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I assume you mean the fraction for -1.414141...
-1.414141... = -141/99
= -140/99
-1.414141... = -1 + -0.414141...
So to solve the fractional bit -0.414141....
let x be the fraction for the decimal; then:
x = -0.414141....
multiply both sides by 100:
100x = -41.414141....
Subtract the first from the second:
100x - x = -41.414141... - -0.414141....
⇒ 99x = -41
⇒ x = -41/99
which has solved the fractional bit, now the whole is:
-1.414141... = -1 + -0.414141....
= -1 + -41/99
= -141/99
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