Final answer:
There is no limit to the number of nonterminating, nonrepeating decimals between 0.5 and 0.6 because the real number system is dense, meaning between any two real numbers there's an infinite number of additional real numbers. This infinite precision allows for an endless creation of new nonrepeating, nonterminating decimals by adding more digits. Trailing zeros in a decimal number are significant for precision but do not limit the number of possible decimals between two numbers.
Step-by-step explanation:
The reason there is no limit to the number of nonterminating, nonrepeating decimals between 0.5 and 0.6 is rooted in the nature of the real number system. Between any two distinct real numbers, there is an infinite number of additional real numbers. This can be illustrated by taking any decimal number between 0.5 and 0.6 and adding another digit to it (for instance, changing 0.55 to 0.551). This process can continue indefinitely, each time yielding a new nonterminating decimal that is still between 0.5 and 0.6.
To put it into context, regardless of how many decimal places you write out for a number between 0.5 and 0.6, you could always add another digit, and it still won't terminate or repeat. Additionally, right-end zeros or trailing zeros in a decimal number are significant, which means that 0.5000 is different from 0.5 in terms of the precision it represents.
While in everyday situations, we may not need this level of precision and can round numbers to a certain number of decimal places for convenience, the mathematical reality is that the set of real numbers is dense, and there are infinitely many decimals between any two given numbers.