{"id":10862,"date":"2026-11-02T02:02:53","date_gmt":"2026-11-02T02:02:53","guid":{"rendered":"https:\/\/kapdec.com\/help\/?p=10862"},"modified":"2026-11-02T02:02:53","modified_gmt":"2026-11-02T02:02:53","slug":"expanded-form-order-relations","status":"publish","type":"post","link":"https:\/\/kapdec.com\/help\/expanded-form-order-relations\/","title":{"rendered":"Expanded Form & Order Relations"},"content":{"rendered":"
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KAPDEC® | Elite STEM Learning Platform | https:\/\/kapdec.com<\/a><\/p>\n

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Unit<\/strong>: Number System<\/h2>\n

Chapter<\/strong>: Expanded Form & Order Relations<\/h3>\n

Reference<\/strong>: \u2013 Expanded Form of Numbers (Indian and International Systems), Writing Numbers in Expanded Notation, Place Value Expansion, Comparing Numbers (Same Number of Digits, Different Number of Digits), Order Relations (<, >, =), Ascending and Descending Order, Arranging Numbers in Order, Forming Numbers from Given Digits<\/em><\/p>\n

After studying this chapter, you should be able to understand:<\/p>\n

    \n
  • Expanded Form of Numbers in Indian and International Systems<\/li>\n
  • Writing Numbers in Expanded Notation<\/li>\n
  • Place Value Expansion & Its Applications<\/li>\n
  • Comparing Numbers with Same Number of Digits<\/li>\n
  • Comparing Numbers with Different Number of Digits<\/li>\n
  • Order Relations: <, >, =<\/li>\n
  • Ascending and Descending Order<\/li>\n
  • Forming Numbers from Given Digits<\/li>\n<\/ul>\n

    The International Place Value System<\/strong><\/p>\n

    In this system, we start grouping the number from right in group of 3 called period.<\/p>\n

    \u00a0<\/p>\n

      \n
    • Starting from the right, the first period is ones, consisting of three place values i.e. ones, tens and hundreds.<\/li>\n<\/ul>\n

      \u00a0<\/p>\n

        \n
      • The next period is thousands, consisting of three places i.e. thousands, ten-thousands and hundred-thousands.<\/li>\n<\/ul>\n

        \u00a0<\/p>\n

          \n
        • The third period is millions consisting of three places i.e. millions, ten-millions and hundred million and then billions, trillions and so on.<\/li>\n<\/ul>\n

          \"\"<\/p>\n

          Source: Kapdec.com<\/p>\n<\/div>\n

          \u00a0<\/p>\n

          Reading and writing a number<\/strong><\/p>\n

            \n
          • While reading a number in the International system, all of the digits in the same period are read together and the name of the period (except the ones) is read along with them.<\/li>\n
          • While writing a number in the International system, we put a comma after every period to separate the period and making it easier to read.<\/li>\n<\/ul>\n

            \u00a0<\/p>\n

            Example 1:<\/strong> Write the following in words:<\/p>\n

              \n
            1. 227,842\u00a0\u00a0\u00a0<\/li>\n
            2. 36,479,111<\/li>\n
            3. 508,541,360<\/li>\n<\/ol>\n

              \u00a0<\/p>\n

              Solution:<\/strong> Let us arrange the digits in International place value chart as follows:<\/p>\n

              \"\"<\/p>\n

              Source: Kapdec.com<\/p>\n<\/div>\n

                \n
              1. Two hundred twenty-seven thousand eight hundred forty two<\/li>\n
              2. Thirty-six million four hundred seventy-nine thousand one hundred eleven<\/li>\n
              3. Five hundred eight million five hundred forty-one thousand three hundred sixty<\/li>\n<\/ol>\n

                \u00a0<\/p>\n

                Example 2 :<\/strong> Write the following in figures :<\/p>\n

                  \n
                1. Three hundred five million thirty-seven thousand sixty three<\/li>\n
                2. Eighty-nine million one hundred twenty-six thousand ninety<\/li>\n
                3. Two million twenty<\/li>\n<\/ol>\n

                  Solution:<\/strong> Let us make the International place value chart and write the digits in the respective places from the number name.<\/p>\n

                  \u00a0<\/p>\n

                  \"\"<\/p>\n

                  Source: Kapdec.com<\/p>\n<\/div>\n

                  The required number is-<\/p>\n

                    \n
                  1. 305,037,063<\/li>\n
                  2. 89,126,090<\/li>\n
                  3. 2,000,020<\/li>\n<\/ol>\n

                    \u00a0<\/p>\n

                    Expanded Form<\/strong><\/p>\n

                      \n
                    • A number when expressed with its place value denotes its expanded form.<\/li>\n<\/ul>\n

                      \u00a0<\/p>\n

                        \n
                      • Suppose we write a number 619, here we actually mean that we have a total of 600 + 10 + 9. This expansion shows the value of each of its digit and hence represents the expanded form.<\/li>\n<\/ul>\n

                        \u00a0<\/p>\n

                          \n
                        • The expanded form varies in the Indian and International structure as per their defined period.<\/li>\n<\/ul>\n

                          \u00a0<\/p>\n

                          International Place Value System<\/strong><\/p>\n

                          Examples:\u00a0 <\/strong><\/p>\n

                          Expand the following numbers as per International Place Value System:<\/strong><\/p>\n

                            \n
                          1. 81,664<\/li>\n
                          2. 1,697,832<\/li>\n<\/ol>\n

                            We can expand any given number in three ways:<\/p>\n

                              \n
                            1. 81,664<\/li>\n<\/ol>\n

                              \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 = 8 ten thousand + 1 thousand + 6 hundred + 6 ten +
                              \n\u00a0\u00a0\u00a0 4 one<\/p>\n

                              Or \u00a0\u00a0 = 8 x 10,000 + 1 x 1,000 + 6 x 100 + 6 x 10 + 4 x 1<\/p>\n

                              Or \u00a0\u00a0 = 80,000 + 1,000 + 600 + 60 + 4<\/p>\n

                              \u00a0<\/p>\n

                                \n
                              1. 1,697,832<\/li>\n<\/ol>\n

                                \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = 1 million + 6 hundred thousand + 9 ten thousand +
                                \n\u00a0\u00a0\u00a0 7 thousand + 8 hundred + 3 ten + 2 one<\/p>\n

                                Or \u00a0\u00a0 = 1 x 1,000,000 + 6 x 100,000 + 9 x 10,000 + 7 x
                                \n\u00a0\u00a0\u00a0 1,000 + 8 x 100 + 3 x 10 + 2 x 1<\/p>\n

                                Or\u00a0\u00a0\u00a0 = 1,000,000 + 600,000 + 90,000 + 7,000 + 800 + 30 +
                                \n\u00a0\u00a0 2<\/p>\n

                                \u00a0<\/p>\n

                                \u00a0<\/p>\n

                                \u00a0<\/p>\n

                                Did you know??<\/u><\/strong><\/p>\n

                                  \n
                                • Zero was invented by Aryabhata. India invented the Number System.<\/li>\n
                                • The place value system and the decimal system were developed in India in 100 BC.<\/li>\n
                                • The largest numbers used by the Greeks and the Romans were 10^6 whereas Hindus used numbers as big as 10^53 with specific names as early as 5000 BC during the Vedic period.<\/li>\n<\/ul>\n

                                  <\/p>\n