Question

express the repeating decimal as ratio of two integers :

Answer 1

\[5.215=5.2151515...\]

Answer 2

15 is the repeating

Answer 3

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

Answer 4

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

Answer 5

then its let the number be x

1000x = number
- 10x = number
------------------ do the subtraction and solve for x

Answer 6

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

Answer 7

@campbell_st wait is this correct 5.215 x 10?

Answer 8

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...

Answer 9

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

Answer 10

yes so 10x = 52.151515.......

and 1000x = 5215.15151515...

the subtraction eliminates the recurring part of the decimal...

Answer 11

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...

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

1721/330

Answer 16

then change the improper fraction to a mixed number

and that's the answer

Answer 17

**it gave me the same but the 15 repeated 4 times only***
on your calculator? it has limited number of digits to show

Answer 18

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

Answer 19

@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)

Answer 20

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

Answer 21

see
http://www.wolframalpha.com/input/?i=1000+digits+1721%2F330%3D

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

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