Question

Please Help IMMEDIATELY

Answer 1

Explanation:

Let the recurring decimal be x

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x = 0.216216216216...

1000x = 216.216216...

1000x - x = 216

999x = 216

x = 216/999

x = 8/37

Answer 2

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:

$\sf \implies \dfrac{999x}{999}=\dfrac{216}{999}$

$\sf \implies x=\dfrac{216}{999}$

Simplify:

$\sf \implies x=\dfrac{216 \div 27}{999 \div 27}=\dfrac{8}{37}$