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Express 0.`Bar(4)` as a Rational Number Simplest Form. - Mathematics

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Express 0.`bar(4)` as a rational number simplest form.

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Solution

Let x be 0.`bar(4)`
x = 0.`bar(4)` ….(1)
Multiplying both sides by 10, we get
10x = 4..`bar(4)`….(2)
Subtracting (1) from (2), we get
10x – x = 4..`bar(4)` - 0..`bar(4)`

⇒9x = 4
⇒x = 49
Thus, simplest form of 0..`bar(4)` as a rational number is `4/9`.

Concept: Revisiting Rational Numbers and Their Decimal Expansions
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