How do you convert #0.bar(45)# (meaning the #45# is being repeated) to a fraction?

Answer 1

#0.45454545.............=5/11#

Let #x=0.45454545.............# ............................(1)
then #100x=45.45454545............# ............................(2)

subtracting (1) from (2) we get

#99x=45#
or #x=45/99=5/11#
Hence #0.45454545.............=5/11#
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Answer 2

#5/11#

When two numbers in a decimal sequence repeat forever, the denominator will be #11#.
To think about the numerator, let's just take the number #45#.
This number would round to #50# or #5# tens. Whatever number of tens the numerator rounds to, this will be our numerator.

Thus, we have

#5/11#

Hope this helps!

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Answer 3

To convert the repeating decimal (0.\overline{45}) to a fraction:

Let (x = 0.\overline{45}). Multiply both sides by 100 to shift the decimal places: (100x = 45.\overline{45}). Subtract the original equation from the multiplied equation: (100x - x = 45.\overline{45} - 0.\overline{45}). Simplify: (99x = 45). Divide both sides by 99: (x = \frac{45}{99}). Simplify the fraction: (x = \frac{5}{11}).

Therefore, (0.\overline{45}) is equivalent to (\frac{5}{11}).

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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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