{"id":790853,"date":"2024-06-21T14:02:17","date_gmt":"2024-06-21T08:32:17","guid":{"rendered":"https:\/\/leverageedu.com\/discover\/?p=790853"},"modified":"2024-06-21T14:02:17","modified_gmt":"2024-06-21T08:32:17","slug":"cbse-ncert-maths-class-6-chapter-8-decimals","status":"publish","type":"post","link":"https:\/\/leverageedu.com\/discover\/school-education\/cbse-ncert-maths-class-6-chapter-8-decimals\/","title":{"rendered":"NCERT Class 6 Maths Chapter 8 ‘Decimals’: Notes and Solutions (Free PDF)"},"content":{"rendered":"\n

In this chapter, students will understand everything related to Decimals. The chapter is very important as it lays the foundation for understanding the Decimals for complex calculations. Students will learn concepts like representing decimals on a number line, decimals as fractions, tenths, and hundredths, comparing decimals, using decimals for length, weight, and money, the addition of numbers with decimals and subtraction of decimals with numbers. In Chapter 8 of Class 6 Maths, students will learn the concept of decimals which will be useful for them in all their future higher study lessons. Read through for CBSE NCERT Class 6 Maths Chapter 8 Decimals Notes, Exercise, and Important Questions.\u00a0<\/p>\n\n\n\n

Click here to download the Class 6 NCERT Maths Chapter 8 Decimals Notes and Important Exercise Questions and Answers Free PDF<\/strong><\/a><\/p>\n\n\n\n

Explore all the Chapters of Class 6 Mathematics:-<\/strong><\/p>\n\n\n\n

Chapter 1<\/strong><\/a><\/td>Chapter 2<\/strong><\/a><\/td>Chapter 3<\/strong><\/a><\/td>Chapter 4<\/strong><\/a><\/td><\/tr>
Chapter 5<\/strong><\/a><\/td>Chapter 6<\/strong><\/a><\/td>Chapter 7<\/strong><\/a><\/td>Chapter 8<\/td><\/tr>
Chapter 9<\/strong><\/a><\/td>Chapter 10<\/strong><\/a><\/td>Chapter 11<\/strong><\/td>Chapter 12<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n\n\n\n

Also Read:<\/strong> Multiplication and Division Word Problems<\/strong><\/a><\/p>\n\n\n\n

Click here to download the Class 6 NCERT Maths Chapter 8 Decimals Notes and Important Exercise Questions and Answers Free PDF<\/strong><\/a><\/p>\n\n\n\n

NCERT Class 6 Maths Chapter 8 Decimals Notes – Free PDF Download<\/h2>\n\n\n\n

Below we have given topic-wise notes for the CBSE NCERT Class 6 Maths Chapter 8 Decimals. We have also provided a downloadable free PDF at the end of these notes so you can download and take a printout to study later when you need quick revision before going to the exam hall. <\/p>\n\n\n\n

Topic 1: Representing Decimals on Number Line<\/h3>\n\n\n\n

We have learned how to represent fractions on a number line. Now let us understand how to represent decimals on a number line with the help of the following example. <\/p>\n\n\n\n

For eg, let us represent 0.6 on the number line. We know 0.6 is greater than 0 but lesser than 1. Let us mark 10 points between 0 and 1 at equal distances, so, 0.6 will be placed at:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Topic 2: Fractions as Decimals<\/h3>\n\n\n\n

To convert fractions into decimals, the best way is to convert the denominator into 10 or a multiple of 10 because we know:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Here, 0.1<\/strong> is called the tenth part of the decimal and 0.01<\/strong> is called the hundredth part of the decimal. <\/p>\n\n\n\n

Topic 3: Comparing Decimals<\/h3>\n\n\n\n

To compare the decimal values, we start our comparison in the following steps:<\/p>\n\n\n\n

    \n
  1. Compare the whole part: <\/strong>To compare the decimal values, we start comparing from left to right. So, we first compare the whole part, i.e. the numbers to the left of the decimal point. <\/li>\n\n\n\n
  2. Compare the tenth part of the decimal: <\/strong>As discussed above, after we compare the whole part of a decimal, we compare its tenth part. <\/li>\n\n\n\n
  3. Compare the hundredth part: <\/strong>If the tenth part of the two given numbers are also equal, then we move on to comparing the hundredth part.  <\/li>\n<\/ol>\n\n\n\n

    Also Read:<\/strong> BODMAS Questions<\/strong><\/a><\/p>\n\n\n\n

    CBSE NCERT Class 6 Maths Chapter 8 Decimals Notes Free PDF Download<\/strong><\/a><\/p>\n\n\n\n

    Explore all the Chapters of Class 6 Mathematics:-<\/strong><\/p>\n\n\n\n

    Chapter 1<\/strong><\/a><\/td>Chapter 2<\/strong><\/a><\/td>Chapter 3<\/strong><\/a><\/td>Chapter 4<\/strong><\/a><\/td><\/tr>
    Chapter 5<\/strong><\/a><\/td>Chapter 6<\/strong><\/a><\/td>Chapter 7<\/strong><\/a><\/td>Chapter 8<\/td><\/tr>
    Chapter 9<\/strong><\/a><\/td>Chapter 10<\/strong><\/a><\/td>Chapter 11<\/strong><\/td>Chapter 12<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    Important Questions in NCERT Class 6 Maths Chapter 8: Free PDF Download<\/h2>\n\n\n\n

    Below we have provided some important exercise questions and their solutions from Chapter 8 of CBSE NCERT Maths for Class 6. <\/p>\n\n\n\n

    Exercise 8.1<\/h3>\n\n\n\n

    Q 1.  Write the following decimals in the place value table. <\/strong><\/p>\n\n\n\n

      \n
    1. 19.4 <\/strong><\/li>\n\n\n\n
    2. 0.3 <\/strong><\/li>\n\n\n\n
    3. 10.6 <\/strong><\/li>\n\n\n\n
    4. 205.9<\/strong><\/li>\n<\/ol>\n\n\n\n

      Ans.<\/strong> The Decimals in the place value table are given below.<\/p>\n\n\n\n

      <\/td>Hundreds<\/td>Tens<\/td>Ones<\/td>Tenths<\/td><\/tr>
      19.4<\/td>0<\/td>1<\/td>9<\/td>4<\/td><\/tr>
      0.3<\/td>0<\/td>0<\/td>0<\/td>3<\/td><\/tr>
      10.6<\/td>0<\/td>1<\/td>0<\/td>6<\/td><\/tr>
      205.9<\/td>2<\/td>0<\/td>5<\/td>9<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

      Q 2.  Write each of the following as decimals :<\/strong><\/p>\n\n\n\n

        \n
      1. Seven-tenths <\/strong><\/li>\n\n\n\n
      2. Two tens and nine-tenths<\/strong><\/li>\n\n\n\n
      3. Fourteen point six <\/strong><\/li>\n\n\n\n
      4. One hundred and two ones<\/strong><\/li>\n\n\n\n
      5. Six hundred point eight<\/strong><\/li>\n<\/ol>\n\n\n\n

        Ans.<\/strong> The decimal forms of each of the given numbers are:<\/p>\n\n\n\n

          \n
        1. <\/li>\n\n\n\n
        2. Two tens = 20<\/li>\n<\/ol>\n\n\n\n
          \"\"<\/figure>\n\n\n\n
            \n
          1. 14.6<\/li>\n\n\n\n
          2. One hundred and two ones = 100 + 2 = 102<\/li>\n\n\n\n
          3. 600.8<\/li>\n<\/ol>\n\n\n\n

            Q 3. Express the following as cm using decimals.<\/strong><\/p>\n\n\n\n

              \n
            1. 116 mm <\/strong><\/li>\n\n\n\n
            2. 4 cm 2 mm <\/strong><\/li>\n\n\n\n
            3. 162 mm<\/strong><\/li>\n<\/ol>\n\n\n\n

              Ans. <\/strong>The conversions of the given values are:<\/p>\n\n\n\n

                \n
              1. We know that 1 cm = 10 mm<\/li>\n<\/ol>\n\n\n\n

                So, 1 mm = 1\/10 cm<\/p>\n\n\n\n

                \u2234 116 mm = 116\/10 = 11.6 cm<\/p>\n\n\n\n

                  \n
                1. 4 cm 2 mm = 4 cm + 2\/10 cm = 4.2 cm<\/li>\n\n\n\n
                2. 162 mm \u21d2 162\/10 cm = 16.2 cm<\/li>\n<\/ol>\n\n\n\n

                  Q 4. Write the natural numbers from 2 to 12. What fraction of them are prime numbers?<\/strong><\/p>\n\n\n\n

                  Ans. <\/strong>The natural numbers from 2 to 12 are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Hence, the total numbers are 11. <\/p>\n\n\n\n

                  Prime numbers from natural numbers 2 to 12 are 2, 3, 5, 7, 11 = 5 prime numbers. <\/p>\n\n\n\n

                  So, the fraction of prime numbers is 5\/11<\/p>\n\n\n\n

                  Exercise 8.2<\/h3>\n\n\n\n

                  Q 1.  Write each of the following as decimals. <\/strong><\/p>\n\n\n\n

                    \n
                  1. <\/strong><\/li>\n\n\n\n
                  2. <\/strong><\/li>\n<\/ol>\n\n\n\n

                    Ans.<\/strong> The decimal value of each of the given problems is:<\/p>\n\n\n\n

                      \n
                    1. <\/li>\n\n\n\n
                    2. <\/li>\n<\/ol>\n\n\n\n

                      Q 2.  Write each of the following decimals in words.<\/strong><\/p>\n\n\n\n

                        \n
                      1. 0.03 <\/strong><\/li>\n\n\n\n
                      2. 1.20 <\/strong><\/li>\n\n\n\n
                      3. 108.56 <\/strong><\/li>\n<\/ol>\n\n\n\n

                        Ans.<\/strong> The given decimals will be expressed in words as follows:<\/p>\n\n\n\n

                          \n
                        1. Zero point zero three<\/li>\n\n\n\n
                        2. One point two zero<\/li>\n\n\n\n
                        3. One hundred eight point five six<\/li>\n<\/ol>\n\n\n\n

                          Q 3.  Between which two numbers in tenth place on the number line does each of the given number lie?<\/strong><\/p>\n\n\n\n

                            \n
                          1. 0.06 <\/strong><\/li>\n\n\n\n
                          2. 0.45 <\/strong><\/li>\n\n\n\n
                          3. 0.19<\/strong><\/li>\n<\/ol>\n\n\n\n

                            Ans. <\/strong>Let us see the answers below:<\/p>\n\n\n\n

                              \n
                            1. 0.06 lies between 0.0 and 0.1 in the tenth place of the number line.<\/li>\n\n\n\n
                            2. 0.45 lies between 0.4 and 0.5 in the tenth place of the number line.<\/li>\n\n\n\n
                            3. 0.06 lies between 0.1 and 0.2 in the tenth place of the number line.<\/li>\n<\/ol>\n\n\n\n

                              Exercise 8.3<\/h3>\n\n\n\n

                              Q 1. Which is greater? <\/strong><\/p>\n\n\n\n

                                \n
                              1. 0.3 or 0.4 <\/strong><\/li>\n\n\n\n
                              2. 0.07 or 0.02 <\/strong><\/li>\n\n\n\n
                              3. 3 or 0.8 <\/strong><\/li>\n\n\n\n
                              4. 0.5 or 0.05 <\/strong><\/li>\n\n\n\n
                              5. 1.23 or 1.2 <\/strong><\/li>\n\n\n\n
                              6. 0.099 or 0.19 <\/strong><\/li>\n\n\n\n
                              7. 1.5 or 1.50 <\/strong><\/li>\n\n\n\n
                              8. 1.431 or 1.490 <\/strong><\/li>\n\n\n\n
                              9. 3.3 or 3.300 <\/strong><\/li>\n\n\n\n
                              10. 5.64 or 5.603<\/strong><\/li>\n<\/ol>\n\n\n\n

                                Ans. <\/strong>As the rule mentioned above, we will start comparing the given numbers from the left side of the decimals. Hence, the answers are:  ><<\/p>\n\n\n\n

                                  \n
                                1. Among 0.3 and 0.4, in the tenth place, 0.4 is greater.<\/li>\n<\/ol>\n\n\n\n

                                  So, 0.3 < 0.4 <\/p>\n\n\n\n

                                  We will solve the rest of the questions in a similar manner.<\/p>\n\n\n\n

                                    \n
                                  1. 0.07 > 0.02<\/li>\n\n\n\n
                                  2. 3 > 0.08<\/li>\n\n\n\n
                                  3. 0.5 > 0.05<\/li>\n\n\n\n
                                  4. 1.23 > 1.2 <\/li>\n\n\n\n
                                  5. 0.099 < 0.19<\/li>\n\n\n\n
                                  6. 1.5 = 1.50<\/li>\n\n\n\n
                                  7. 1.431 < 1.490<\/li>\n\n\n\n
                                  8. 3.3 = 3.300<\/li>\n\n\n\n
                                  9. 5.64 > 5.603<\/li>\n<\/ol>\n\n\n\n

                                    Exercise 8.4<\/h3>\n\n\n\n

                                    Q 1. Express as rupees using decimals. <\/strong><\/p>\n\n\n\n

                                      \n
                                    1. 5 paise <\/strong><\/li>\n\n\n\n
                                    2. 75 paise <\/strong><\/li>\n\n\n\n
                                    3. 20 paise <\/strong><\/li>\n\n\n\n
                                    4. 50 rupees 90 paise<\/strong><\/li>\n<\/ol>\n\n\n\n

                                      Ans. <\/strong>We know that 1 Rs = 100 Paisa<\/p>\n\n\n\n

                                      So, 1 Paisa = 1\/100 Rs<\/p>\n\n\n\n

                                        \n
                                      1. <\/li>\n\n\n\n
                                      2. <\/li>\n\n\n\n
                                      3. <\/li>\n\n\n\n
                                      4. <\/li>\n<\/ol>\n\n\n\n

                                        Exercise 8.5 <\/h3>\n\n\n\n

                                        Q 1.  Rashid spent \u20b9 35.75 for the Maths book and \u20b9 32.60 for the Science book. Find the total<\/strong><\/p>\n\n\n\n

                                        amount spent by Rashid.<\/strong><\/p>\n\n\n\n

                                        Ans. <\/strong>The total amount paid by Rashid = \u20b9 35.75 + \u20b9 32.60 = \u20b9 68.35 <\/strong><\/p>\n\n\n\n

                                        Q 2.  Radhika\u2019s mother gave her \u20b9 10.50 and her father gave her \u20b9 15.80, find the total<\/strong><\/p>\n\n\n\n

                                        amount given to Radhika by the parents<\/strong><\/p>\n\n\n\n

                                        Ans. <\/strong>The total amount given to Radhika is = \u20b9 10.50 + \u20b9 115.80 = \u20b9 26.30<\/p>\n\n\n\n

                                        Exercise 8.6 <\/h3>\n\n\n\n

                                        Q 1.  Tina had 20 m 5 cm long cloth. She cuts 4 m 50 cm length of cloth from this for making a curtain. How much cloth is left with her?<\/strong><\/p>\n\n\n\n

                                        Ans. <\/strong>We know that 1 m = 100 cm, so, 1 cm = 1\/100 m.<\/p>\n\n\n\n

                                        Total length of cloth = 20 m 5 cm = 20.05 m<\/p>\n\n\n\n

                                        Piece of cloth taken by Tina for making curtain = 4 m 50 cm = 4.5 m<\/p>\n\n\n\n

                                        Cloth left with Tina = 20.05 m – 4.5 m = 15.55 m<\/p>\n\n\n\n

                                        \n