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

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

#### 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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