Question

What is the difference in the place value of the digits\[8\] and \[6\] in the numeral \[8962321\]?
A) \[7994000\]
B) \[7904000\]
C)\[7960000\]
D)\[7940000\]

Answer 1

Hint: To solve this question we should have the knowledge of place value of digits in a number. In mathematics, every digit in a number has a place value. The first step we need to perform is finding the place value of both the digits given in the question with respect to the given numeral. To find the difference in the place value of given digits we have to subtract the smaller place value from the greater place value.

Complete step-by-step solution:
In this question we require the concept of the place value of a digit in a number. We need to understand how we can apply the concept on the given question by finding the respective place values and taking their difference to get the final answer. Let us discuss the above concepts one by one.
Place value of a digit: Place value of a digit can be defined as the value represented by a digit in a number on the basis of its position in the number. The place value of the digit depends upon the position and face of the digit. The position of the digit in a number can be one, ten, hundred, thousand, ten thousand, lakh, ten lakh, crore, ten crore, etc.
For e.g. Take a number \[542\].
In the above number \[2\]is present at one’s place, \[4\]is present at ten’s place and \[5\]is present at hundreds place.
Let, \[P\]be the place value of the digit, \[F\]be the face value of the digit and \[V\]be the value of the place.
The formula for place value of a digit is given by,
\[P=F\times V\]
Considering the above number\[542\], the place value of \[5\] is given by,
     \[P=5\times 100\]
\[\Rightarrow P=500\]
After knowing all the concepts now we move forward to solve the main question.
In the question we have been given a number \[8962321\].
We have to find the difference in the place value, place value of digits \[8\] and \[6\] in the above number.
By above formula,
For digit \[8\] we have,
      \[P=8\times 1000000\]
\[\Rightarrow P=8000000\]
For digit \[6\] we have,
     \[P=6\times 10000\]
\[\Rightarrow P=60000\]
Let, \[D\] be different in the place value of the digits.
Hence,
     \[D\]\[=(P\] of \[8\]\[)-(P\] of \[6\]\[)\]
\[\begin{align}
  & \Rightarrow D=8000000-60000 \\
 & \Rightarrow D=794000 \\
\end{align}\]
From this we can conclude that option D is the correct answer.

Note: This is a multiple choice question, but there is no need to check all the options. The structure of the question is such that we will get one and only definite answer. This question just needed the concept of place value of a digit in a number. It has a simple precise formula, we have to just substitute the value by applying our concepts and get the required answer.