Prove algebraically that 0.5 recurring = 5/9
1 answer:
Answer and Step-by-step explanation:
We want to prove that 0.5555... = 5/9.
First, let's set 0.555... equal to x:
x = 0.555...
Now multiply this by 10:
10x = 5.555...
Now subtract the original from this new one:
10x = 5.555...
- x = 0.555...
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9x = 5
Note that we could cancel all the recurring terms because they were the same for both 5.555... and 0.555... since the 5's go up to infinity.
We now have 9x = 5, so divide both sides by 9:
x = 5/9, as desired
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