Answer:
281/198
Explanation:
You want the fraction equivalent of the rational number 1.41919....
Repeat
The given number has a 2-digit repeat, so we can express it as a fraction this way:
Multiply by 10^2, where the exponent is the number of repeating digits.
10X = 141.91919...
Cancel
Subtract the original number
10X -X = 141.91919... -1.41919... = 140.5 . . . . . now we have a finite decimal
99X = 140.5
Divide by 99 and express as a ratio of integers.
X = 140.5/99 = 281/198 . . . . . . multiply by 2/2
1.4191919... = 281/198
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Additional comment
Having done this before, we know that 0.191919... = 19/99. Then 1.91919... is 10 times that, or 190/99. This number has a 9 in the tenths place, not a 4, so is 0.5 more than the required number. Our number is ...
190/99 - 1/2 = (380 -99)/(99·2) = 281/198
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