Question

The smallest 8 digit number is?
$(A)00000001$
$(B)10000000$
$(C)10000111$
$(D)12345678$

Answer 1

Hint: Here, First we need to discuss some of the basic definitions in the number system. Then we need to find the successor of the largest $7 - $ digit number which gives the smallest $8 - $ digit number. Finally we get the required answer.

Complete step-by-step solution:
Here we discuss some basic definitions of the number system.
Number: A number, which is we count how many times a unit is contained in a quantity.
Numerals: A group of figures or digits, representing a number is called a numeral.
Successor: The term successor refers to the number directly after a given number, respectively.
Now we have to find the successor of the given number we need to add one to the given number.
Let us assume that the given number is $n$
Hence, successor function is denoted by $S$
So, the formula for getting the successor is as follows:
$S(n) = n + 1$ Where ‘$n$’ is the given number.
As we already know that the largest $7 - $ digit number is $9999999.$
Let us assume that this largest $7 - $ digit number is the given number:
Now we put the value of $n$, we get
$S = 9999999 + 1$
On adding the expression,
We can write it as,
$\therefore S = 10000000$
Thus, the smallest $8 - $ digit is $10000000.$

Hence, the correct option is $(B)$ that is $10000000.$

Note: In either way we can also say that the predecessor of the smallest number $8 - $ digit number gives the largest $7 - $ digit number.
A successor function, it is one of the basic components which we used to build a primitive recursive function.
Predecessor: It is the number directly before the given number.
$P(n) = n - 1$, here $n$ is the given number.
Numeric values are represented by using digits $0$ to $9.$