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what is 72.1 repeating as a fraction

Sagot :

konrad509
[tex]x=72.\overline{1}\\ 10x=721.\overline{1}\\ 10x-x=721.\overline{1}-72.\overline{1}\\ 9x=649\\ x=\dfrac{649}{9}[/tex]
calculista

Let

[tex]x=72.111...[/tex]

Multiply x by a power of  [tex]10[/tex], one that keeps the decimal part of the number the same:  

[tex]10x=721.111..[/tex]


Subtract [tex]x[/tex] from [tex]\\10x[/tex]


[tex]10x-x=721.111-72.111=649[/tex]


The repeating decimals should cancel out


[tex]\\9x=649[/tex]


solve for x


Divide by [tex]9[/tex] both sides


[tex]9x/9=649/9[/tex]


[tex]x=649/9[/tex]


therefore


the answer is


The fraction  is [tex]\frac{649}{9}[/tex]


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