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n200080 [17]
3 years ago
14

Convert 11.42424242 … to a rational expression in the form of a over b, where b ≠ 0.

Mathematics
1 answer:
Lapatulllka [165]3 years ago
5 0

Let <em>x</em> = 0.424242... . Then 100<em>x</em> = 42.424242... . So we can write

100<em>x</em> - <em>x</em> = 99<em>x</em> = 42.424242... - 0.424242... = 42

which means

<em>x</em> = 42/99 = 14/33

and so

11.424242... = 11 + 14/33 = 377/33

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