-understand, free downloadable PDF format. This enables you to use it for studies and score better in the board exams.

CBSE Class 6 Maths Revision Notes Chapter 8- Decimals Introduction

Use of a dot while expressing a number/numbers in mathematical form is what we call a decimal point. A dot-like decimal point is used to represent the part of a whole number. For example, 0.9

Tenths and Hundredths in a Decimal

As we know that 1 meter = 100 centimetres, thus if we want to identify the opposite then

1centimeter = 1/100 meter or one-hundredth meter or 0.10 cm.

Therefore, it is to say that the 1st number after the decimal shows the 10th part of the whole.

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This read as seventeen point five nine one. 

Class 6 Maths Chapter 8 Revision Notes for Representation of Decimals on Number Line

Vedantu’s Revision Notes on Class 6 Maths Chapter 8 representing decimals on a number line worksheet includes clear illustrative examples of how to show various numbers on a number line for easy understanding and utmost convenience of the learners.

In order to represent decimals on the number line, divide the gap of each number into 10 equal parts as the decimal reveals the 10th part of the number. Check below for examples.

Example: Represent 0.4, 0.6 and 0.8 on the number line.

Solution: Seeing that all the given three numbers are less than 1 are greater than 0. Thus, we will require forming a number line with 0 and 1 and then dividing the gap into 10 equal parts.

Then mark as illustrated below.

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Conclusion

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