CBSE Class 6 Mathematics Chapter 8: Decimals NCERT Solutions

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NCERT Solutions PDF Class 6 PDF

This chapter provides comprehensive NCERT Solutions for Class 6 Mathematics, focusing on Decimals (Chapter 8). Students will learn to understand and represent decimal numbers using place value tables, including ones, tens, and tenths. The solutions cover writing decimals as numbers and vice versa, converting word forms into decimals, and understanding the relationship between fractions and decimals. These solutions are designed to clarify concepts and provide step-by-step guidance for solving problems related to decimal representation and basic operations. They are an excellent resource for students to reinforce their learning, practice exercises, and prepare effectively for their examinations by mastering the fundamentals of decimals.

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Quick info

BoardCBSE
ClassClass 6
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 8

Chapter summary

Chapter 8 of the Class 6 NCERT Mathematics textbook introduces the concept of Decimals. This solution set covers Exercise 8.1, focusing on understanding decimal notation through place value tables. It includes writing decimals as numbers, representing given decimals in a place value table, and converting word descriptions into decimal form. The exercises aim to build a strong foundation in recognizing and writing decimal numbers.

Learning outcomes

  • Understand the concept of decimals and their representation.
  • Use a place value table to represent decimal numbers.
  • Write decimal numbers from given place values.
  • Convert decimals into numbers and vice versa.
  • Express word descriptions of numbers as decimals.

Topics covered

Paper topics

  • Decimals
  • Place Value
  • Tenths
  • Ones
  • Tens
  • Hundreds
  • Writing Decimals
  • Decimal Representation
  • Fractions to Decimals
  • Word Problems on Decimals

Important topics

  • Understanding Decimal Place Value
  • Representing Decimals in Place Value Tables
  • Converting Word Forms to Decimals
  • Writing Decimals from Given Place Values

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Questions and Solutions

Exercise 8.1

Question 1

Write the following as numbers in the given table:

The table shows the place values (Hundreds, Tens, Ones, Tenths) and the digits placed in them for two numbers, labeled 'a' and 'b'. You need to write these numbers in their standard decimal form based on the table's structure.

Solution:

The table helps us understand how to construct decimal numbers from their place values. The digits are placed according to their position relative to the decimal point (which is after the Ones place).

For number 'a':

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

Constructing the number by placing the decimal point after the Ones place, we get: 110.4

For number 'b':

  • Hundreds: 0
  • Tens: 3
  • Ones: 1
  • Tenths: 2

Constructing the number by placing the decimal point after the Ones place, we get: 31.2

Answer:

a) 110.4

b) 31.2

Question 2

Write the following decimals in the place value table:

The decimals to be placed in the table are: (a) 19.4, (b) 0.3, (c) 10.6, (d) 205.9. You need to identify the digit for each place value (Hundreds, Tens, Ones, Tenths) for each given decimal.

Solution:

We will place each digit of the given decimals into the correct column of the place value table.

(a) 19.4

  • Hundreds: 0 (since there is no digit in the hundreds place)
  • Tens: 1
  • Ones: 9
  • Tenths: 4

(b) 0.3

  • Hundreds: 0
  • Tens: 0
  • Ones: 0
  • Tenths: 3

(c) 10.6

  • Hundreds: 0
  • Tens: 1
  • Ones: 0
  • Tenths: 6

(d) 205.9

  • Hundreds: 2
  • Tens: 0
  • Ones: 5
  • Tenths: 9

Question 3

Write each of the following as decimals:

Convert the given word descriptions into their equivalent decimal numbers. The descriptions involve place values like tenths, tens, ones, hundreds, and the term 'point'.

(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 word description into its decimal form by understanding the place value of each part.

(a) seven-tenths

This means 7 divided by 10. In decimal form, it is written as 0.7.

7 \text{ tenths} = \frac{7}{10} = 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} = 0.9. Adding these together gives 20 + 0.9 = 20.9.

2 \text{ tens} + 9 \text{ tenths} = (2 \times 10) + \frac{9}{10} = 20 + 0.9 = 20.9

(c) Fourteen point six

The phrase 'point six' directly translates to the decimal part .6. So, fourteen point six is 14.6.

\text{Fourteen point six} = 14.6

(d) One hundred and two-ones

One hundred is 100. Two-ones is equal to 2 \times 1 = 2. Adding these gives 100 + 2 = 102. Since there are no tenths mentioned, the decimal part is zero.

\text{One hundred} + 2 \text{ ones} = 100 + (2 \times 1) = 100 + 2 = 102

(e) Six hundred point eight

This means 600 followed by the decimal point and then 8 in the tenths place. So, it is 600.8.

\text{Six hundred point eight} = 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 with ones or tens.
  • Incorrectly placing digits in the place value table.
  • Errors in converting word forms to decimal numbers.
  • Misinterpreting the meaning of 'point' in decimal numbers.

Revision tips

  • Practice drawing and filling place value tables for various decimals.
  • Read decimal numbers aloud to reinforce their structure.
  • Convert between fractions with denominators 10 and their decimal equivalents.
  • Work through each example and exercise problem step-by-step.

Practice MCQs

Q1. Which place value is to the right of the ones place in a decimal number?

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

Q3. What is the decimal representation of 'Two tens and nine-tenths'?

Q4. In the number 19.4, what is the digit in the tenths place?

Q5. How do you write 'One hundred and two-ones' as a decimal?

Frequently asked questions

What is Chapter 8 of Class 6 Maths about?

Chapter 8 of Class 6 Mathematics NCERT focuses on introducing and understanding Decimals, including their representation using place value and conversion from word forms.

How do these NCERT Solutions help students?

These solutions provide clear, step-by-step explanations for each question in Exercise 8.1, helping students grasp the concepts of decimals and practice problem-solving.

What is the place value of digits in a decimal number?

Digits to the left of the decimal point represent ones, tens, hundreds, etc., while digits to the right represent tenths, hundredths, thousandths, and so on.

How can I convert 'seven-tenths' into a decimal?

Seven-tenths means 7 divided by 10, which is written as the decimal 0.7.

What does 'Two tens and nine-tenths' mean in decimal form?

It means (2 * 10) + (9 / 10), which equals 20 + 0.9, resulting in the decimal 20.9.

Important links

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