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Sagot :
This is a periodic decimal, which means a fixed part of the number will repeat forever, this part is called period. In this case the period is equal to 3. To convert a periodic decimal to a fraction we need to do as below.
We need to subtract the part of the number that doesn't repeat with one period of that part that repeats without the dot, which would be "183" and subtract it with the part that doesn't repeat without the dot "18". This would be "183 - 18 = 165". We then count the number of algarisms in the period of the number, in this case we only have one, which is "3". For every algarism in the period we add a "9" to the denominator. If there are numbers on the decimal part that don't repeat we add "0" after the 9. So we have the following fraction.
[tex]1.833333\ldots\text{ = }\frac{183-18}{90}\text{ = }\frac{165}{90}[/tex]
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