Question

what is 0.194 with 94 repeating into a fraction?
will medal

Answer 1

let x = 0.19494949494......

multiply the decimal by 1000 (equation 1) and by 10 (equation 2)

find the difference of the 2 equations

equation 1 - equation 2

get an answer then solve for x

Answer 2

what do you mean equation 1 - equation 2?

Answer 3

oh nvm

Answer 4

i don't get it

Answer 5

@campbell_st can u explain again?

Answer 6

ok...x = 0.194949494.....

so mutiply by a value that only has the recurring decimal to the left of the decimal point.

you will need 2 equations... and you and normally multiplying by multiples of 10.

then then you have 2 equations subtract the smaller from the larger

1000x = 194.9494949494 equation 1
- 10x = 1.9494949494 equation 2
-----------------------
get the answer... and you should see the recurring
decimal disappears...


then its a case of just solving for x

Answer 7

so 193 over 999?

Answer 8

you will get a fraction as the answer... that may need to be simplified.


as an example 0.2222222222

10x = 2.22222222
- x = 0.22222222
-----------------
9x = 2

then x = 2/9

so 0.222222 as a fraction is 2/9

hope it makes sense

Answer 9

no, its not 999 its 990...

Answer 10

but otherwise your solution is great

Answer 11

oh so 193 over 990?

Answer 12

that's correct

Answer 13

thanks

Answer 14

these questions all work the same... it just a case of identifying the multiple of 10 to use