To determine the cardinal number of the set [tex]\( Q \)[/tex] containing all the unique digits in the number [tex]\( q = 777,898,870,003 \)[/tex]:
1. Identify the Digits: List out all individual digits in the number [tex]\( q \)[/tex].
[tex]\[ q = 777,898,870,003 \][/tex]
The digits are: 7, 7, 7, 8, 9, 8, 8, 7, 0, 0, 3.
2. Extract Unique Digits: Identify and keep only the unique digits from the list.
The unique digits in [tex]\( q \)[/tex] are: 7, 8, 9, 0, 3.
3. Form the Set [tex]\( Q \)[/tex]: Write the unique digits as elements of a set.
[tex]\[ Q = \{ 7, 8, 9, 0, 3 \} \][/tex]
4. Determine the Cardinal Number: The cardinal number of a set is the number of distinct elements it contains. Count the elements in the set [tex]\( Q \)[/tex].
The set [tex]\( Q \)[/tex] has 5 elements.
Thus, the cardinal number of the set [tex]\( Q \)[/tex] is:
[tex]\[ \boxed{5} \][/tex]
