Numbers in Indian & International Systems

The position of the commas tells us which system to use — Indian commas (grouped as 3, 2, 2, .. from the right) for parts (i) to (iii) and International commas (grouped as 3, 3, 3, .. from the right) for parts (iv) to (vi).

(i) In the Indian system, 4,35,342 is grouped as:

Lakhs	Ten Thousands	Thousands	Hundreds	Tens	Ones
4	3	5	3	4	2

∴ 4,35,342 = Four lakh thirty five thousand three hundred forty two.

(ii) In the Indian system, 36,71,430 is grouped as:

Ten Lakhs	Lakhs	Ten Thousands	Thousands	Hundreds	Tens	Ones
3	6	7	1	4	3	0

∴ 36,71,430 = Thirty six lakh seventy one thousand four hundred thirty.

(iii) In the Indian system, 4,28,30,004 is grouped as:

Crores	Ten Lakhs	Lakhs	Ten Thousands	Thousands	Hundreds	Tens	Ones
4	2	8	3	0	0	0	4

∴ 4,28,30,004 = Four crore twenty eight lakh thirty thousand four.

(iv) In the International system, 75,132,684 is grouped as:

Ten Millions	Millions	Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Ones
7	5	1	3	2	6	8	4

∴ 75,132,684 = Seventy five million one hundred thirty two thousand six hundred eighty four.

(v) In the International system, 815,906 is grouped as:

Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Ones
8	1	5	9	0	6

∴ 815,906 = Eight hundred fifteen thousand nine hundred six.

(vi) In the International system, 5,420,700 is grouped as:

Millions	Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Ones
5	4	2	0	7	0	0

∴ 5,420,700 = Five million four hundred twenty thousand seven hundred.

In the Indian system, starting from the right, the first comma is placed after 3 digits and then after every 2 digits.

(i) 835629 → mark off 629, then 35, then 8.

∴ 835629 = 8,35,629.

(ii) 35640254 → mark off 254, then 40, then 56, then 3.

∴ 35640254 = 3,56,40,254.

(iii) 2826040 → mark off 040, then 26, then 28.

∴ 2826040 = 28,26,040.

In the International system, starting from the right, a comma is placed after every 3 digits.

(i) 6509820 → mark off 820, then 509, then 6.

∴ 6509820 = 6,509,820.

(ii) 428140584 → mark off 584, then 140, then 428.

∴ 428140584 = 428,140,584.

(iii) 63560981 → mark off 981, then 560, then 63.

∴ 63560981 = 63,560,981.

(i) Four lakh sixty seven thousand three hundred six.

Writing the digits in the place value chart of the Indian system :

Lakhs	Ten Thousands	Thousands	Hundreds	Tens	Ones
4	6	7	3	0	6

So, the number in Indian numeral form = 4,67,306.

Placing the commas according to the International system (after every 3 digits from the right) = 467,306.

In International numeration, 467,306 = Four hundred sixty seven thousand three hundred six.

∴ 4,67,306 (Indian numeral form) = 467,306 (International numeral form) = Four hundred sixty seven thousand three hundred six (International numeration).

(ii) Thirteen lakh forty five.

Writing the digits in the place value chart of the Indian system :

Ten Lakhs	Lakhs	Ten Thousands	Thousands	Hundreds	Tens	Ones
1	3	0	0	0	4	5

So, the number in Indian numeral form = 13,00,045.

Placing the commas according to the International system = 1,300,045.

In International numeration, 1,300,045 = One million three hundred thousand forty five.

∴ 13,00,045 (Indian numeral form) = 1,300,045 (International numeral form) = One million three hundred thousand forty five (International numeration).

(i) Six hundred four thousand eight hundred forty seven.

Writing the digits in the place value chart of the International system :

Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Ones
6	0	4	8	4	7

So, the number in International numeral form = 604,847.

Placing the commas according to the Indian system (after 3 digits and then after every 2 digits from the right) = 6,04,847.

In Indian numeration, 6,04,847 = Six lakh four thousand eight hundred forty seven.

∴ 604,847 (International numeral form) = 6,04,847 (Indian numeral form) = Six lakh four thousand eight hundred forty seven (Indian numeration).

(ii) Two million three hundred ten thousand one hundred four.

Writing the digits in the place value chart of the International system :

Millions	Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Ones
2	3	1	0	1	0	4

So, the number in International numeral form = 2,310,104.

Placing the commas according to the Indian system = 23,10,104.

In Indian numeration, 23,10,104 = Twenty three lakh ten thousand one hundred four.

∴ 2,310,104 (International numeral form) = 23,10,104 (Indian numeral form) = Twenty three lakh ten thousand one hundred four (Indian numeration).

Seventeen lakh = 17,00,000 and ninety five = 95.

So, seventeen lakh ninety five = 17,00,000 + 95 = 17,00,095.

Hence, option 2 is the correct option.

Five million = 5,000,000; five hundred fifty five thousand = 555,000; five hundred fifty five = 555.

So, the number = 5,000,000 + 555,000 + 555 = 5,555,555.

Hence, option 3 is the correct option.

From the relationship between the two systems, 1 crore = 10 million.

So, 10 million = 1 crore.

Hence, option 1 is the correct option.

From the relationship between the two systems, 10 lakh = 1 million.

So, 1 million = 10 lakh.

Hence, option 2 is the correct option.

Nine crore = 9,00,00,000; five lakh = 5,00,000; forty one = 41.

So, the number = 9,00,00,000 + 5,00,000 + 41 = 9,05,00,041.

Hence, option 2 is the correct option.

1 million = 1,000,000 and ten thousand = 10,000.

Number of ten-thousands in one million = 1,000,000 ÷ 10,000 = $\frac{1,000,000}{10,000}$ = 100.

So, 1 million = 100 ten thousand.

Hence, option 2 is the correct option.

In the Indian system, starting from the right, the first comma is placed after 3 digits and then after every 2 digits.

Forty five lakh = 45,00,000 and thirteen = 13.

So, the number = 45,00,000 + 13 = 45,00,013.

Writing the digits in the place value chart of the Indian system :

Ten Lakhs	Lakhs	Ten Thousands	Thousands	Hundreds	Tens	Ones
4	5	0	0	0	1	3

So, in the Indian numeral form, the number is written as 45,00,013.

Hence, option 2 is the correct option.

Four hundred six thousand = 406,000 and seven hundred forty eight = 748.

So, the number = 406,000 + 748 = 406,748.

Writing the digits in the place value chart of the International system :

Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Ones
4	0	6	7	4	8

So, in the International numeral form, the number is written as 406,748.

Hence, option 1 is the correct option.

The given number is 5762983.

Statement 1 : In the Hindu-Arabic (Indian) system, the commas are placed after 3 digits and then after every 2 digits from the right, giving 57,62,983 — and not 5,762,983. So, Statement 1 is false.

Statement 2 : In the International system, the commas are placed after every 3 digits from the right, giving 5,762,983. So, Statement 2 is true.

So, Statement 1 is false and Statement 2 is true.

Hence, option 4 is the correct option.

The given number is 515006200.

Statement 1 : In the Hindu-Arabic (Indian) system, 515006200 = 51,50,06,200, which is read as fifty one crore fifty lakh six thousand two hundred — not "five hundred fifteen million and six thousand two hundred". So, Statement 1 is false.

Statement 2 : In the International system, 515006200 = 515,006,200, which is read as five hundred fifteen million six thousand two hundred — not "fifty one crore fifty lakh six thousand two hundred". So, Statement 2 is false.

So, both the statements are false.

Hence, option 2 is the correct option.

Assertion (A) : In the Hindu-Arabic (Indian) system, 9365217 = 93,65,217, which is read as ninety three lakh sixty five thousand two hundred seventeen. This agrees with the assertion, so A is true.

Reason (R) : In the Hindu-Arabic system, counting from the right hand side, the first three digits form the one's period (ones, tens and hundreds), the next two digits form the thousand's period (thousands and ten thousands) and the next two digits form the lakh's period (lakhs and ten lakhs). This is correct, so R is true.

So, both A and R are true.

Hence, option 3 is the correct option.

Assertion (A) : In the International system, 638452179 = 638,452,179, which is read as six hundred thirty eight million four hundred fifty two thousand one hundred seventy nine. This agrees with the assertion, so A is true.

Reason (R) : In the International system, counting from the right hand side, the first three digits form the one's period (ones, tens and hundreds), the next three digits form the thousand's period (thousands, ten thousands and hundred thousands) and the next three digits form the million's period (millions, ten millions and hundred millions). This is correct, so R is true.

So, both A and R are true.

Hence, option 3 is the correct option.