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

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

(i)  0. bar(365)

#### 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
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