1.55555....as a fraction

[darkyadoo]

Hi,
It is asked to write [imath]1.\dot 5[/imath] as a fraction (GCSE Higher)

I use the geometric series formula but I don't know whether I can use it at this level or not?

[imath]1.\dot 5=1+5\sum\limits_{k^\ge 1}(10^{-1})^k=1+5\left(\dfrac{1}{1-10^{-1}}-1\right)=\dfrac{14}{9}[/imath]

Thanks

 

[topsquark]

What level are you at? IMHO if you know the formula, use it!

-Dan

PS Here's the Algebraic method:
Let S = 1.5555...

10S - S = 15.5555... - 1.5555... = 14

9S = 14

S = 14/9.

 

[darkyadoo]

What level are you at? IMHO if you know the formula, use it!

-Dan

I must take the GCSE exam or an equivalent so I imagine I can't use any tools from A level or University

 

[Otis]

Hi darkyadoo. I'm not familiar with GSCE, but you could experiment with dividing Whole numbers by 9. (I learned that pattern in grade school, so maybe it's kosher for GSCE.)

There's also an algebraic method, for converting repeating decimals to rational form.

?

 

[darkyadoo]

Thanks !!!

 

[darkyadoo]

What level are you at? IMHO if you know the formula, use it!

-Dan

PS Here's the Algebraic method:
Let S = 1.5555...

10S - S = 15.5555... - 1.5555... = 14

9S = 14

S = 14/9.

Perfect, I didn't notice your answer !