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

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1. 1018

$5.215=5.2151515...$

2. 1018

15 is the repeating

3. campbell_st

multiply you number by 10, what do you get..?

4. campbell_st

then multiply the number by 1000 what do you get...?

5. campbell_st

then its let the number be x 1000x = number - 10x = number ------------------ do the subtraction and solve for x

6. 1018

@phi so should i separate the 5 first and solve for the decimals only?

7. 1018

@campbell_st wait is this correct 5.215 x 10?

8. phi

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

but how bout the two? its not repeating is that ok? @phi

10. campbell_st

yes so 10x = 52.151515....... and 1000x = 5215.15151515... the subtraction eliminates the recurring part of the decimal...

11. phi

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

@campbell_st so that leaves me with 990x =5163? then x right?

13. campbell_st

thats correct... so now solve for x, you'll have an improper fraction

14. 1018

it gave me the same but the 15 repeated 4 times only

15. 1018

1721/330

16. campbell_st

then change the improper fraction to a mixed number and that's the answer

17. phi

**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

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

@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

the original question wants a ratio of two integers, so leave the answer 1721/330

21. phi
22. campbell_st

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

oh wait now what. hahaha. so just remove the 5?

24. 1018

how bout you @phi you still think its the original one?

25. phi

***express the repeating decimal as ratio of two integers : $5.2\overline{15} = \frac{1721}{330}$

26. 1018

ok thanks ill see what to put as the answer. haha. thanks guys!

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