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1018

  • one year ago

express the repeating decimal as ratio of two integers :

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  1. 1018
    • one year ago
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    \[5.215=5.2151515...\]

  2. 1018
    • one year ago
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    15 is the repeating

  3. campbell_st
    • one year ago
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    multiply you number by 10, what do you get..?

  4. campbell_st
    • one year ago
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    then multiply the number by 1000 what do you get...?

  5. campbell_st
    • one year ago
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    then its let the number be x 1000x = number - 10x = number ------------------ do the subtraction and solve for x

  6. 1018
    • one year ago
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    @phi so should i separate the 5 first and solve for the decimals only?

  7. 1018
    • one year ago
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    @campbell_st wait is this correct 5.215 x 10?

  8. phi
    • one year ago
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    0.2151515... 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...

  9. 1018
    • one year ago
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    but how bout the two? its not repeating is that ok? @phi

  10. campbell_st
    • one year ago
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    yes so 10x = 52.151515....... and 1000x = 5215.15151515... the subtraction eliminates the recurring part of the decimal...

  11. phi
    • one year ago
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    we 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...

  12. 1018
    • one year ago
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    @campbell_st so that leaves me with 990x =5163? then x right?

  13. campbell_st
    • one year ago
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    thats correct... so now solve for x, you'll have an improper fraction

  14. 1018
    • one year ago
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    it gave me the same but the 15 repeated 4 times only

  15. 1018
    • one year ago
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    1721/330

  16. campbell_st
    • one year ago
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    then change the improper fraction to a mixed number and that's the answer

  17. phi
    • one year ago
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    **it gave me the same but the 15 repeated 4 times only*** on your calculator? it has limited number of digits to show

  18. campbell_st
    • one year ago
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    an 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

  19. 1018
    • one year ago
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    @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)

  20. phi
    • one year ago
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    the original question wants a ratio of two integers, so leave the answer 1721/330

  21. phi
    • one year ago
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    see http://www.wolframalpha.com/input/?i=1000+digits+1721%2F330%3D

  22. campbell_st
    • one year ago
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    well 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

  23. 1018
    • one year ago
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    oh wait now what. hahaha. so just remove the 5?

  24. 1018
    • one year ago
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    how bout you @phi you still think its the original one?

  25. phi
    • one year ago
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    ***express the repeating decimal as ratio of two integers : \[ 5.2\overline{15} = \frac{1721}{330}\]

  26. 1018
    • one year ago
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    ok thanks ill see what to put as the answer. haha. thanks guys!

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