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How do you convert 0.809 (09 being repeated) to a fraction?

Answer 1

Isaiah Anthony

#89/110#

We first let 0.809 (09 being repeated) be #x#.

Since #x# is recurring in 2 decimal places, we multiply it by 100.

#100x = 80.909#

We then deduct them.

#100x - x = 80.909 - 0.809#

#99x = 80.1#

Lastly, we divide both sides by 99 to get #x# as a fraction.

#x = 80.1/99#

#= 801/990#

#= 89/110#

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Answer 2

Kennedy Adams

To convert 0.809 (09 being repeated) to a fraction, the repeating decimal can be represented as (0.\overline{09}). To convert this to a fraction, you can use the following steps:

Let (x = 0.\overline{09})
Multiply both sides by 100 to shift the decimal two places to the right: (100x = 9.\overline{09})
Subtract the original equation from the shifted equation: (100x - x = 9.\overline{09} - 0.\overline{09})
Simplify: (99x = 9)
Solve for (x): (x = \frac{9}{99} = \frac{1}{11})

So, (0.\overline{09}) as a fraction is (\frac{1}{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.