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IMMEDIATELY

Please Help IMMEDIATELY-example-1

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Answer:

Let x equal the recurring decimal:


\sf Equation\:1: \quad x=0.216216216...

Create another number with recurring 216s by multiplying the above expression by 1000:


\sf Equation\:2: \quad 1000x=216.216216...

Subtract Equation 1 from Equation 2 to eliminate the recurring digits after the decimal:


\sf \implies 1000x-x=216.216216...-0.216216...


\sf \implies 999x=216

Divide both sides by 999:


\sf \implies (999x)/(999)=(216)/(999)


\sf \implies x=(216)/(999)

Simplify:


\sf \implies x=(216 / 27)/(999 / 27)=(8)/(37)

User Gajo
by
8.0k points
5 votes

Step-by-step explanation:

Let the recurring decimal be x

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

x = 0.216216216216...

1000x = 216.216216...

1000x - x = 216

999x = 216

x = 216/999

x = 8/37

User Alistair Nelson
by
8.3k points

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