Express each of the following repeating decimals as a fraction:
0.426 (repeating sign over 6) as a fraction=?
0.426 (repeating sign over the 26) as a fraction=?
0.426 (repeating sign over 426) as a fraction=?

Question

anonymous · Answer

$$0.42\overline{6}=\frac{42}{100} + \frac{0.\overline{6}}{100}=\frac{42}{100}+\frac{x}{100}$$
$$x=0.\overline{6}$$$$10x=6.\overline{6}$$$$10x=6+x$$$$9x=6$$$$x=\frac{6}{9}$$
$$0.42\overline{6}=\frac{42}{100}+\frac{\frac{6}{9}}{100}$$And then you can do some manipulation of fractions to make it a single fraction.

anonymous · Answer

Okay I see! and then would the next one be 10x=.26 ?\
Thank yoU!

anonymous · Answer

Yes, that's the jist of it. Then your fractions would be $$0.4\overline{26}=\frac{4}{10}+\frac{0.\overline{26}}{10}$$, and you can replace the 0.26 with whatever fraction x is.

anonymous · Answer

Oh I see!! Thank you :)

anonymous · Answer

Oh actually, I misread your text a bit. You set $$x=0.\overline{26}$$ first of all. Then your next step is to multiply by some power of 10, so that there is one block of the repeating digits before the decimal point, and then the repeating block after it, so:$$100x=26.\overline{26}$$, and so on.

anonymous · Answer

oh i see now. thank you!