Maths-
General
Easy
Question
Without performing the actual division, check whether the following rational numbers are terminating or non-terminating ![125 over 325](data:image/png;base64,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)
Hint:
Hint:
Numbers with a fixed or finite number of digits following the decimal point are known as terminating decimals and numbers with infinite decimal places are known as non-terminating decimals.
The correct answer is: non-terminating decimal expansion.
Let x = p/q be a rational number such that the prime factorisation of q is in form 2m5n, where m and n are non-negative integers, then x will have a terminating decimal expansion.
x = ![125 over 325](data:image/png;base64,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)
The given rational number is not in its simplified form. So, let’s first covert it in the simplified form
x = ![5 over 13](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABwAAAAjCAYAAACHIWrsAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAPBJREFUeNpjYCAe/MeDaQJoZvCohXS18BcQfwLibUBcBMQ89LCYBYiNgbgWiG8AsQY9fe0GxAfpHdQ/6GmZDhDfpZXh64DYEoiZoNgDalkQrSwMBeJbQPwHiN8B8SogNmUYBaOA3mUlLfEoGAW0AWrQivYCDnlHaO3/DVpNgcraCUAsTK6Fi4E4DU+y3g+tLdiQxAyAeAe9G1Cf6GmhErStQ3MLxYE4ERqPXrS0EL0IK6BXI1gQiAOA+CQQ29MzDnmgltI1lf6gp4V60IRDEwsPQltzLNCmI6jkuQ/E8dSslJGBLRBvgQbhD2jJ44PPQADv2VyamlFMXQAAAGN0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZyYWM+PG1uPjU8L21uPjxtbj4xMzwvbW4+PC9tZnJhYz48L21hdGg+Tr+YlQAAAABJRU5ErkJggg==)
In the simplified rational number, the value of q is 13. The factorisation of 13 is given as
![13 equals 1 cross times 13 not equal to 2 to the power of m 5 to the power of n](data:image/png;base64,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)
Final Answer:
As the factoriation of 13 is not in the form of 2m5n,
will have non-terminating decimal expansion.
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Maths-
![](data:image/png;base64,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)
Which of the following is an equation of line
in the xy -plane above?
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAVQAAAEXCAYAAADyXrx3AAAWWElEQVR4nO3da3RU5b3H8V8MaiMBkQW0NCihEF3ShUgQBXUJpVYKFjjQcg1IC6hcpI0VSCkCVQEFgsDhEjhYC4ZoQSsFNRwqWjwHiQhEIw1IQiVcAl44CZqYEUyyzwtMCGFymcme2fuZ+X7W8gW57PzdmXyzL5N5IizLsgT4oTRzibr//pyWbZ6mu66LdHocwHFXOD0ADGV9pve2ndboxQ/rTmIKSCKo8If1pQ6+8IxWNR6isfHXKcLpeQCXaOT0ADBM6efKXPeEkvberVXLblMTagpUIqiov/OH9fLv/qANV/5cc/40WHHfo6ZAVRHclAIAe3ANFQ3i8XicHgFwDYKKBlm/br3TIwCuwSk//ObxeNTp5o56591diomJcXocwHEcocJvOTk5kqRDhw45PAngDgQVfvvXgQOSpA8yMx2eBHAHggq/7d69W5K0LT3d4UkAdyCo8EtBQYG2p2+TJB3PO6bc3FyHJwKcR1Dhl8OHD1/y74PZ2Q5NArgHQYVfsj7MuuTfe/fudWgSwD142hT80rtXLx3PO3bJ2w4cOqioqCiHJgKcxxEqfJafn39ZTKWLT6MCwlVQgtohth3bd2Dbgdr+mTNnNDxhZOW/hyeM1PCEkSopKbH9a5m4f4Kx7VDYfiji1abgs86dO6tz5876a9qLkqS58+Y5PBHgDpzyA4BNCCoA2ISgAoBNCCoA2ISgAoBNCCoA2ISgAoBNCCoA2ISgAoBNCCoA2ISgAoBN/Hr5Pl40AYA3R/KOOj2Co4LyeqgdYtsFdEebvH3TZ5cC+0Nk+v4xdfZgbD8UccoPADYhqABgE4IKADYhqABgE4IKADYhqABgE4IKADYhqABgE4IKADYhqABgE4IKADYhqABgE4IKADYhqABgE4IKADYhqABgE4KKGlmFu7Xo/kFamlns9CiAEQgqvCs9qq1zZmhN9jmnJwGMQVDhRbFyNvxZe5reqGinRwEMQlBRTZmK9qdq2ZcDNW1QRzVyehzAIAQVl7AK92j1c9K4sfFqEuH0NIBZWEYakr5budT6VDv/9IyyBszRb7tep7LMJeo++E2NenWTEuOj+b6jTuG+SirLSDu8fffMXq6id5/WzxKe0xkv743sv1K7lvdTy2rbllhG2olth8L2QxGXyPCdK9Tkrpl6L29m5VtKqx2hAqgd11ABwCYEFV6c1YGXl2v+qnQV6Zi2rkpWys4TKnd6LMDlOOWHF83UacgUdRoyRbOdHgUwCEeoAGATggoANiGoAGATggoANiGoAGATggoANiGoAGATggoANiGoAGATggoANiGoAGATggoANiGoAGATggoANiGoAGATggoANiGoAGATggoANvFrGWnWZwfgTbgvO+1XUH1l+vrhrN1e87alwP4Qmb5/TJ09GNsPRZzyA4BNCCoA2ISgAoBNCCoA2ISgAoBNCCoA2ISgAoBNCCoA2ISgAoBNCCoA2ISgAoBNCCoA2ISgAoBNCCoA2ISgAoBNCCoA2ISg4lKl+dq1cpJ6t2+nDrG3qf/0jTpYXOb0VIARCCqqKFZO2hq93niYns/6QDvWjVXrt2Zp7LMZKnJ6NMAABBUXWSX6ul2CHh/TU7HRzRTba4TGDLxeZzbvVW6p08MB7tfI6QHgIhGt1OWeVlXeEKkrr26kyM5t1DLSsakAY3CEipqdP6p9O0rVb2gPtYlwehjA/ThCRQ08+uSVNdrSPUnr7osRPQXq5tcy0hXLByN0XLpccJmKs1M1bUUjTVk0Qh2jL5zv831HXcJ+2WkrCNq3jWX7Dmzbv+2XW9+eSrdmJ6Za2UWlF95SdNL6+ESRVe5l2+6b3z3bN3n2YGw/FHENFVVYKj39tp5J3K42A27SNzlZyszMUPrKuUo78g2n/UAduIaKi4r3acX4RK3LLpb2bLn49sgBWvxAM+fmAgxBUHFRdDclvnFAiU7PARiKU34AsAlBBQCbEFQAsAlBBQCbEFQAsAlBBQCb+BXU/Px8FRQU2D0LABjNr6CmrFql2+O7KiMjw+55AMBYfgX1/l/8QpI0esRIogoA3/ErqD169FDqSy9KIqoAUMHvm1JEFQAu1aC7/EQVAC5q8NOmiCoAXGDL81CJKgDY+MR+ogog3Nn6l1JEFUA4s/1PT4kqgHAVkL/lrx5VAAgHAXtxlKpRlS78/T8AhLIIy7IsXz+J9dkBeHMk76jTIzjKr6D6qiLAN8S2VWpammJiYmzffiC/kYHcvumzS4H9ITJ9/5g6ezC2H4qC9nqoqS+9qON5xzQ6IYHTfwAhKWhBrbimSlQBhKqgvmI/UQUQyoK+BApRBRCqHFlTiqgCCEWOLdJHVAGEGkdXPSWqAEKJ48tIE1UAocLxoEpEFUBocEVQJaIKwHyuCapEVAGYzVVBlYgqAHO5LqgSUQVgJlcGVSKqAMzj2qBKRBWAWVwdVImoAjCH64MqEVUAZjAiqBJRBeB+xgRVIqpAaLJUevqfWjS0p/ov3K1Cy1Lp6bc09/5bdfvj/1Sh0+P5wKigSkQVcKvJkyYpbcMGZWVl+faJ1hd6N/2Uuv7qbn2xdrPePfi2lqac0L1P/5eWjumqZoEZNyAaOT2APyqiOnrESI1OSHB6HACStqdv0/b0bZX/Hp4wUt26ddNt3brVvjBnRCv1HJcglezR4CVj9eQTrfXsyt+qe0vz8sQy0gAC7obYturbr5+6xMcrPj5ezZs3v/yDrFPa9rtf6veapf9Z1k8tI4I/Z0MZd8oPwDzH844pc/9+Hck9osOHD3v5iDIVvr9Zb537ka7d9k/tO1Ma9Bnt4NcRqq+CsX64dOG3YGpaWu2nF35un7XbvW9bkrHzB3r7Js/uz/arn7lWPSq9+eabvf9cWl8oc3OG/q/xSb3xdhs9NrOVXuozSfuHztTwr/+tyHGPakDrKxv6vxI05l2kqMHUpCQlL1ig0QkJAYkqgLpVXDft+OMfKy4uru5PKD6sN56eqtfiZ2vd4vt1ffR5Dfn9PXpl/qs6smShHjUoplIIBXXCxAmSRFQBh/h1tNzkbs3am6NZlW+IUrshS/X+EBsHC6KQCapEVO1RpuKju/S3F1L1+ict1K3zNcrf+YHO/eQhPfbgfYqLjnR6QMC1QiKoVX8zmhbVQF4D8905nd65Qol/+kQ/WzxfL3VtdeEB8uhZfZTyiAaMPa6Nz4/XLSEUVXftf9+YPHuoCsm7/BMmTtDUpCSe/O8TS9/kbNKMB7eqdeJU/boippIU0UydhoxUnw9S9MzWoyp3ckzAxUIiqFbhbi26f5CWZhZXvs31US3N166Vk9S7fTt1iL1N/adv1MHiMufmsU5o+7PLtSt2mMb1i73s1CWixU26Pb5M7295X8cD/ryQAHPbvveTt8c9nGV+UEuPauucGVqTfe6yd7k3qsXKSVuj1xsP0/NZH2jHurFq/dYsjX02Q0UOTWTl7dJf//usOgztpY5XeXlGdcTVatzkSinnMxWY154q3Lfv/VLL4x7OMTyoxcrZ8GftaXqjomv4CFdG1SrR1+0S9PiYnoqNbqbYXiM0ZuD1OrN5r3IdeT5zuYqOHVa2rtddHVvL6xVS65y+LvpWahmtKAP/gqWS6/a9P+p+3MMZBge1TEX7U7Xsy4GaNqhjrXfXXBfViFbqcs9Niq4MU6SuvLqRIju3UUtH7veUq+RsoUp0tZpE1fC8v6ITOnSgWNfcHqcYk+9JuW7f+6r+j3sEn7FBtQr3aPVz0rix8WpSjyMm10W1qvNHtW9HqfoN7aE2jhz9Rappy1aK1jkVeb718v4yFex5U1tKbtXYwfFqGvT5Asjxfe8bXx/3CC4zg2p9qneWbtJV44erS5P6H1a4M6oeffLKGm3pnqTp98XImZ+RCF1zSy/9suWn2vXhcZ2v9l6r+CNtXLtN1wybqIQuoZRTN+x7H/j5uEcQWUHQvm2sTx9fmrXCuqdtrNX+sv/aW/esyLQKds217vD6/ljrxkfesD6vY/spq1Ks9m1jrZ/07GmdPHkyyPNnWaUXP9Iq+tdfrAkTUq3sotJatui/+s/usY5vnmp1i59q/f24p/Kt5UW5VvoTg607Hrp8xor/r0AK3PbdtO/ro8z6qoGPe18F+nsbilwZVF99u/9Zq2vbvtaS/UX1/hxfohqY+cutb0+lW7MTL/5AlxedtD4+UWSV2/hVfJv9G+v0e89b0/r3t0b/8Wnr2ScetcY8kGgt3LTf+vzby6cyN6hu3Pe+8+dx7wuC6ruwvabt7F9UWSo9/baeSdyuNhMS9E1OljJ1TqfffEF77nhKT7Zx6t7t1frBHb/Rwq2/cejrB4Nb9z1CgeFBPasDL6dq8/Z0FemUtq5K1tWjxunhXtfX6+KwY1Et3qcV4xO1LrtY2rPl4tsjB2jxAyYt+GCgkNj3DXvcI3BC4vVQG2p1ymolL1hQ4+upun3+2vB6qM4xeXbJ/PmdwC80ufXuPwDThERQ7Vjjyqmosj6Xs0ze/ybPHqpCIqh24UgVQEMQ1GqqRnX+vHnyeDxOjwTAEIbf5Q+Mqnf/AaC+/LrLz7UbAN6E/bMCgvHXA2b+Nc0FFX9RNWniRKukpMT27Zu8b8z9S6ngbN/k2YOx/VDENdQ6VJz+b0/fpqmPPcY1VQA1Iqj1NDUpiagCqBU3peqp+o2q5MWLFRUV5eRIAFyGoPqAqAKoDUH1EVEFUBOC6geiCsAbguonogqgOoLaAEQVQFUEtYGIKoAKBNUGRBWARFBtQ1QBEFQbEVUgvBFUmxFVIHwR1AAgqkB4IqgBQlSB8ENQA4ioAuGFoAYYUQXCB0ENAqIKhAeCGiREFQh9vGJ/EFUsUe3qV/4vzdeulZPUu307dYi9Tf2nb9TB4jKnpwKMwBFqkLl7iepi5aSt0euNh+n5rPnSvhc1/7FZGhsdozdn360mTo8HuBxHqA6YMHGChieM1Pb0bZLkniNVq0Rft0vQ42N6Kja6mWJ7jdCYgdfrzOa9yi11ejjA/SIsy7J8/aQOse0CMQuCrO411L/S+wuGaPSh8drxlyH6STu+76hd3Y+p0ObXKb+vO61DbLuA7mhTt+/xeNTp5o6SpD79+gbkRlWDZj9/VPt2lKrfoz3UJuLy73vFL1YT930wtm/y7MHYfijiGqqDKuLZp1/fytN/99z99+iTV9ZoS/ckrbsvRhFOjwMYgKC6QPLixZIU8KiWfbRSvQckK/+y90QqZtqrenvyLYq88JEqzt6oRf97p5Ys+qlaNyKnQH0QVBeIiooKSlQjb5msd/Im1/FRlkpP/0OLnmukKYtGqGN0pKzifOWcvVY3tonmSBWoBUF1iWBFtXaWSk+/rWcSt6vNhAR9k5OlTJ3T6Tdf0J47ntKTbaKDOAtgHoLqIo5HtXifVoxP1LrsYmnPlotvjxygxQ80C84MgMEIqss4GtXobkp844ASA/+VgJBEUF3I8SNVAH4hqC5FVAHzEFQXI6qAWQiqyxFVwBwE1QBEFTADQTUEUQXcj6AahKgC7kZQDUNUAfciqAYiqoA7EVRDEVXAfQiqwYgq4C4E1XBEFXAPghoCvEV15apVTo4EhCVWPQ0RFVGtWE5ldcpqp0cCwg5HqCGk6pFq8oIFDk8DhB+CGmKIKuCcCMuyLF8/qWL5YACoKtyXnfYrqL4yff1wU9du93g86nRzR0nS1KQkTZg4wdbtV/xiNXXfB3r7Js8ejO2HIm5KhbCKp0716ddXyQsWcKMKCDCuoYaB6tdU7T5SBXABQQ0D3m5UEVXAfgQ1TBBVIPAIahghqkBgEdQwQ1SBwCGoYYioAoFBUMMUUQXsx/NQw1jVF1QJieeplp/SzjkD1aHjHO38qtzpaRCGOEINc24/Uq3/X+qcVeayKfrt56P017knlf3Zeanp9wI6G1AdQYXro1of5ad26rm1UXpsy8907cd7dWd7YorgI6iQZF5UCwoKJEnNmzeXdFYfbkzVP+L669F2X+jwx7Hqx8UsOICHHSq5/ZpqQUGBduzYocmTJulXgwcrMzPzwju++lCb136sToPuUKvdH0pd2/LAhiM4QsUl3HikWlBQoE0bNyl5wQJNTUrSQw8/rM6dO1e+v/yzPP2rpIsGxB7VC5+012/uucrBaRHOCCou46aoZmRkaOaMGRo6bLjez9z/3Sl+VeUqzj+qf1/zmbbuKNPKJ+MV7cikAEFFDdwQ1YqYrlm7VnFxcTV8VLlKzhaqpG0v/e6RPvoh5/pwEEFFjZyMakFBgUaPGKl33t2lmJiYGj+u/NO9evn1Q+r98HT1+gGn+nAWv89RK6duVGVmZmpqUlKtMVV5rl772zn9ctoYNTp6WsXlp7Tzyae0/vBXQZkRqI4jVNTIKtyt5FGLdOVTqY4cqTZpUsfV0CviNHBynFR+SkPPTtStP5JGrUvR7JuaBnw2wBuCCu9Kj2rrnBlak91Yjyj4q6nGx8frV4MHKzo6Wvf16VO5nItXV/xQvZ7YoiNPBHwsoFac8sOLYuVs+LP2NL3xkjvmUVFRemruXN0Q2zbgUW3evLlS09K0d+9e3d+3rzIyMgL69QA7EFRUU6ai/ala9uVATRvU8bJTmIrQ3RDbNuCTxMTEaO68eVqzdq1mzpih/Pz8gH9NoCH8Wka6YvlgmK/6i49YhbuV/Mcs/XThQ7ol9z/VffCbGvXqJiXGRwf0+17Xi6AsWrhQXeLjde+990riMehW4b7stF/XUH3daaavHx42a7dbn+qdpZt01fg56tIkUmXV3l19O1WjNjUpKWA3qjwejzL379fIhIQaZ/FX2HxvXbj9UMRNqTBS9tFK9R6QrMtPnCMVM+1l/f3WdP1h/RadWb9Fy6u8d8XgTkrpv1K7lvdTSy/brXpNNRBRXb9uvdp36FD7U6gAFyCoYSTylsl6J29yLR/RRe/lzaz8V2nmkktO+WuSmpam0QkJtkfV4/Fo3ty5KiwsrHyGAeBm3JRCg8XExFTeqLLryf+5ubka++tf69prr1Xy4sW1P20KcAmCCi/O6sDLyzV/VbqKdExbVyUrZecJ1baoSEOiWlBQoNzcXEkXjkpXp6zWww8+qHEPPqhp06cTUxiDU3540UydhkxRpyFTNNuHz6qIqi+n//n5+RqdkKAWLVoqYVSCli1dqqHDhuuNbdsIKYxDUGErX6KakZGh0SNGSpKO5x3Tdc2vq+OVpQB345QftqvP6X/ahg2VMa3QsmVLYgqjcYSKgKjpSNXj8WjF8uVasypFN8S21Z133aVu3bqp1fe/rxYtWjg8NdAwBBUB4y2q/Qf0138MGqRHpkyp1zVSnlwOk3DKj4Cqfvr/2tbXFBcXxw0nhCSCioALxPNUATciqAgKoopwQFARNEQVoY6gIqiIKkIZQUXQEVWEKoIKRxBVhCKCCscQVYQaggpHVY9q2oYNTo8E+I2gwnFVozrn8VmscApjEVS4QtWojh4xkqjCSAQVrkFUYTqWkQZgm3B/IRu/guor05e7ZanhmrctBeaHqOKV/I/nHVPqSy+qR48etn8Nie+tk9sPRZzyw5UqTv8lcfoPYxBUuFZMTIwkcU0VxiCocD1uVMEUBBWux91/mIKgwghEFSYgqDAGUYXbEVQYhajCzQgqjENU4VYEFUYiqnAjggpjVY9qVlaW0yMhzP0/gXsf8uJBLrcAAAAASUVORK5CYII=)
Which of the following is an equation of line
in the xy -plane above?
Maths-General
General
Identify the synonym for the word ‘draw on’
Identify the synonym for the word ‘draw on’
GeneralGeneral
General
Identify the thesaurus for the word ‘negative’.
Identify the thesaurus for the word ‘negative’.
GeneralGeneral
Maths-
Express 23.324242424….. in p/q form, where p and q are integers
Express 23.324242424….. in p/q form, where p and q are integers
Maths-General
General
Identify the synonym for the word ‘brings out’.
Identify the synonym for the word ‘brings out’.
GeneralGeneral
General
Identify the definition of a ‘complete sentence’.
Identify the definition of a ‘complete sentence’.
GeneralGeneral