https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:real-numbers/x06d55bfa213a79fd:rational-numbers/v/rational-number-terminating-decimal 2026-03-11T10:11:27.775666738Z Rational number - Terminating decimal Why do some fractions turn into neat decimals like 0.375 while others go on forever? This video explores the hidden patterns within rational numbers. We'll start by converting terminating decimals into fractions and analyzing their denominators. You'll discover the ""2 and 5"" rule: a fundamental pattern where every terminating decimal's denominator, when simplified, only contains prime factors of 2 and 5. We'll walk through multiple examples, including 7/16 and 9/125, and formally break down Theorems 1.3 and 1.4 to show you how to predict a decimal's behavior without doing long division! Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Rational number - Terminating decimal Why do some fractions turn into neat decimals like 0.375 while others go on forever? This video explores the hidden patterns within rational numbers. We'll start by converting terminating decimals into fractions and analyzing their denominators. You'll discover the ""2 and 5"" rule: a fundamental pattern where every terminating decimal's denominator, when simplified, only contains prime factors of 2 and 5. We'll walk through multiple examples, including 7/16 and 9/125, and formally break down Theorems 1.3 and 1.4 to show you how to predict a decimal's behavior without doing long division! https://cdn.kastatic.org/ka-youtube-converted/eT2W2v5dDSA.mp4/eT2W2v5dDSA.mp4 556 Real Numbers: Decimals and Cyclic Patterns https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:real-numbers/x06d55bfa213a79fd:rational-numbers/v/non-terminating-decimal-expansion 2026-03-11T10:11:27.775666738Z Non-Terminating Decimal Expansion Why do some fractions like 1/3 or 1/7 never seem to end? In this video, we dive into the world of non-terminating, repeating decimals. We’ll use long division to uncover the infinite patterns hidden within these rational numbers and discover a powerful shortcut to predict them! What we’ll cover: 1. Step-by-step long division for 1/7 and 1/3 to see the "loop" in action. 2. Identifying prime factors in denominators (3, 7, 11, 13, etc.). 3. A breakdown of the formal Theorem for non-terminating decimals. 4. Real-world verification with examples like 2/7, 5/11, and 1/6. Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Non-Terminating Decimal Expansion Why do some fractions like 1/3 or 1/7 never seem to end? In this video, we dive into the world of non-terminating, repeating decimals. We’ll use long division to uncover the infinite patterns hidden within these rational numbers and discover a powerful shortcut to predict them! What we’ll cover: 1. Step-by-step long division for 1/7 and 1/3 to see the "loop" in action. 2. Identifying prime factors in denominators (3, 7, 11, 13, etc.). 3. A breakdown of the formal Theorem for non-terminating decimals. 4. Real-world verification with examples like 2/7, 5/11, and 1/6. https://cdn.kastatic.org/ka-youtube-converted/MKWpqjUxGR8.mp4/MKWpqjUxGR8.mp4 293 Real Numbers: Decimals and Cyclic Patterns https://www.khanacademy.org/math/8th-grade-illustrative-math/unit-8-pythagorean-theorem-and-irrational-numbers/lesson-14-decimal-representations-of-rational-numbers/v/converting-repeating-decimals-to-fractions-part-1-of-2 2025-03-28T07:05:36.573142233Z Converting repeating decimals to fractions (part 1 of 2) Converting repeating decimals to fractions (part 1 of 2) (Indian Accent) Aakash Bagga video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Converting repeating decimals to fractions (part 1 of 2) Converting repeating decimals to fractions (part 1 of 2) (Indian Accent) https://cdn.kastatic.org/ka-youtube-converted/GMXAckRulSU.mp4/GMXAckRulSU.mp4 242 Real Numbers: Decimals and Cyclic Patterns https://www.khanacademy.org/math/8th-grade-illustrative-math/unit-8-pythagorean-theorem-and-irrational-numbers/lesson-14-decimal-representations-of-rational-numbers/v/converting-repeating-decimals-to-fractions-part-2-of-2-india 2025-03-28T07:05:36.573142233Z Converting repeating decimals to fractions (part 2 of 2) Converting repeating decimals to fractions (part 2 of 2) (Indian Accent) Aakash Bagga video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Converting repeating decimals to fractions (part 2 of 2) Converting repeating decimals to fractions (part 2 of 2) (Indian Accent) https://cdn.kastatic.org/ka-youtube-converted/4hrdbrDtT_M.mp4/4hrdbrDtT_M.mp4 545 Real Numbers: Decimals and Cyclic Patterns https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:real-numbers/x06d55bfa213a79fd:rational-numbers/e/express-rational-numbers-as-decimals 2026-02-20T04:00:32.356270105Z Express Rational Numbers as decimals In this exercise, we will study that (1) Express rational numbers expressed as terminating decimal or non terminating decimals. (2) Represent recurring decimal numbers in p/q form, For ex: 1.62(Overline on 62) in p/ q form where q is not 0 ; p, q are integers.(3) Finding without actually dividing which are terminating decimals. A rational number is a terminating decimal, only when the prime factors of denominator are 2, 5 only i.e. if the denominator is expressed as 2m . 5n, where m and n are non negative integers(P1). Khan Academy exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:irrational-numbers/x2f8bb11595b61c86:irrational-numbers-intro/v/recognizing-irrational-numbers 2023-07-28T22:13:00.844712665Z Classifying numbers: rational & irrational We can write any rational number as the ratio of two integers. We cannot write irrational numbers, such as the square root of 8 and pi, in this way. Learn other forms, such as decimals, in which these types of numbers can appear. Sal Khan video https://cdn.kastatic.org/googleusercontent/4WPdubD4d1Ql_fVW2zq0QqwKQlT-eMY8Lgob9RjtvGw7KQR5Ej8FxkfSAXf25au4WtlFfBIxvdUxGYzYASLo1WII Classifying numbers: rational & irrational We can write any rational number as the ratio of two integers. We cannot write irrational numbers, such as the square root of 8 and pi, in this way. Learn other forms, such as decimals, in which these types of numbers can appear. https://cdn.kastatic.org/ka-youtube-converted/d9pO2z2qvXU.mp4/d9pO2z2qvXU.mp4 138 Real Numbers: Decimals and Cyclic Patterns https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:irrational-numbers/x2f8bb11595b61c86:irrational-numbers-intro/e/recognizing-rational-and-irrational-numbers 2026-05-19T08:30:42.784038807Z Classify numbers: rational & irrational Practice identifying whether numbers and single operation expressions are rational or irrational. Rhonda Hughes exercise