https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:irrational-numbers/x2f8bb11595b61c86:irrational-numbers-intro/v/introduction-to-rational-and-irrational-numbers 2023-07-28T22:13:00.844712665Z Intro to rational & irrational numbers Learn the difference between rational and irrational numbers, learn how to identify them, and discover why some of the most famous numbers in mathematics, like Pi and e, are actually irrational. Did you know that there's always an irrational number between any two rational numbers? Sal Khan video https://cdn.kastatic.org/googleusercontent/TW91vVssinJ9NoXzUVhHLxwtgBPWLaDb19VLK7IQru9kKFKuL4vfLUlA8lWl5RYhHF3ESvUlSZCJXP_xHRrLuTAMIA Intro to rational & irrational numbers Learn the difference between rational and irrational numbers, learn how to identify them, and discover why some of the most famous numbers in mathematics, like Pi and e, are actually irrational. Did you know that there's always an irrational number between any two rational numbers? https://cdn.kastatic.org/ka-youtube-converted/cLP7INqs3JM.mp4/cLP7INqs3JM.mp4 355 Number Systems https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-repeating-decimals/v/converting-a-fraction-to-a-repeating-decimal 2023-07-17T20:04:18.610848495Z Converting a fraction to a repeating decimal To convert a fraction like 19/27 into a decimal, you should divide 27 into 19, and use the remainder to figure out the decimal. The decimal begins 0.703703..., and the notation for a repeating decimal like this is to write the numbers that repeat and then put a line above them. The first six digits of the decimal should be included in the answer. Sal Khan video https://cdn.kastatic.org/googleusercontent/NVyuuWSvwxfY-Xr_n6iAspQY4wujrE7zremxpkhxsER33ixHW-eC6c__YxpxMvfHuEVsv0KhgEIQdltGopy0jApLeg Converting a fraction to a repeating decimal To convert a fraction like 19/27 into a decimal, you should divide 27 into 19, and use the remainder to figure out the decimal. The decimal begins 0.703703..., and the notation for a repeating decimal like this is to write the numbers that repeat and then put a line above them. The first six digits of the decimal should be included in the answer. https://cdn.kastatic.org/ka-youtube-converted/Y2-tz27nKoQ.mp4/Y2-tz27nKoQ.mp4 265 Number Systems https://www.khanacademy.org/math/algebra-home/alg-exp-and-log/miscellaneous-radicals/v/how-to-rationalize-a-denominator 2020-06-23T07:22:43Z Intro to rationalizing the denominator When we have a fraction with a root in the denominator, like 1/√2, it's often desirable to manipulate it so the denominator doesn't have roots. To do that, we can multiply both the numerator and the denominator by the same root, that will get rid of the root in the denominator. For example, we can multiply 1/√2 by √2/√2 to get √2/2 Sal Khan video https://cdn.kastatic.org/googleusercontent/JXfSR01H3KvsGGAU_AzzpKr_Q4eXYS2kFNlfGoDPHZuldyFfyGJ5popeCmrRgayoYvTTGqvO0jIXadM5mbczaCOr Intro to rationalizing the denominator When we have a fraction with a root in the denominator, like 1/√2, it's often desirable to manipulate it so the denominator doesn't have roots. To do that, we can multiply both the numerator and the denominator by the same root, that will get rid of the root in the denominator. For example, we can multiply 1/√2 by √2/√2 to get √2/2 https://cdn.kastatic.org/ka-youtube-converted/gY5TvlHg4Vk.mp4/gY5TvlHg4Vk.mp4 618 Number Systems https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:exp/x2ec2f6f830c9fb89:eval-exp-rad/v/fractional-exponents-with-numerators-other-than-1 2021-06-30T17:32:34Z Evaluating fractional exponents Sal shows how to evaluate 64^(2/3) and (8/27)^(-2/3). Sal Khan video https://cdn.kastatic.org/googleusercontent/pXAmfMZsqH2xAtjK2EzBECFVFOnNV4BtHT_nrzCYQeQHRzektnSy0thWzpaUQFhOPH0YoCIx5vlmDpzaw1kBlUKG Evaluating fractional exponents Sal shows how to evaluate 64^(2/3) and (8/27)^(-2/3). https://cdn.kastatic.org/ka-youtube-converted/S34NM0Po0eA.mp4/S34NM0Po0eA.mp4 354 Number Systems https://www.khanacademy.org/math/ka-revision-class-9-math/x4d0389c6e7b01cca:week-1/x4d0389c6e7b01cca:irrational-numbers/e/revision-number-systems-ncert-for-up-math-class-9 2025-02-04T16:48:48.672026948Z Revision Number Systems Revision for the unit Number Systems. Aakash Bagga exercise