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1018
 one year ago
express the repeating decimal as ratio of two integers :
1018
 one year ago
express the repeating decimal as ratio of two integers :

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campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0multiply you number by 10, what do you get..?

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0then multiply the number by 1000 what do you get...?

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0then its let the number be x 1000x = number  10x = number  do the subtraction and solve for x

1018
 one year ago
Best ResponseYou've already chosen the best response.0@phi so should i separate the 5 first and solve for the decimals only?

1018
 one year ago
Best ResponseYou've already chosen the best response.0@campbell_st wait is this correct 5.215 x 10?

phi
 one year ago
Best ResponseYou've already chosen the best response.10.2151515... the trick is to give that infinitely repeating expansion a name like x x= 0.2151515... then multiply both sides by 10 10x = 2.151515... now do 1000x 1000x = 215.151515...

1018
 one year ago
Best ResponseYou've already chosen the best response.0but how bout the two? its not repeating is that ok? @phi

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0yes so 10x = 52.151515....... and 1000x = 5215.15151515... the subtraction eliminates the recurring part of the decimal...

phi
 one year ago
Best ResponseYou've already chosen the best response.1we multiply by 10 to move the "2" to the left, leaving 0.151515.. then we multiply the original by 1000 to get another number with 0.1515...

1018
 one year ago
Best ResponseYou've already chosen the best response.0@campbell_st so that leaves me with 990x =5163? then x right?

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0thats correct... so now solve for x, you'll have an improper fraction

1018
 one year ago
Best ResponseYou've already chosen the best response.0it gave me the same but the 15 repeated 4 times only

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0then change the improper fraction to a mixed number and that's the answer

phi
 one year ago
Best ResponseYou've already chosen the best response.1**it gave me the same but the 15 repeated 4 times only*** on your calculator? it has limited number of digits to show

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0an altenate method is to treat the recurring decimal as a geometric series... the common ratio is < 1 so you can find the infinite sum but the multiplication by multiples of 10 is the easiest

1018
 one year ago
Best ResponseYou've already chosen the best response.0@phi no sorry, what i meant was it gave me almost the same but this time the number 15 only showed up 4 times, and yeah its limited @campbell_st is this correct? 5(71/330)

phi
 one year ago
Best ResponseYou've already chosen the best response.1the original question wants a ratio of two integers, so leave the answer 1721/330

phi
 one year ago
Best ResponseYou've already chosen the best response.1see http://www.wolframalpha.com/input/?i=1000+digits+1721%2F330%3D

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0well that is 1650 + 71 = 721 so that seems correct... so I'm unsure if you only need the faction 71/330 or the improper fraction as the answer. I'd probably give the mixed number answer

1018
 one year ago
Best ResponseYou've already chosen the best response.0oh wait now what. hahaha. so just remove the 5?

1018
 one year ago
Best ResponseYou've already chosen the best response.0how bout you @phi you still think its the original one?

phi
 one year ago
Best ResponseYou've already chosen the best response.1***express the repeating decimal as ratio of two integers : \[ 5.2\overline{15} = \frac{1721}{330}\]

1018
 one year ago
Best ResponseYou've already chosen the best response.0ok thanks ill see what to put as the answer. haha. thanks guys!
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