RS Aggarwal Class 6 Solutions Chapter-7 Decimals

Decimal 

Numbers can be classified into various types, namely real numbers, natural numbers, whole numbers, rational numbers, and so on. Decimal numbers are also one of them. Here in the  RS Aggarwal Class 6 Chapter 7 Solutions PDF, we will learn about Decimal numbers, their type, and properties.

Definition of Decimal

Decimal is a type of number which has a whole number and the fractional part in it, separated by a decimal point. The dot present between the whole number and fractional part is known as the decimal point. For example, 45.6 is a decimal number. 

Here 45 is a whole number part and 6 is the fractional part. “.” is a decimal point. The decimal point of  45.6 has 4 Tens, 5 Ones, and 6 Tenths. 

All the Exercise questions with solutions in Chapter-7 Decimals are given below:

• Exercise (Ex 7A) 7.1

• Exercise (Ex 7B) 7.2

• Exercise (Ex 7C) 7.3

• Exercise (Ex 7D) 7.4

• Exercise (Ex 7E) 7.5

Types of Decimal Number

• Recurring Decimal Numbers are those which have one or more repeating numbers or sequences of numbers after the decimal point, which continue infinitely. ( also known as Repeating or Non-Terminating Decimals)

Example

3.125125 (Finite)

3.121212121212….. (Infinite)

• Non-Recurring Decimal Numbers is a decimal number that continues endlessly, with no group of digits repeating endlessly (also known as Non Repeating or Terminating Decimals)

Example

3.2376 (Finite)

3.137654….(Infinite)

Properties of Decimals

Following are properties of decimal numbers under multiplication and division operations.

• If we multiply any two decimal numbers in any order, the product remains the same.

• If a whole number and a decimal number are multiplied in any order then the product remains the same.

• If a decimal fraction is multiplied by 1, the product is also the decimal fraction itself.

• If a decimal fraction is multiplied by 0, the product is also zero (0).

• If a decimal number is divided by 1 then the quotient is the decimal number.

• If a decimal number is divided by the same number, the quotient is 1. 

• If 0 is divided by any decimal then the quotient will become 0. 

• Division of a decimal number by 0 is not possible because the reciprocal of 0 does not exist.

Decimal to Fraction Conversion

The conversion of decimal to fraction or fraction to decimal values can be performed easily. 

Now, we will discuss both the conversion methods below:

• Decimal to Fraction Conversion

As we know the numbers after the decimal point represent the tenths, hundredths, thousandths, and so on. Thus, while converting from decimal to fraction first write down the decimal numbers in the expanded form and simplify the values

For example, 0.25 

The expanded form of 0.25 is 25 x (1/100) = 25/100 = 1/4.

• Fraction to Decimal Conversion

To convert the fraction to the decimal, we divide the numerator by denominator.

For example, 5/2 is a fraction. If it’s divided, we get 2.5.

Place Value in Decimals

The place value system is used to define the position of a digit in a number, also used to determine its value. When we write specific numbers then the position of each digit is important.

In the number 327:

the "7" is in the one’s position, meaning 7 ones (which is 7),

the "2" is in the tens position meaning 2 tens (which is 20),

and the "3" is in the hundreds position, meaning 3 hundred.

As we move left, each position becomes 10 times bigger. For example- Tens are 10 times bigger than Ones. Hundreds are 10 times bigger than Tens.

In a similar way, as we move right, each position is 10 times smaller. It starts from Hundreds to Tens, to Ones.

Let’s Have a Look at Place Value Chart:-

The power of 10 can be found with the help of  following Place Value Chart

Solve the sums given in the exercises of this chapter and revise the most effective problem-solving methods from these RS Aggarwal Solutions Class 6 Chapter 7, to prepare this chapter thoroughly for the exams. Also, compare your answers with the given step-wise solutions in this PDF, so that you can identify and analyze if there are any silly mistakes in your solutions. This will enhance your accuracy level for the exams, thereby, helping you to secure good marks in the exams.

RS Aggarwal Class 6 Maths Chapter 7 Decimals is available free to download. These solutions are given with a detailed explanation so that students can easily understand them and solve various types of sums easily during the exams. You can also get all chapter-wise RS Aggarwal Solutions on Vedantu which will help you to revise the complete syllabus. On Vedantu you can get Class 6 Maths Revision Notes, Formulas, and Previous Year questions along with solutions that are prepared by subject experts.