{"id":10909,"date":"2026-11-02T02:04:39","date_gmt":"2026-11-02T02:04:39","guid":{"rendered":"https:\/\/kapdec.com\/help\/?p=10909"},"modified":"2026-11-02T02:04:39","modified_gmt":"2026-11-02T02:04:39","slug":"decimals-introduction-types","status":"publish","type":"post","link":"https:\/\/kapdec.com\/help\/decimals-introduction-types\/","title":{"rendered":"Decimals-introduction & Types"},"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>: Decimals \u2013 Introduction & Types<\/h3>\n

Reference<\/strong>: \u2013 Introduction to Decimals, Decimal Point and Place Value, Tenths, Hundredths, Thousandths, Like and Unlike Decimals, Terminating Decimals, Recurring (Repeating) Decimals, Non-Terminating Non-Recurring Decimals, Comparison of Decimals<\/em><\/p>\n

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

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  • Introduction to Decimals & Their Need<\/li>\n
  • Decimal Point and Place Value<\/li>\n
  • Tenths, Hundredths, Thousandths<\/li>\n
  • Like and Unlike Decimals<\/li>\n
  • Terminating Decimals<\/li>\n
  • Recurring (Repeating) Decimals<\/li>\n
  • Non-Terminating Non-Recurring Decimals<\/li>\n
  • Comparison and Ordering of Decimals<\/li>\n<\/ul>\n

    \nIntroduction to Decimals<\/strong><\/p>\n

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

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    Decimals are numbers representing special fractions with denominators as 10, 100, 1000, etc.<\/strong><\/p>\n

    They are nothing but a way of writing whole number and fractional number together separated by a decimal point (dot).<\/p>\n

    Decimals are used to represent numbers that are smaller than the unit 1, e.g. 0.47, 0.25, 0.73, etc.<\/p>\n

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

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    For example,<\/strong> in the following figure, one block is divided into 10 equal parts. In fractional terms, each part represents 1\/10 (one-tenth) of a unit. In decimals, it can be denoted as 0.1<\/p>\n

    The decimal point is represented by the dot and it comes between the units place and the tenths place.<\/strong><\/p>\n

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    Representing decimals on a number line<\/strong><\/p>\n

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    We have learnt how to represent fractions and integers on a number line.<\/p>\n

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    A decimal is represented on number line just like fractions.<\/p>\n

    Let us look at decimals on number line up to one decimal point.<\/p>\n

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    • We divide one unit of the number line into ten equal parts such that each part is one-tenth of the whole.<\/li>\n<\/ul>\n

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      • When we further divide one-tenth part into ten equal parts, we get one-hundredth of the whole.<\/li>\n<\/ul>\n

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        • This way we can keep on dividing to represent smaller decimal fractions.<\/li>\n<\/ul>\n

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

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

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          Example- <\/strong>Represent 8.45 on number line<\/p>\n

          First let us represent the tenths place i.e. 8.4<\/p>\n

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

          The segment between 8 and 9 is divided into 10 equal parts and the 4th<\/sup> part represents 8.4<\/p>\n

          Now, to represent 8.45 on the number line, we further divide the segment between 8.4 and 8.5 into ten equal parts.<\/p>\n

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

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          Here each part represents hundredth place and the arrow which is five parts to the right of 8.4 points at 8.45.<\/p>\n

          \nSimilarly, we can represent 8.456 on a number line by dividing the segment between 8.45 and 8.46 into ten equal parts.<\/p>\n

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

          The arrow which is six parts to the right of 8.45 points at 8.456.<\/p>\n

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          Examples<\/strong>–<\/p>\n

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          • \u00a0Write\u00a0as decimals:\u00a0Nine-tenths<\/li>\n<\/ul>\n

            \u00a0<\/p>\n

            Solution:<\/strong><\/p>\n

            = 9 \u00d7 0.1<\/p>\n

            = 0.9<\/p>\n

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              \n
            • Write\u00a0as\u00a0decimals: Four tens and six-tenths<\/li>\n<\/ul>\n

              \u00a0<\/p>\n

              Solution:<\/strong><\/p>\n

              = <\/strong>4 \u00d7 10 + 6 \u00d7 0.1<\/p>\n

              = 40 + 0.6<\/p>\n

              = 40.6<\/p>\n

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

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              • Locate 2.5 on the number line.<\/li>\n<\/ul>\n

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                Solution:<\/strong><\/p>\n

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                • We know that 2.5 is located between 2 and 3.<\/li>\n
                • So, we divide the block between 2 and 3 into ten equal parts.<\/li>\n
                • Then we mark 2.5 on the number line.<\/li>\n<\/ul>\n

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

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                  Hundredths<\/strong><\/p>\n

                  In Hundredth, one block is divided into 100 equal parts and each part comprises 1\/100th part of the entire block.<\/p>\n

                  Suppose a square is divided into 100 small parts or squares, then the area of each small square will be 1\/100 or one hundredth of the entire square.<\/p>\n

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

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                  • The area of the smaller square shaded red is one hundredth of the entire square.<\/li>\n
                  • The decimal notation is 1\/100 = 0.01.<\/li>\n<\/ul>\n

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                    Examples<\/strong>–<\/p>\n

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                    • \u00a0Write the number given in the following place value table in decimal form.<\/li>\n<\/ul>\n

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

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                      a) The number is 1 \u00d7 10 + 0 \u00d7 1 + 7 \u00d7 0.1\u00a0\u00a0 + 5 \u00d7 0.01<\/p>\n

                      = 10 + 0 + 0.7 + 0.05<\/p>\n

                      = 10 + 0.7 + 0.05<\/p>\n

                      = 10 + 0.75<\/p>\n

                      = 10.75<\/p>\n

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                      b) The number is 7 \u00d7 10 + 6 \u00d7 1 + 2 \u00d7 0.1\u00a0 + 3 \u00d7\u00a0 0.01<\/p>\n

                      = 70 + 6 +0.2\u00a0 + 0.03<\/p>\n

                      = 76 + 0.23<\/p>\n

                      = 76.23<\/p>\n

                      \u00a0<\/p>\n

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                      • Write each of the following in decimals.<\/li>\n<\/ul>\n
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                        • Five point zero one = 5.01<\/li>\n<\/ul>\n
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                          • One hundred two point five nine = 102.59<\/li>\n<\/ul>\n

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