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## Main Question or Discussion Point

**Simple maths but i don't understand why (about recurring/repeating decimals)**

When calculating recurring decimals, we let X to be that number to calculate it for example:

0.4* = x

4.4* = 10x

10x - x = 4.4* - 4*

9x = 4

x = 4/9

Therefore 0.4* = 4/9

But I when I calculate 0.9* this, i get

0.9* = X

9.9* = 10X

10X - X = 9.9* - 0.9*

9X = 9

X = 1

Therefore 0.9* = 1

but we know that 0.9* = 0.999999999............................. is close to 1 and not equal to 1

but how can we prove 0.9* is not equal to 1?

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