Question

The difference between the local value and the face value of $7$ in the numeral $32675149$ is.
(a) $75142$
(b) $64851$
(c) $5159$
(d) $69993$
(e) None of these

Answer 1

Hint: For solving this question first we will find the face value and local value of 7 in 32675149 and then we will find the difference between them.

Complete step-by-step solution:
Given:
32675149
Before, we find the local value and face value. We should know that the face value of any integer is itself and local value may vary for an integer.
Let us consider the number 11.
We can write, 11 = $1\times 10+1$ .
Similarly, we can write, 123 = $1\times 100+2\times 10+3$ .
Thus, we can write, $32675149=3\times {{10}^{7}}+2\times {{10}^{6}}+6\times {{10}^{5}}+7\times {{10}^{4}}+5\times {{10}^{3}}+1\times 100+4\times 10+9$ .
So, the local value of each integer in 32675149 can be written as:
Local value of 3 = $3\times {{10}^{7}}$ .
Local value of 2 = $2\times {{10}^{6}}$ .
Local value of 6 = $6\times {{10}^{5}}$ .
Local value of 7 = $7\times {{10}^{4}}$ .
Local value of 5 = $5\times {{10}^{3}}$ .
Local value of 1 = $1\times 100$ .
Local value of 4 = $4\times 10$ .
Local value of 9 = $9$ .
From above, we get,
Local value of 7 = $7\times {{10}^{4}}=70000$ .
And, as we know that the face value of 7 will be always 7 itself.
Difference between local value and face value = $70000-7=69993$ .
Hence, (d) is the correct answer.

Note: Here, students must know how to find the face value and local value of any integer in any number and then carefully do the subtraction and match the correct option.