What is the value of 0.3̅4̅2̅1?

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Original question: What is the value of 0.3̅4̅2̅1?

The bars above have two meanings

  1. Forever Recurring decimals
  2. Negation of that place.

Since recurrence has to be forever, so we can never tell when will 1 come at the end.

But in this case, decimal can be written as (342/999) + (1/10000).

Simplification is an homework for you.

In second case, 0.3̅4̅2̅1 Would mean that those places with bars are negative.

So, 0.3̅4̅2̅1 = (1–0.342) + (1/10000) = 0.6581

Please upvote is you think this resolves your query. Or please comment and let me know if anything is wrong in here. I will correct it.

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