Write the following rational numbers as ratios of integers. -5.0828282 and 7.421421421

- anonymous

Write the following rational numbers as ratios of integers. -5.0828282 and 7.421421421

- katieb

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- amistre64

the .421 is 421/999

- anonymous

Isn't there more to it or is that just the first step?

- amistre64

1000(-5.08282...) = -5082.8282...
- 10(-5.08282...) = -50.8282...
------------------------------
1090=-5082-50
then divide of the left side

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## More answers

- amistre64

990, forgot how to subtract

- amistre64

this is a simple way to do it without having to resot to mathematical induction

- amistre64

spose you get:
.abcabcabc
then there are 3 numbers repeating; put the repeaters over 3 9s
abc/999

- anonymous

wait where is 990 supposed to go? And what is final answer to -5.08282?

- amistre64

rename: A=-5.08282...
1000 A = -5082.8282...
- 10 A = -50.8282...
------------------------------
990 A= -5082-50
A= -5132/990

- amistre64

so A = A
-5.08282.... = -5132/990

- amistre64

reduce as needed

- anonymous

alright i will reduce and thanks... what about the other problem or was that the final answer at the top?

- amistre64

the final answer up top; just dont forget to add back in the 7
7+ 421/999
and reduce ;)

- anonymous

wait so reduce and add 7 to the numerator or denominator or both haha

- amistre64

its just a 7, nothing special about it.
7 + fraction

- amistre64

and i need to recheck my calculations on the other one prolly

- anonymous

alright haha can i put it in the calculator and also how do i show my work for this problem?

- amistre64

depends on what level your spose to know; if this is for mathematical induction proofs, then youll have to go another route, otherwise id just do as i did

- amistre64

the -5 is throwing me off i think; lets avoid it and go for the deci instead
A = .08282
1000A = 82.8282
- 10A = .8282
----------------
990A = 82
A = 82/990 let me see what the wolf makes of that

- amistre64

http://www.wolframalpha.com/input/?i=-5-82%2F990
much better

- amistre64

-(5+frac) so include back in the number part

- anonymous

wait now i am confused more

- amistre64

tell me where you got lost :)

- anonymous

on both answers haha i thought i had the 1st one right then you said you might have got it wrong.

- amistre64

the first one was good; it was the last one that the negative part was messing with me.
7 + frac = 7 + 421/999
-(5 + frac) = -(5 + 82/990 )

- anonymous

alright so for the first one i got 7414/999 cause the fraction is added by 7 is that correct?

- amistre64

yep that ones good

- anonymous

Ok so the answer is 7141/999 and that can't be reduced... i am just making sure.

- anonymous

sorry meant 7414/999

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