How do you write 27/99 as a decimal?

Answer 1

#0.27272727...->0.27bar(27)#

Since there are 99 digits in the denominator, I believe the decimal has an infinitely repeating set of digits. A fraction written as a decimal is either terminating (has a fixed number of decimal places) or has a cycle of digits that repeat for ever.

#color(blue)("Using a calculator I get "0.272727....)#

Putting a bar over the relevant digits indicates the repeating portion. Therefore, I would choose to write this as:

#0.27bar(27)# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("What if you do not have a calculator?")#

99 is to be divided by a smaller number (do NOT use the word'smaller').

However I can do a sort of cheat. 27 is the same as #270xx1/10#
This idea can be repeated as many times as you wish as long as you apply the #xx1/10xx1/10xx# however many # 1/10# you end up with. This will be clearer when I use it.
#color(white)()# #color(white)()#
#27 ->color(white)("ddd")270 color(magenta)(xx1/10)#
#color(red)(2)xx99-> ul(198larr" Subtract")# #color(white)("ddddddddd")72# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ But #72<99" so write it as "720xx1/10#
#color(white)("ddddddddd")720color(magenta)(xx1/10)#
#color(red)(7)xx99->color(white)("d")ul( 693 larr" Subtract")# #color(white)("dddddddddd")27# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(purple)("And so the cycle goes on and on for ever.")#

Thus far, we have:

#color(red)(27)color(magenta)(xx1/10xx1/10) = 0.27#
But the repeats give: #0.27272727...... ->0.27bar27#
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Answer 2

To write 27/99 as a decimal, divide 27 by 99 using long division. The result is 0.272727... or 0.27 (rounded to two decimal places).

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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.

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.

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.

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.

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