Which one is the biggest between .1 and .11111...

Question

anonymous · Answer

.11111...

anonymous · Answer

.1111.... can be rounded of to just .1 but technically .1111... is bigger

anonymous · Answer

for solving such questions, we first make the number of digits after the decimal point same by just adding zeros as follows :

0.10000      and 0.11111

now convert them to decimal numbers as follows

  10000                  11111
--------   and    ---------
100000                  100000

denominator is same now, so we just compare the numerators and find
10000 < 11111

so

  10000                  11111
--------    <     ---------
100000                  100000

Hence   0.1  <   0.11111

anonymous · Answer

Thank you guys. 
@Harkirat - Nice description :)

anonymous · Answer

u r welcome....☺

jamesj · Answer

Alternatively $$0.1 = \frac{1}{10}$$
and$$0.1111... = \frac{1}{10} +\frac{1}{100} +\frac{1}{1000} +\frac{1}{10000} + ...$$

Since all the additional terms after the 1/10 are also positive, it must be the case that 
$$0.1111... > 0.1$$

jamesj · Answer

Alternatively,$$0.111... - 0.1 = 0.0111... > 0$$
hence
$$0.111... > 0.1$$

So as you can see, there's lots of ways to attack this problem.

anonymous · Answer

@ JamesJ

Yes, your answer also r great !!!! Medal for u ...☺