Question

Please Help
IMMEDIATELY

Answer 1

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)`

Answer 2

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