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Question
Express the following decimal expression into rational number
`-21.213bar(7)`
Solution
Let x = −21.2137777… ………..(1)
10x = −212.137777…… ………..(2)
100x = −2121.37777…… …………(3)
1000x = −21213.77777…. ………..(4)
10000x = 212137.77777….. …………(5)
(Now period of decimal is 1, multiply equation (4) it by 10)
(5) – (4)
10000x – 1000x = (−212137.7777…) – (−21213.7777…)
9000x = −190924
x = `-190924/9000`
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