Question

Difference between the place values of 3’s in 31,16,365 is _ _.
(a) 2999700
(b) 3000700
(c) 2990700
(d) None of these

Answer 1

Hint: Understand the difference between the terms ‘face value’ and ‘place value’ of a digit represented in Indian number system. Write the place value of the two 3’s as 3000000 (30 lakh) and 300 (3 hundred), then take the difference of these numbers to get the answer.

Complete step-by-step answer:
Here, we have been provided with the number 31,16,365 and we have to determine the difference between the place values of 3’s present here. But first we have to understand the meaning of two terms namely place value and face value.
Face value of a digit in a number shows the actual value of the digit while the place value shows the position of the digit. For example: - let us consider a number 465. Let us see what are the face values and place values and place values of the given three digits here. So, according to Indian number system, we have,

Digit	Face value	Place value
5	5	(5\[\times \]1) ones
6	6	(6\[\times \]10) tens
4	4	(4\[\times \]100) hundredth

From the above table, we can say that the given number 465 can be represented as: -
\[465=\left( 4\times 100 \right)+\left( 6\times 10 \right)+\left( 5\times 1 \right)\]
Now, let us come to the question. Here, we have the number 31, 16, 365. So, according to the Indian number system we can write the given number as: -
\[31,16,365=\left( 3\times 1000000 \right)+\left( 1\times 100000 \right)+\left( 1\times 10000 \right)+\left( 6\times 1000 \right)+\left( 3\times 100 \right)+\left( 6\times 10 \right)+\left( 5\times 1 \right)\]
So, we can see that the place value of one of the 3’s is \[3\times 100=300\] and the other is \[3\times 1000000=3000000\]. Therefore, the required difference between the place values of both the 3’s is: -
\[\Rightarrow 3000000-300=2999700\]

So, the correct answer is “Option A”.

Note: One may note that here the number is represented in Indian number system and not the International number system. Here, you must know the difference between place value and face value of a digit in a number because at many places you will not be given with the options and if definitions are not known then it will not be possible for you to solve the question.