Question

Express in Indian system of numeration.
Three million four hundred thirty-five thousand two hundred twenty-five.
A. 345,225
B. 34,352,25
C. 3,43,52,25
D. 34,35,225

Answer 1

Hint: Here, we are required to find the numeral value of the given number. Since the given number consists of millions hence, we will use the International System of numerals instead of the Indian one. After expressing this in the international system, we will convert it to the Indian system and hence, find the required answer. Drawing a place value table and substituting the given numbers in the correct place in the table, we will be able to find the required numeral value of sixty million and sixty-six which will be further converted to the Indian system of numeration.

Complete step-by-step answer:
In order to find the numerical answer to this question, we should know the difference between the international numeration system and the Indian numeration system.
In the international system of expressing numbers, we have the place values of the numbers as Ones, tens, hundreds, thousands, ten thousand, hundred thousand, million, ten million, hundred million, billion, and so on.
Whereas, if we observe the Indian system, then, we write the place values as Ones, tens, hundreds, thousands, ten thousand, lakhs, ten lakhs, crores, ten crores, and so on.
Also, in the International system, commas are put after every 3 places starting from the unit’s place. Whereas, in the Indian system, after putting a comma after hundreds of places, we put a comma after every two places.
Thus, both systems are having a lot of differences.
Now, in order to find the numerical value, we will draw a place value table of the international system and substitute the given value in the table.

HUNDRED MILLION	TEN MILLION	MILLION	HUNDRED THOUSAND	TEN THOUSAND	THOUSAND	HUNDREDS	TENS	ONES
		3	4	3	5	2	2	5

We have drawn this table using the fact that we are given the number Three million four hundred thirty-five thousand two hundred twenty-five. Hence, substituting these values in the place value table, we get the international value as:
3,435,225
But, this is in the international system.
As we know, in the Indian system of numeration, we put the commas after 2 digits starting from the hundreds.
Thus, after converting this to Indian system of numeration, we get,
\[{\rm{3}},{\rm{435}},{\rm{225}} = {\rm{34,35}},{\rm{225}}\]
Hence, Three million four hundred thirty five thousand two hundred twenty five can be expressed in Indian system of numeration as: 34,35,225

Therefore, option D) is the correct answer.
Note: In mathematics, an expanded form of a number means that the specific number is represented as the sum of each digit present in that number multiplied by its place value respectively. Whereas, a numeral form of a number is the mathematical symbol or name that stands for a number. In order to write a number name of a numeral, we use the modern numeral system i.e. the place-value systems to construct all the number names of the given numbers and vice-versa. Also, the difference between the Indian system and the international system plays a vital role to answer these types of questions.