In my dreams

Algebra Level 1

Rohan had a dream one night. In the dream, he was asking his maths teacher a question. The question was 'is 0.999999... equal to 1?'. The teacher replied 'no they aren't equal as 0.999999... is not terminating, but 1 is terminating.' The next day when the same question was asked in a math exam, Rohan wrote that they are not equal. Was his answer right ?

No Yes

Rohan Aggrawal by Rohan Aggrawal , 27, India

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1 solution

Rohan Aggrawal
Jan 8, 2016

Way 1 Imagine you divide 1 by 3. You get 3 1/3 parts. These three add up to make 1 whole. Now, 1/3 is technically, 0.333333.... so three times this will be 0.999999... which, as stated earlier, is equal to 1.

Way 2 If we take x=0.9999... then, 10x= 9.9999...

10x-x=(9.9999...)-(0.9999...) = 9 so, 9x=9 therefore, x=1 if x=0.9999... and x=1, then 0.9999...=1

1 Helpful 0 Interesting 0 Brilliant 0 Confused

It's very interesting subject, however, it always got on my mind how weird it is. There's an infinitely small number that is the difference between 1 1 and 0.9999... 0.9999... , and yet everyone prove it otherwise! Gah! ;) (Thanks for the problem, it's fun to remember such things)

Zyberg NEE - 5 years, 5 months ago

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Thank you Zyberg Nee. Im glad to see that memories were evoked into you while solving my problem. Were you able to solve it ?

Rohan Aggrawal - 5 years, 5 months ago

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Yes, I was able to solve it. Thank you once again!

Zyberg NEE - 5 years, 5 months ago

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