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RS Aggarwal Solutions

RS Aggarwal Class 6 Solutions Chapter-7 Decimals

RS Aggarwal Class 6 Solutions Chapter-7 Decimals

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Class 6 RS Aggarwal Chapter-7 Decimals Solutions - Free PDF Download

RS Aggarwal Solutions for Class-6 Maths Chapter-7 Decimals are now available on Vedantu. These solutions are available in PDF format and can be downloaded for free from Vedantu. These RS Aggarwal Solutions Class 6 Maths Chapter-7 are prepared by our subject experts in a simplified way for a better understanding of students. These solutions are prepared in a stepwise manner, as per the latest CBSE guidelines. Students can revise the concepts covered in this chapter by going through the Class 6 RS Aggarwal Chapter 7 Solutions on Vedantu, and prepare well for their examinations.

Every NCERT Solution is provided to make the study simple and interesting on Vedantu. You can also register Online for NCERT Solutions Class 6 Science and NCERT Maths Class 6 tuition on Vedantu.com to score more marks in your examination.

Class 6 Chapter-7 RS Aggarwal Solutions - 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:

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.

FAQs on RS Aggarwal Class 6 Solutions Chapter-7 Decimals

1. How do you determine the place value of each digit in a decimal number like 24.578, as per the methods in RS Aggarwal solutions?

To find the place value of a digit in a decimal, you can use a place value chart. For 24.578:

The digit '2' is in the Tens place, so its value is 20.
The digit '4' is in the Ones place, so its value is 4.
The digit '5' is in the Tenths place (the first digit after the decimal point), so its value is 5/10 or 0.5.
The digit '7' is in the Hundredths place (the second digit after the decimal point), so its value is 7/100 or 0.07.
The digit '8' is in the Thousandths place, so its value is 8/1000 or 0.008.

This step-by-step method is crucial for solving comparison and conversion problems in Chapter 7.

2. What is the correct step-by-step method to convert a fraction like 3/4 into a decimal?

To convert a fraction to a decimal, the goal is to make the denominator a power of 10 (like 10, 100, 1000). For the fraction 3/4:

Step 1: Find a number that you can multiply the denominator (4) by to get 100. In this case, 4 x 25 = 100.
Step 2: Multiply both the numerator and the denominator by that same number (25). This gives you (3 x 25) / (4 x 25) = 75/100.
Step 3: Convert the resulting fraction into a decimal. 75/100 is written as 0.75.

This method ensures the value of the fraction remains the same while preparing it for decimal conversion.

3. How do you correctly add or subtract decimals that have a different number of decimal places, for example, 12.5 + 3.45?

The correct procedure involves aligning the numbers properly:

Step 1: Write the numbers one below the other, ensuring the decimal points are aligned vertically.
Step 2: To handle the different lengths, add placeholder zeros to the end of the number with fewer decimal places. So, 12.5 becomes 12.50.
Step 3: Now perform the addition as you would with whole numbers: 12.50 + 3.45.
Step 4: Place the decimal point in the answer directly below the other decimal points. The result is 15.95.

4. Why is it so important to align the decimal points before adding or subtracting decimals?

Aligning the decimal points is a critical step because it ensures you are combining the correct place values. When you add or subtract, you must add tenths to tenths, hundredths to hundredths, and so on. If you don't align the points, you might accidentally add tenths from one number to hundredths from another, which would give a completely incorrect answer. For instance, in 5.2 + 3.14, aligning the points ensures you add the '2' (tenths) to the '1' (tenths), not to the '4' (hundredths).

5. When comparing 0.8 and 0.08, why is 0.8 the larger number?

This is a common point of confusion. The value of a digit depends on its position relative to the decimal point.

In 0.8, the digit '8' is in the tenths place, which means its value is 8/10.
In 0.08, the digit '8' is in the hundredths place, which means its value is 8/100.

Since one-tenth is ten times larger than one-hundredth, 8/10 is much greater than 8/100. Therefore, 0.8 is the larger number. An easy way to compare is to make them like decimals: 0.80 vs 0.08. Clearly, 80 is greater than 8.

6. How are the concepts from RS Aggarwal Class 6 Chapter 7 on Decimals used in real-life situations?

The decimal concepts from this chapter are used daily. For example:

Handling Money: When you see a price tag like ₹45.50, it means 45 rupees and 50 paise. The decimal separates the whole rupees from the fractions of a rupee.
Measurements: When measuring length or weight, you might get results like 2.5 kg (2 kilograms and 500 grams) or 1.75 metres (1 metre and 75 centimetres).

Solving problems in this chapter helps you learn to accurately calculate costs, distances, and weights in the real world.

7. What are the key steps to solve word problems involving decimals, such as those in RS Aggarwal Exercise 7D?

A systematic approach is best for solving decimal-based word problems. Follow these steps:

Step 1: Read the problem carefully to identify the given quantities and what you need to find.
Step 2: Determine the mathematical operation required (e.g., addition for total cost, subtraction for remaining distance).
Step 3: Write down the decimal numbers, ensuring you align the decimal points correctly.
Step 4: Perform the calculation.
Step 5: Write the final answer with the correct units (e.g., ₹, kg, m, km).