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Rewrite as a simplified fraction. \large{3.\overline{5} = {?}}3. 5 =?3, point, start overline, 5, end overline, equals, question mark

Sagot :

Given:

The number is [tex]3.\overline{5}[/tex].

To find:

The simple fraction of the given number.

Solution:

Let us assume,

[tex]x=3.\overline{5}[/tex]

Then,

[tex]x=3.555...[/tex]                 ...(i)

Multiply both sides by 10.

[tex]10x=35.555...[/tex]          ...(ii)

Subtracting (i) from (ii), we get

[tex]10x-x=35.555...-3.555...[/tex]

[tex]9x=32[/tex]

[tex]x=\dfrac{32}{9}[/tex]

Therefore, the simplified fraction form of the given number is [tex]\dfrac{32}{9}[/tex].

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