Question

When writing 3.7272727272... as a ratio of integers, what is the common ratio?

Answer 1

The answer is:    "41 / 11 " ;  or, write as:  " 41 : 11 " .
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Explanation:
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72/99 = (72÷9) / (99÷9) = 8/ 11 . 

So, 3.727272727272...   =   "3 $\frac{8}{11}$ " .

→  "3 $\frac{8}{11}$ " =   [(11 *3) + 8] / 11 =  (33 + 8) / 11 = 41 / 11 .
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  "41 / 11" cannot be simplified any further; so the answer is:
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  "41 / 11 " ;  or, write as:  " 41 : 11 " .
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