- #1
donaldcat
- 7
- 0
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?
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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