Recurring decimals my ass! (1 Viewer)

[Gavvvvvin]

Express 0.909 (where that last 9 is a recurring decimal) as a fraction.

So i go let 0.909 = x
1000x = 909.999 . . .
100x = 90.999 . . .
therefore 900x = 1000x - 100x
900x = 819
x = 819/900
x = 91/100
= 0. 91

I fail to see where i am going wrong. Someone please enlighten me.

 

[Xayma]

I can't remember who posted it (but it was an issue with 0.9^..

For 2 numbers to be different, there must be a number between them. Now there is no number between 0.91 and 0.909^. ∴ they are the same number.

 

[Gavvvvvin]

So there was nothing wrong with my method? ive sitting here for like half an hour stuck on the first question of this stupid test paper =P

 

[Xayma]

Nothing wrong with it the fractional equivalent is 91/100.

 

[Estel]

0.9099999... does = 0.91 I can confirm.

Three methods:
Yours

Definition: Xayma mentioned it.

Limiting series:
0.9099999...
= 0.9 + 0.009 + 0.0009...
= 0.9 + a GP with a=0.009 and r=0.1
= 0.9 + 0.009/0.9
= 0.91

Identifying 0.909999... by inspection allows you to get the fraction 91/100 immediately, saving valuable test time [unless your school, like mine, sets retarded tests].

 

[Iota]

My teacher would mark my answer as incorrect for placing "0.91" in place of the answer "0.909...".

 

[jhakka]

Express 0.909 (where that last 9 is a recurring decimal) as a fraction.

So i go let 0.909 = x
1000x = 909.999 . . .
100x = 90.999 . . .
therefore 900x = 1000x - 100x
900x = 819
x = 819/900
x = 91/100
= 0. 91

I fail to see where i am going wrong. Someone please enlighten me.

You should have left it at 91/100 and not changed it to 0.91?

 

[Iota]

You should have left it at 91/100 and not changed it to 0.91?

There is nothing wrong with that step, so I don't see how it would have any impact.

Of course, from the perspective that they usually want the answer in fraction form, you are correct.

 

[jhakka]

There is nothing wrong with that step, so I don't see how it would have any impact.

Of course, from the perspective that they usually want the answer in fraction form, you are correct.

The only reason it would impact is because the question specified that it should be expressed as a fraction.