1 dollar = 100 cents = 10 cents * 10 cents = 1/10 dollar * 1/10 dollar = 1/100 dollar = 1 cent
Here is the proof that 1 dollar = 1 cent. Is there an error in my calculations?
Step 1: 1 dollar = 100 cents
Step 2: = 10 cents * 10 cents
Step 3: = 1/10 dollar * 1/10 dollar
Step 4: = 1/100 dollar = 1 cent
The flaw lies in the Second step, where we are replacing 100 cents by 10 cents * 10 cents, which cannot be done, if the dimensions are taken into consideration. (As 100a cannot be written as 10a*10a).
That is it.