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Express Each of the Following as a Rational Number in Its Simplest Form: (I) ` 0. Bar(365)` - Mathematics

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Express each of the following as a rational number in its simplest form: 

(i) ` 0. bar(365)`

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Solution 1

Let x =`  bar (0.365)`
∴ x = 0.3656565                             …(1)
10x = 3.656565                                  …(2)
1000x = 365.656565                           …(3)
On subtracting equation (2) from (3), we get
990x = 362 ⇒ x = `362/990 = 181/495`
∴ `bar( 0.365 )= 181/495`

Solution 2

Let x =`  bar (0.365)`
∴ x = 0.3656565                             …(1)
10x = 3.656565                                  …(2)
1000x = 365.656565                           …(3)
On subtracting equation (2) from (3), we get
990x = 362 ⇒ x = `362/990 = 181/495`
∴ `bar( 0.365 )= 181/495`

Solution 3

Let x =`  bar (0.365)`
∴ x = 0.3656565                             …(1)
10x = 3.656565                                  …(2)
1000x = 365.656565                           …(3)
On subtracting equation (2) from (3), we get
990x = 362 ⇒ x = `362/990 = 181/495`
∴ `bar( 0.365 )= 181/495`

Concept: Euclid’s Division Lemma
  Is there an error in this question or solution?

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