Express 0.45̅̅̅̅ in the form of p/q where p, q are co-primes and q≠ 0

Sure, let's solve this step by step.

Step 1: Let's denote the number 0.45̅̅̅̅ as 'x'. So, x = 0.45̅̅̅̅

Step 2: The bar over 45 indicates that 45 is the repeating part. So, we can write it as x = 0.454545...

Step 3: To get rid of the decimal, we multiply both sides by 100 (because there are two digits in the repeating part). So, we get 100x = 45.454545...

Step 4: Now, subtract the original equation (step 1) from this new equation (step 3). This gives us 100x - x = 45.454545... - 0.454545..., which simplifies to 99x = 45.

Step 5: To find the value of x, we divide both sides by 99. So, x = 45/99.

Step 6: Simplify the fraction 45/99 by dividing both numbers by their greatest common divisor, which is 9. So, x = 5/11.

So, 0.45̅̅̅̅ in the form of p/q where p, q are co-primes and q≠ 0 is 5/11.