CBSE Class 6 Mathematics Chapter 8: Decimals NCERT Solutions

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NCERT Solutions PDF Class 6 PDF

This chapter introduces students to the concept of decimals in Class 6 Mathematics. The NCERT Solutions for Chapter 8: Decimals provide a clear understanding of decimal numbers, their representation, and their relationship with fractions. The solutions cover writing decimals in place value tables, converting fractions to decimals, and vice versa. Students will learn to identify the place value of digits in decimal numbers, including tenths and hundredths. These solutions are designed to help students grasp the fundamental principles of decimals, build a strong foundation for future mathematical concepts, and prepare effectively for their exams by offering step-by-step explanations and accurate answers.

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Quick info

BoardCBSE
ClassClass 6
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 8: Decimals

Chapter summary

Chapter 8 of the Class 6 NCERT Mathematics textbook focuses on introducing Decimals. The NCERT Solutions for this chapter cover exercises that help students understand the representation of decimals using place value tables, including ones, tens, and tenths. It also includes converting decimal numbers into words and vice versa, and understanding the relationship between fractions and decimals.

Learning outcomes

  • Understand the concept of decimals and their representation.
  • Represent decimal numbers in a place value table.
  • Write decimals in numbers and words.
  • Convert fractions with denominators 10 and 100 into decimals.
  • Convert decimals into fractions.

Topics covered

Paper topics

  • Introduction to Decimals
  • Place Value of Decimals
  • Tenths
  • Hundreds
  • Ones
  • Tens
  • Writing Decimals in Numbers
  • Writing Decimals in Words
  • Converting Fractions to Decimals
  • Converting Decimals to Fractions

Important topics

  • Understanding Place Value in Decimals
  • Representing Decimals in Place Value Tables
  • Converting Fractions (denominator 10) to Decimals
  • Writing Decimals in Words and Vice Versa

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Questions and Solutions

Question 1

Write the following as numbers in the given table:

The table shows digits in different place values (Hundreds, Tens, Ones, Tenths). You need to combine these digits to form the decimal numbers represented by the table structure.

Solution:

To write the numbers, we combine the digits based on their place values as shown in the table. The decimal point separates the whole number part from the fractional part (tenths).

For the first table:

  • Hundreds: 1
  • Tens: 1
  • Ones: 3
  • Tenths: 2

Combining these, we get the number 113.2.

For the second table:

  • Hundreds: 1
  • Tens: 1
  • Ones: 0
  • Tenths: 4

Combining these, we get the number 110.4.

Answer: The numbers are 113.2 and 110.4.

Question 2

Write the following decimals in the place value table:

(a) 19.4 (b) 0.3 (c) 10.6 (d) 205.9

Solution:

We need to place each digit of the given decimal numbers into the correct place value column (Hundreds, Tens, Ones, Tenths).

(a) 19.4

  • The digit 1 is in the Tens place.
  • The digit 9 is in the Ones place.
  • The digit 4 is in the Tenths place.

Place value table representation: Hundreds (0), Tens (1), Ones (9), Tenths (4).

(b) 0.3

  • The digit 0 is in the Ones place.
  • The digit 3 is in the Tenths place.

Place value table representation: Hundreds (0), Tens (0), Ones (0), Tenths (3).

(c) 10.6

  • The digit 1 is in the Tens place.
  • The digit 0 is in the Ones place.
  • The digit 6 is in the Tenths place.

Place value table representation: Hundreds (0), Tens (1), Ones (0), Tenths (6).

(d) 205.9

  • The digit 2 is in the Hundreds place.
  • The digit 0 is in the Tens place.
  • The digit 5 is in the Ones place.
  • The digit 9 is in the Tenths place.

Place value table representation: Hundreds (2), Tens (0), Ones (5), Tenths (9).

Question 3

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

Solution:

We will convert each given description into its decimal number representation.

(a) seven-tenths

This means 7 divided by 10. As a decimal, this is written as 0.7.

(b) Two tens and nine-tenths

Two tens is equal to 2 \times 10 = 20. Nine-tenths is equal to \frac{9}{10} or 0.9. Combining these, we get 20 + 0.9 = 20.9.

(c) Fourteen point six

This phrase directly translates to the decimal number 14.6.

(d) One hundred and two-ones

One hundred is 100. Two ones is equal to 2 \times 1 = 2. Combining these, we get 100 + 2 = 102. Since there are no tenths mentioned, the decimal part is zero, so it is 102.0 or simply 102.

(e) Six hundred point eight

This phrase directly translates to the decimal number 600.8.

Answer:

(a) 0.7

(b) 20.9

(c) 14.6

(d) 102

(e) 600.8

Common mistakes

  • Confusing the place value of tenths and hundredths.
  • Incorrectly converting fractions to decimals, especially with denominators other than 10 or 100.
  • Errors in writing decimal numbers in words or words into numbers.
  • Misplacing the decimal point during conversions.

Revision tips

  • Practice writing decimals in the place value table for better visualization.
  • Work through the conversion exercises between fractions and decimals multiple times.
  • Pay close attention to the place value of each digit, especially after the decimal point.
  • Use the examples provided in the solutions to understand the logic behind each step.

Practice MCQs

Q1. Which digit is in the tenths place in the number 19.4?

Q2. What is 'seven-tenths' written as a decimal?

Q3. How is 'Two tens and nine-tenths' represented as a decimal?

Q4. What is the decimal representation of 'Fourteen point six'?

Q5. In the number 110.4, which place value does the digit '1' in the leftmost position represent?

Frequently asked questions

What is the main focus of Chapter 8: Decimals for Class 6 Maths?

Chapter 8 introduces students to the concept of decimal numbers, their representation using place value tables (including tenths and hundredths), and how to write them in both numerical and word forms.

How do these NCERT Solutions help students understand decimals?

The solutions provide step-by-step explanations for each question, clarifying how to place digits in the correct place value columns and how to convert between fractions and decimals accurately.

What is the relationship between fractions and decimals covered in this chapter?

The chapter explains how fractions with denominators like 10 can be easily converted into their decimal equivalents, and vice versa, helping students see the connection between these two number forms.

Are the questions in the source document preserved in these solutions?

Yes, all questions from the original source document are kept exactly the same, including their numbering and problem statement. The solutions have been rewritten for clarity and detail.

How can I use these solutions for exam preparation?

These solutions offer a clear and concise way to revise the concepts of decimals. By understanding the methods used to solve each problem, students can build confidence and accuracy for their exams.

Important links

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