Question

The smallest 8-digit number is?
(a) 00000001
(b) 10000000
(c) 10000111
(d) 12345678

Answer 1

Hint: In this question, we first need to look into some of the basic definitions of the number system. Then we need to find the successor of the largest 7-digit number which gives the smallest 8-digit number.

Complete step-by-step answer:
Some basic definitions of the number system.
NUMBER: A number tells us how many times a unit is contained in a given quantity.
NUMERAL: A group of figures or digits, representing a number is called a numeral.
FACE VALUE AND PLACE VALUE OF THE DIGITS:
In a numeral, the face value of the digit is the value.
In a numerical, the place value of a digit changes according to the change of its place.

Types of number system:
A. Binary number system
B. Octal number system
C. Hexadecimal number system
D. Roman number system
E. Decimal number system
DECIMAL NUMBER SYSTEM: Numeric values are represented by using digits from 0 to 9.
Again numbers in the decimal system are classified as real numbers.
Real numbers are classified into rational numbers and irrational numbers.
Rational numbers are again classified into integer and non-integer rational numbers.
Again integers are classified into:
a. Positive integer
b. Negative integer
c. Whole number
d. Natural number
The decimal number system is the standard system for denoting integer and non-integer numbers.
NATURAL NUMBERS: Numbers starting from 1, having no fraction part, which we use in counting the objects, denoted by N.
N = {1, 2, 3, etc}
Successor: The term succession refers to the number directly after a given number, respectively.
To find the successor of a given number we need to add one to the given number.
Let us assume that the given number is a.
Hence, Successor of a will be a+1.
The successor function is denoted by S. So,
\[S\left( n \right)=n+1\]
As we already know that the largest 7-digit number is 9999999
Let us assume that this largest 7-digit number as n.
Now, successor of the largest 7-digit number is:
\[\begin{align}
  & \Rightarrow S=n+1 \\
 & \Rightarrow S=9999999+1 \\
 & \therefore S=10000000 \\
\end{align}\]
Thus, the smallest 8-digit number is 10000000.
Hence, the correct option is (b).

Note: The successor function is one of the basic components used to build a primitive recursive function.
We calculated the successor of the largest 7-digit number because the number right after the largest 7-digit number gives the smallest 8-digit number. As it is the first number where 8-digit numbers start.
In either way we can also say that the predecessor of the smallest 8-digit number gives the largest 7-digit number. Predecessor refers to the number directly before a given number.
_{\[P\left( n \right)=n-1\]}