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How can we write #3.11....# (repeated) as fraction?

Answer 1

#3.1# repeated#=28/9=3 1/9#

#3.1# repeated can be written as #3.11111111111............#

and when a single digit, say #k# (where #k# is a natural number from #1# and #9#) is repeated after decimal point, the result is #k/9# plus the number before decimal.

Hence, #3.1# repeated is #3 1/9# i.e. #28/9# There is another way too.

Let #x=3.1111111.......# and then

#10x=31.111111..........#

Subtracting former from latter we get

#9x=31-3=28#

i.e. #x=28/9=3 1/9#

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Answer 2

Zoe Adams

To express 3.11... (repeated) as a fraction, we can set it up as follows:

Let x = 3.111...

Then, multiplying both sides by 100 (to shift the decimal two places to the right):

100x = 311.111...

Subtracting the original equation from the second:

100x - x = 311.111... - 3.111...

This simplifies to:

99x = 308

Dividing both sides by 99:

x = 308/99

Therefore, 3.11... (repeated) can be written as the fraction 308/99.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.