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MaRussiya
1 month ago
12

Write the number 0.21212121.. as a fraction let x=

Mathematics
1 answer:
AnnZ [12.3K]1 month ago
7 0
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
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This question reveals an intriguing pattern.

The rule or pattern to follow here is:

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For the right side: (Second digit x Fourth digit -1)

For instance, consider 6447. Next, let's examine its previous number, 9876.

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