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OpenStudy (anonymous):
convert recurring decimal 2,232323 to to common fraction
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OpenStudy (unklerhaukus):
\[\qquad x=2.232323...\]\[100x=223.232323...\] \[99x=\]
OpenStudy (tyteen4a03):
I assume that you mean \[2.2323232323...\] in the question. Let x be 2.232323.... Then 100x would be 223.232323... Now this is the tricky part, we subtract x from 100x. Visualization is: 223.232323... 002.232323... ------------- 221 <- This is 99x. Now that we have 99x = 221, just solve this equation. Because x and 100x have this common part .232323..., it is safe to subtract each other to get rid of this part.
OpenStudy (unklerhaukus):
tyteen4a03 has explained this very well
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