Show that (0. dot{1} dot{8}) is according to (frac{2}{11}).
First, address the alternating decimal as a continued number. Use a few iterations (it doesn’t amount absolutely how abounding are used).
[0. dot{1} dot{8} = 0.181818 dotsc]
Give this cardinal a name ((x)):
[x = 0.181818 dotsc]
Examine how abounding digits recur. In this case, there are two digits that recur, so accumulate by 100.
This gives:
[100x = 18.181818 dotsc]
[x = 0.181818 dotsc]
To break these two equations and address (0. dot{1} dot{8}) as a fraction, booty (x) abroad from (100x) to abolish all the alternating decimal places:
This gives:
[100x – x = 18.181818 dotsc – 0.181818 dotsc]
So, (99x = 18)
Next, bisect anniversary ancillary by 99, to get the amount of (1x):
[99x = 18]
[div 99]
[x = frac{18}{99}]
Simplify this atom by demography out any accepted factors. In this case, 9 is a accepted factor:
[x = frac{18}{99} = frac{2}{11}]
(0. dot{1} dot{8}) as a atom is (frac{2}{11}).
How To Write A Remainder As A Fraction – How To Write A Remainder As A Fraction
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