To determine which of the given numbers is a terminating decimal, let's analyze the options one by one:
A) [tex]\(10.\overline{3}\)[/tex]
The notation [tex]\(10.\overline{3}\)[/tex] indicates a repeating decimal, specifically [tex]\(10.3333\ldots\)[/tex]. Since it repeats indefinitely, it is not a terminating decimal.
B) [tex]\(\sqrt{10}\)[/tex]
The square root of 10 is an irrational number, which means its decimal representation is non-repeating and non-terminating. Hence, [tex]\(\sqrt{10}\)[/tex] is not a terminating decimal.
C) 10.101
The number 10.101 is a decimal with a finite number of digits after the decimal point. Since it does not have an infinite sequence of digits, it is indeed a terminating decimal.
D) [tex]\(100.\overline{6}\)[/tex]
The notation [tex]\(100.\overline{6}\)[/tex] represents a repeating decimal, specifically [tex]\(100.6666\ldots\)[/tex]. Since the decimal part repeats indefinitely, it is not a terminating decimal.
Based on the analysis above, the correct choice is:
C) 10.101
