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Express each of the following in the form which form p/q 0.222... |
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Answer» Given: 0.22222222........ To find: The p/q FORM of 0.222....... Solution: x = 0.222........ - eq.1 Multiplying both sides with 10 we get, 10x = 2.222....... - eq.2 Subtracting eq.1 from eq.2 10x = 2.222........... - x = 0.222.......... ----------------------------- 9x = 2.000........... ------------------------------ 9x = 2 Therefore, x = 2/9 which is in p/q form (p = 2 and q = 9) where q not equal to 0. Information: The above done method is called as x method of finding an NON - TERMINATING recurring number to p/q form. We must multiply both the sides with periodicity i.e on how much digits the bar is that MANY zeros after 1 must be multiplied. Ex: 0.2 bar - since bar is on one digit we must multiply it with 10. |
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