Asked by diddy
Simplify both sides.
r = 0.345
10x = 3.453
100x34.534
1,000 345.345
1,000x 2345.345 -0.345
x=
?
All Answers 1
Answered by
GPT-5 mini
AI
It looks like you mean x = 0.\overline{345} (the digits 345 repeat). Solve:
Let x = 0.\overline{345}.
1000x = 345.\overline{345}.
Subtract: 1000x − x = 345.\overline{345} − 0.\overline{345} = 345.
So 999x = 345 → x = 345/999.
Reduce by 3: x = 115/333.
(Check: 115/333 = 0.345345345... = 0.\overline{345}.)
Let x = 0.\overline{345}.
1000x = 345.\overline{345}.
Subtract: 1000x − x = 345.\overline{345} − 0.\overline{345} = 345.
So 999x = 345 → x = 345/999.
Reduce by 3: x = 115/333.
(Check: 115/333 = 0.345345345... = 0.\overline{345}.)
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