How to convert decimals to fractions ? (2 Viewers)

[bubb]

e.g 0.2297297297 = 17/74

How do we know it is 17/74?

 

[enigma_1]

0.2297297297 = 0.2 + (0.0297 + 0.0000297 + 0.0000000297 +......)


^ the part in brackets is a GP, and using the limiting sum formula..


= 0.2 + (a/1-r )
a=0.0297
r=0.001

:. = 0.2 + [0.0297/(1-0.001)]
= 0.2 + (0.0297/0.999)
= 17/74

 

[astroman]

 

[Squar3root]

spam your calculator

 

[astroman]

spam your calculator

wont get u full marks

 

[Squar3root]

wont get u full marks

While I am spamming my calculator some other asian is doing some legit working out and in the end we're going to get the same mark for it. Doesn't seem fair right? So they stopped putting these questions in the HSC because it is unfair to people who have different calculators.

 

[jkerr138]

This is another way to do it.
Proof;
Let x = 0.2297297297297.. (1)
10x = 2.297297297297 (2)
(2-1) 9x = 153/74
x= 153/74 / 9
x= 153/74 * 1/9
x= 17/74
Proven