0.99999 and it goes on forever

Algebra Level 1

True or false :

0.99999 = 1. \large 0.99999\ldots = 1 .

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3 solutions

Hung Woei Neoh
May 12, 2016

......I've lost count the number of times I answered this same question. Anyway...

0.999999 = 0.9 + 0.09 + 0.009 + 0.999999\ldots\\ =0.9 + 0.09 + 0.009 + \ldots

This is a sum of a geometric progression to infinity, where

a = 0.9 r = 0.09 0.9 = 0.1 a=0.9 \quad\quad r=\dfrac{0.09}{0.9} = 0.1

Therefore,

0.999999 = a 1 r = 0.9 1 0.1 = 0.9 0.9 = 1 0.999999\ldots\\ =\dfrac{a}{1-r}\\ =\dfrac{0.9}{1-0.1}\\ =\dfrac{0.9}{0.9}\\ =1

0.999999 = 1 0.999999\ldots = 1 , therefore the statement is True \boxed{\text{True}}

Some problems keep on coming again and again,which I even fruste to answer.Phew...!

Rohit Udaiwal - 5 years, 1 month ago

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This problem has security definitely come over a hundred times... if not thousand ;)

A Former Brilliant Member - 5 years, 1 month ago

+1 just for the first line of your answer as I too feel the same ;)

A Former Brilliant Member - 5 years, 1 month ago

Easiest question and standardest solution.

Ashish Menon - 5 years ago
Hopfhen Shane
May 16, 2016

There's another way to prove this.

Lets divide this 0.999999999999.... by 3. The resultant would be 0.3333333333..... which is 1 3 \frac{1}{3}

1 3 \frac{1}{3} Is a third of a one. Therefore if we m u l t i p l y multiply (0.333333333333..... = 1 3 \frac{1}{3} ) b y 3 by 3 , the result would be

0.99999999999999...... = 1

Therefore, the statement made above is || True ||

But you are making here another approximation by stating that a third is equal to 0.333333.... Basically you proved an approximation with another approximation, thus it's not a proof.

Alejandro Miguel - 4 years, 10 months ago
Rex Holmes
May 12, 2016

if 0.999999999999999... goes on forever and ever it equals one just as 1.999999999999999999999999999... equals 2!

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