What is negative 1.41 repeating as a fraction?

Answer 1

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