Question

Express 0.22... in p/q form. Where p and q be any integers and q not is equal to 0

Answer 1

The p/q form of the repeating decimal 0.22... is 22/99. This is obtained through a calculation process involving algebraic manipulation and division.

Step-by-step explanation:

The p/q form or rational number representation of a repeating decimal like 0.22... can be found using the algebraic method.

1. Let's express the repeating decimal 0.22... as variable x.
   So, x = 0.22...
2. Multiply x by 100 (or a power of 10) to shift the decimal point which gives us another equation, 100x = 22.22...
3. Then, subtract the first equation from the second equation to get: 99x = 22.
4. Finally, solve for x by dividing both sides by 99 to get: x = 22/99.

So, 0.22... in the p/q form is 22/99.

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