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Express 0.`Bar (23)` as a Rational Number in Simplest Form. - Mathematics

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Express 0.`bar (23)` as a rational number in simplest form.

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Solution

Let x be 0.`bar (23)`
x = 0 .`bar (23)` ….(1)
Multiplying both sides by 100, we get
100x = 23.`bar (23)` ….(2)
Subtracting (1) from (2), we get
100x – x = 23.`bar (23)` - 0.`bar (23)`
⇒99x = 23
⇒x = `23/99`
Thus, simplest form of 0.`bar (23)` as a rational number is` 23/99`.

Concept: Revisiting Rational Numbers and Their Decimal Expansions
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