Maths question recurring decimals

Convert the recurring decimal 0.29999 etc into a fraction? I cannot for the life of me remember how to do these questions could somebody please help and show me their method. Much appreciated good luck all edexcel maths people!

Reply 1

calcium878

18

if x = 0.29* (* = dot above the 9, for recurring)
then 10x = 2.9*
so 10x-x = 9x = 2.9* - 0.29* = 2.7

so 9x = 2.7, x = 2.7/9 = 27/90
divide through by 9 to get: 3/10

unbelievably, 0.299999999....... = 0.3!!!

Reply 2

Mustardseed

1

calcium878

unbelievably, 2.99999999....... = 0.3!!!

Heh, my favourite one of those is that 0.999999999... = 1. :smile:

The first time I saw that, I laughed for ages!

Reply 3

calcium878

18

Mustardseed

Heh, my favourite one of those is that 0.999999999... = 1. :smile:

The first time I saw that, I laughed for ages!

it's bloody great, isn't it!!! :cool:

Reply 4

Will Grimes1

OP

1

Thanks i remember now that is weird equalling 0.3 i dont really understand how but i know how to get to that conclusion. In the exam how can i do 2.7/9 without a calculator though or could i leave it as 2.7/9. Thanks again.

Reply 5

arpeggio

12

It's probably best to multiply it by 10 to get rid of the decimal, so that x = 27/90. Then you can divide by 9 to get 3/10, which is obviously 0.3 :smile:

Reply 6

Mustardseed

1

Will Grimes1

Thanks i remember now that is weird equalling 0.3 i dont really understand how but i know how to get to that conclusion. In the exam how can i do 2.7/9 without a calculator though or could i leave it as 2.7/9. Thanks again.