To work with the repeating decimals, note that since there are two digits repeating, you will be using a 1 followed by two zeros, which is 100. This factor will be important for subsequent calculations.
Let’s denote the repeating decimal as x.
Thus, you can write
x = 0.212121...
Now, if you multiply this equation by 100, you can write it on top of the previous equation.
This results in:
100x = 21.212121...
x = 0.212121...
Next, set up a subtraction by taking the second equation from the first:
100x = 21.212121...
x = 0.212121...
- ----------------------------
99x = 21
Solving for x involves dividing both sides by 3:
33x = 7
Then, divide both sides by 33:
x = 7/33
Thus, we conclude that the repeating decimal 0.212121... equates to the fraction 7/33.
Answer: the fraction is 7/33
The rate at which the windows are washed can be described by the number of windows cleaned each minute. Thus, the missing value represents how many windows she has managed to wash.
Parce qu'en connaissant les techniques pour identifier les nombres rationnels, vous saurez automatiquement quand un nombre n'est pas rationnel.
