{"id":5366,"date":"2022-02-06T17:39:43","date_gmt":"2022-02-06T17:39:43","guid":{"rendered":"https:\/\/oryxlearning.com\/company\/?page_id=5366"},"modified":"2022-02-06T17:39:43","modified_gmt":"2022-02-06T17:39:43","slug":"terminating-and-repeating-decimals","status":"publish","type":"page","link":"https:\/\/oryxlearning.com\/learn\/terminating-and-repeating-decimals\/","title":{"rendered":"Terminating and Repeating Decimals"},"content":{"rendered":"[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text]\n<h5>Terminating and Repeating Decimals<\/h5>\n[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]The decimal representation of a rational number is converting a rational number into a decimal number that has the same mathematical value as the rational number. A rational number can be represented as a decimal number with the help of the long division method. We divide the given rational number in the long division form and the quotient which we get is the decimal representation of the rational number. A rational number can have two types of decimal representations (expansions):<\/p>\n<p>Terminating<br \/>\nNon-terminating but repeating<\/p>\n<p>While dividing a number by the long division method, if we get zero as the remainder, the decimal expansion of such a number is called terminating. And while dividing a number, if the decimal expansion continues and the remainder does not become zero, it is called non-terminating or repeating. The decimal form of a fraction usually represented by a bar over the repeating numbers.[\/vc_column_text][vc_column_text el_class=”headingnew”]Rules[\/vc_column_text][vc_column_text]1. If the number is a mixed number, convert it into an improper fraction.<br \/>\n2. Just divide the numerator by the denominator. If you end up with a remainder of 0 , then you have a terminating decimal. Otherwise, the remainders will begin to repeat after some point, and you have a repeating decimal.<br \/>\n3. Determine which answers are repeating decimals and put a bar over the repeating numbers in the decimal.[\/vc_column_text][vc_column_text el_class=”headingnew”]Example[\/vc_column_text][vc_column_text]\n<p style=\"margin-top: 0px; color: #16a085;\"><strong>Write the number as a decimal. Use bar notation if necessary.<br \/>\n<img style=\"margin-top: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;{&space;-2\\frac{7}{9}}\" alt=\"\\fn_phv { -2\\frac{7}{9}}\" align=\"absmiddle\" \/><br \/>\n<\/strong><\/p>\n[\/vc_column_text][vc_column_text el_class=”headingnew”]Solution[\/vc_column_text][vc_column_text]1. If the number is a mixed number, convert it into an improper fraction.<br \/>\n<img style=\"margin-top: 10px; margin-bottom: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;{&space;-2\\frac{7}{9}}&space;=&space;-\\frac{25}{9}\" alt=\"\\fn_phv { -2\\frac{7}{9}} = -\\frac{25}{9}\" align=\"absmiddle\" \/><br \/>\n2. Just divide the numerator by the denominator. If you end up with a remainder of 0 , then you have a terminating decimal. Otherwise, the remainders will begin to repeat after some point, and you have a repeating decimal.<br \/>\n<img style=\"margin-top: 10px; margin-bottom: 10px;\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\fn_phv&space;-\\frac{25}{9}=-2.777...\" alt=\"\\fn_phv -\\frac{25}{9}=-2.777...\" align=\"absmiddle\" \/><br \/>\n3. The answer is a repeating decimal. Put a bar over the repeating number in the decimal.<br \/>\n<img style=\"margin-top: 10px; margin-bottom: 0px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;Answer:&space;{\\color{Red}&space;-2.\\overline{7}}\" alt=\"\\fn_phv Answer: {\\color{Red} -2.\\overline{7}}\" align=\"absmiddle\" \/>[\/vc_column_text][vc_column_text el_class=”headingnew”]Practice Terminating and Repeating Decimals[\/vc_column_text][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 1<\/h5>\n<p><strong><span style=\"color: #16a085;\">Write the number as a decimal. Use bar notation if necessary.<br \/>\n<img style=\"margin-top: 10px; margin-bottom: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;5\\frac{6}{7}\" alt=\"\\fn_phv 5\\frac{6}{7}\" align=\"absmiddle\" \/><\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/terminating-and-repeating-decimals\"><img loading=\"lazy\" class=\"alignnone wp-image-5368 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/1-23.png\" alt=\"\" width=\"105\" height=\"43\" \/><\/a>[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/terminating-and-repeating-decimals”][\/vc_column_inner][\/vc_row_inner][vc_empty_space][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 2<\/h5>\n<p><strong><span style=\"color: #16a085;\">Write the number as a decimal. Use bar notation if necessary.<br \/>\n<\/span><\/strong><img style=\"margin-bottom: 10px; margin-top: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;-\\frac{2}{11}\" alt=\"\\fn_phv -\\frac{2}{11}\" align=\"absmiddle\" \/><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/terminating-and-repeating-decimals\"><img loading=\"lazy\" class=\"alignnone wp-image-5368 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/1-23.png\" alt=\"\" width=\"105\" height=\"43\" \/><\/a>[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/terminating-and-repeating-decimals”][\/vc_column_inner][\/vc_row_inner][vc_empty_space][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 3<\/h5>\n<p><strong><span style=\"color: #16a085;\">Fill in the chart. Write the fraction and mixed numbers in reduced form.<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/terminating-and-repeating-decimals\"><img loading=\"lazy\" class=\"alignnone wp-image-5370 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/11-14.png\" alt=\"\" width=\"333\" height=\"145\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/11-14.png 333w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/11-14-300x131.png 300w\" sizes=\"(max-width: 333px) 100vw, 333px\" \/><\/a>[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/terminating-and-repeating-decimals”][\/vc_column_inner][\/vc_row_inner][vc_empty_space][\/vc_column][vc_column width=”1\/3″ css=”.vc_custom_1633369011398{margin-bottom: 50px !important;}”][vc_row_inner el_class=”stickynotee”][vc_column_inner][vc_single_image image=”2265″ img_size=”full” alignment=”center” css_animation=”fadeIn” css=”.vc_custom_1633509989314{border-radius: 10px !important;}” el_class=”stickypin”][vc_column_text]<strong>Terminating Decimal<\/strong>– a decimal which can be expressed in a finite number of figures or for which all figures to the right of some place are zero.<\/p>\n<p><strong>Repeating Decimal<\/strong> – a decimal in which after a certain point a particular digit or sequence of digits repeats itself indefinitely.[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”boxxborder2″]<span style=\"color: #ed5600;\"><strong>Pre-requisite Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/4th-grade\/division-with-remainders\"><span style=\"color: #ed5600;\">Division With Remainders<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/4th-grade\/convert-between-mixed-numbers-and-improper-fractions\"><span style=\"color: #ed5600;\">Convert Between Mixed Numbers and Improper Fractions<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/4th-grade\/write-fractions-as-decimals\"><span style=\"color: #ed5600;\">Write Fractions as Decimals<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/4th-grade\/decimals-fractions-and-mixed-numbers\"><span style=\"color: #ed5600;\">Decimals, Fractions, and Mixed Numbers<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/5th-grade\/write-fractions-as-decimal-numbers\"><span style=\"color: #ed5600;\">Write Fractions as Decimal Numbers<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/5th-grade\/write-improper-fractions-as-mixed-number\"><span style=\"color: #ed5600;\">Write Improper Fractions as Mixed Number<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/5th-grade\/write-mixed-number-as-improper-fraction\"><span style=\"color: #ed5600;\">Write Mixed Number as Improper Fraction<\/span><\/a><br \/>\n[\/vc_column_text][vc_column_text el_class=”boxxborder2″ css=”.vc_custom_1637302031362{border-top-width: 7px !important;border-right-width: 7px !important;border-bottom-width: 7px !important;border-left-width: 7px !important;background-position: center !important;background-repeat: no-repeat !important;background-size: contain !important;border-left-color: #333399 !important;border-left-style: solid !important;border-right-color: #333399 !important;border-right-style: solid !important;border-top-color: #333399 !important;border-top-style: solid !important;border-bottom-color: #333399 !important;border-bottom-style: solid !important;border-radius: 35px !important;}”]<span style=\"color: #333399;\"><strong>Related Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/compare-and-order-rational-numbers\"><span style=\"color: #333399;\">Compare and Order Rational Numbers<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/add-and-subtract-like-fractions\"><span style=\"color: #333399;\">Add and Subtract Like Fractions<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/add-and-subtract-unlike-fractions\"><span style=\"color: #333399;\">Add and Subtract Unlike Fractions<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/add-and-subtract-mixed-numbers\"><span style=\"color: #333399;\">Add and Subtract Mixed Numbers<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/multiply-rational-numbers\"><span style=\"color: #333399;\">Multiply Rational Numbers<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/divide-rational-numbers\"><span style=\"color: #333399;\">Divide Rational Numbers<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/convert-units\"><span style=\"color: #333399;\">Convert Units<\/span><\/a>[\/vc_column_text][vc_row_inner equal_height=”yes” el_class=”btninlinespacing”][vc_column_inner][vc_btn title=”Grade 1″ color=”warning” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F1st-grade%2Fmaths|title:Grade%201%20Math||”][vc_btn title=”Grade 2″ color=”danger” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F2nd-grade%2Fmaths|title:Grade%202%20Math||”][vc_btn title=”Grade 3″ color=”violet” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F3rd-grade%2Fmaths|title:Grade%203%20Math||”][vc_btn title=”Grade 4″ color=”blue” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F4th-grade%2Fmaths|title:Grade%204%20Math||”][vc_btn title=”Grade 5″ color=”green” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F5th-grade%2Fmaths|title:Grade%205%20Math||”][vc_btn title=”Grade 6″ color=”info” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F6th-grade%2Fmaths|title:Grade%206%20Math||”][vc_btn title=”Grade 7″ color=”vista-blue” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F7th-grade%2Fmaths|title:Grade%207%20Math||”][vc_btn title=”Grade 8″ color=”mulled-wine” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F8th-grade%2Fmaths|title:Grade%208%20Math||”][\/vc_column_inner][\/vc_row_inner][vc_row_inner equal_height=”yes” el_class=”btninlinespacing”][vc_column_inner][vc_btn title=”Decimals” color=”warning” link=”url:https%3A%2F%2Fen.oryxlearning.com%2Ftopics%2Fmaths%2Fdecimals|title:Decimals||”][vc_btn title=”Fractions” color=”danger” link=”url:https%3A%2F%2Foryxlearning.com%2Ftopics%2Fmaths%2Ffractions|title:Fractions||”][vc_btn title=”Word Problems” color=”violet” link=”url:https%3A%2F%2Foryxlearning.com%2Ftopics%2Fmaths%2Fword-problems|title:Word%20Problems||”][\/vc_column_inner][\/vc_row_inner][\/vc_column][\/vc_row][\/vc_section]\n","protected":false},"excerpt":{"rendered":"<p>[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text] Terminating and Repeating Decimals [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]The decimal representation of a rational number is converting a rational number into a decimal number that has the same mathematical value as the rational number. A […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.0 (Yoast SEO v17.6) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Terminating and Repeating Decimals | Oryx Learning<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/oryxlearning.com\/learn\/terminating-and-repeating-decimals\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Terminating and Repeating Decimals\" \/>\n<meta property=\"og:description\" content=\"[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text] Terminating and Repeating Decimals [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]The decimal representation of a rational number is converting a rational number into a decimal number that has the same mathematical value as the rational number. 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