basic arithmetic help (1 Viewer)

[kaha167]

how do you express [reoccuring decimals i.e. 0.8 repeated] as fractions in lowest terms?
i.e. as in 0.216 [6 is reoccuring]

thankyou

 

[steve001]

hey there is two ways you can do this

the first way is the way you do it if its a 3 mark question

x=0.21666666....
1000x=216.666666
1000x-x=999x
999x=216.45
x=(216.45)/999
which is also equal to 13/60

the other way is if its only worth 1 mark
what you do is get where the number keeps recurring and minus the non-recurring numbers from it
therefore in this case 216-21
fr the denominator you put a 9 for every reurring number and a 0 for non-recurring
therefore 900
so (216-21)/900
=13/60
much quicker but 3 markers want you to use the top one

hope it helps

 

[bored.of.u]

how do you express [reoccuring decimals i.e. 0.8 repeated] as fractions in lowest terms?
i.e. as in 0.216 [6 is reoccuring]

thankyou

Let x = 0.2166....
.'. 100x = 21.66... ---> 1.
.'.1000x=216.66..... ---> 2.
Let, 2 - 1
900x = 195
.'. x = 195/900
.'. x = 13/60
Here you dont have to worry about subtracting a negative make sure only the recurring decimal is on the right hand side of the decimal. =D