express 7.84684846 as a rational number in the form p/q were p and q have no common factors

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07-10-2020
Mathematics

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express 7.84684846 as a rational number in the form p/q were p and q have no common factors

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LammettHash LammettHash · Answer 1 · 2020-10-07T02:25:54+02:00

It's not clear what the pattern is supposed to be for the digits in the givne number. It looks like the repeating block should be 846, but it could just as easily be 84684.

Assume the first case, and let x = 7.846846846... . Then

1000x = 7846.846846846...

Subtract x from this to cancel the repeating decimal part, then solve for x :

999x = 7846 - 7 = 7839

x = 7839/999 = 871/111

If instead you meant the second case, let x = 7.846848468484684... . Then

10⁵ x = 784,684.846848468484684...

Solve for x :

99,999 x = 784,684 - 7 = 784,677

x = 784,677/99,999 = 261,559/33,333

Maybe you meant something else altogether?