What is the cardinality of the set of all numbers in the int

What is the cardinality of the set of all numbers in the interval [0,1] which have decimal expansions with a finite number of nonzero digits?

Solution

Numbers whose decimal expansions consists of finite numer of nonzero digits are comes under rational number.

And every interval consists of infinitely many rational numbers as well as infinitely many irrational numbers.

Cardinakity of a set means number of elements in that set.

In the interval [0,1] there are infinitily many rational numbers as well as infinitely many irrtional numbers.

So cardinality of the set of numbers lies in [0,1] whose have decimal expansions consists of finite number of no zero terms is infinite.

for example,

1.1,1.11,1.111,1.111, ...

consists of infinite number of terms whichi are lies in the interval [0,1]