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covert this repeating decimal into a fraction

Covert This Repeating Decimal Into A Fraction class=

Sagot :

Answer: 4311/9900 or 479/1100

Step-by-step explanation:

Okie so in order to do this, we need to get rid of the repeating part of the decimal

==============================================================

Right now we have x = 0.435454545454...

If we multiply this by 100, we get

100x = 43.545454545454

And if we multiply by 10000 we get

10000x = 4354.5454545454

==============================================================

Subtract the two equations

10000x = 4354.5454545454

100x = 43.545454545454

------------------------------------------------- (notice: the repeating part will cancel out)

9900x = 4311

x = 4311/9900

If you simplify the fraction you get: 479/1100

The fraction that represents the repeating decimal is

[tex]\frac{479}{1100}[/tex]

Given :

A repeating decimal  [tex]0.4354545454...............[/tex]

there is bar at 54 , so 54 is repeating

We need to convert this decimal into fraction

54 is repeating so we multiply by 100

Let x= [tex]0.4354545454...............\\[/tex]

[tex]100x=43.54545454...............[/tex]

Now we subtract x from 100x

[tex]100x=43.54545454...............\\ x= 0.4354545454...............\\-----------------------------------------\\ 99x=43.11[/tex]

Now divide both side by 99

[tex]x=\frac{43.11}{99} \\[/tex]

multiply top and bottom by 100 to remove the decimal

[tex]x=\frac{4311}{9900} \\Divide \; top \; and \; bottom \; by 9\\x=\frac{479}{1100}[/tex]

Learn more :

brainly.com/question/15666599

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