Numbers in Indian & International Systems Class 6

Class 6 Mathematics • Selina Concise • Exercise 2

Numbers in Indian & International Systems

Learn comma placement, place-value periods, number names, conversions, MCQs, statement-based questions and assertion–reason questions through step-by-step solutions.

Indian Numeration International Numeration Place Value Solved Exercise

Understanding number systems becomes easy when the comma pattern is clear.

Quick Concepts Number Lab Exercise 2 MCQs Statement Questions Assertion–Reason FAQs

1Quick Concepts

Indian System

Starting from the right, place the first comma after three digits. After that, place a comma after every two digits.

12,34,56,789

International System

Starting from the right, place a comma after every three digits. The periods are ones, thousands and millions.

123,456,789

1 lakh100,000

10 lakh1 million

1 crore10 million

100 lakh1 crore

Memory trick: Indian grouping is 3, 2, 2, 2... from the right, while International grouping is 3, 3, 3... from the right.

2Interactive Number Lab

Enter digits only. The tool will place commas in both systems so you can compare the patterns.

Indian System —

International System —

3Exercise 2: Descriptive Questions

Question 1

Write the following numerals using the Indian System or International System, as required, in words.

1. 4,35,342
2. 36,71,430
3. 4,28,30,004
4. 75,132,684
5. 815,906
6. 5,420,700

Step-by-step solution

The position of the commas tells us which system to use. Parts (i) to (iii) use Indian grouping, while parts (iv) to (vi) use International grouping.

(i) 4,35,342

In the Indian system, the number is grouped as follows:

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) 36,71,430

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) 4,28,30,004

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) 75,132,684

In the International system, the number is grouped as follows:

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) 815,906

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

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

(vi) 5,420,700

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.

Question 2

Write the following numbers by placing commas according to the Indian system.

1. 835629
2. 35640254
3. 2826040

Solution

In the Indian system, starting from the right, the first comma is placed after three digits and every later comma is placed after two digits.

(i) Mark off 629, then 35, then 8.

∴ 835629 = 8,35,629.

(ii) Mark off 254, then 40, then 56, then 3.

∴ 35640254 = 3,56,40,254.

(iii) Mark off 040, then 26, then 28.

∴ 2826040 = 28,26,040.

Question 3

Write the following numbers by placing commas according to the International system.

1. 6509820
2. 428140584
3. 63560981

Solution

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

(i) Mark off 820, then 509, then 6.

∴ 6509820 = 6,509,820.

(ii) Mark off 584, then 140, then 428.

∴ 428140584 = 428,140,584.

(iii) Mark off 981, then 560, then 63.

∴ 63560981 = 63,560,981.

Question 4

Fill in the blanks as indicated.

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

= ________ (Indian numeral form)
= ________ (International numeral form)
= ________ (International numeration)

(ii) Thirteen lakh forty five.

= ________ (Indian numeral form)
= ________ (International numeral form)
= ________ (International numeration)

Solution

(i) Four lakh sixty seven thousand three hundred six

Write the digits in the Indian place-value chart:

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

Indian numeral form: 4,67,306

International numeral form: 467,306

International numeration: Four hundred sixty seven thousand three hundred six.

∴ 4,67,306 = 467,306 = Four hundred sixty seven thousand three hundred six.

(ii) Thirteen lakh forty five

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

Indian numeral form: 13,00,045

International numeral form: 1,300,045

International numeration: One million three hundred thousand forty five.

∴ 13,00,045 = 1,300,045 = One million three hundred thousand forty five.

Question 5

Fill in the blanks.

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

= ________ (International numeral form)
= ________ (Indian numeral form)
= ________ (Indian numeration)

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

= ________ (International numeral form)
= ________ (Indian numeral form)
= ________ (Indian numeration)

Solution

(i) Six hundred four thousand eight hundred forty seven

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

International numeral form: 604,847

Indian numeral form: 6,04,847

Indian numeration: Six lakh four thousand eight hundred forty seven.

∴ 604,847 = 6,04,847 = Six lakh four thousand eight hundred forty seven.

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

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

International numeral form: 2,310,104

Indian numeral form: 23,10,104

Indian numeration: Twenty three lakh ten thousand one hundred four.

∴ 2,310,104 = 23,10,104 = Twenty three lakh ten thousand one hundred four.

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4Multiple Choice Questions

MCQ 1

Seventeen lakh ninety five is equal to:

1. 1,795
2. 17,00,095
3. 17,095
4. 170095

Explanation

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

17,00,000 + 95 = 17,00,095

Correct option: 2

MCQ 2

Five million five hundred fifty five thousand five hundred fifty five is equal to:

1. 5,000,555
2. 5,000,55
3. 5,555,555
4. 5,550,055

Explanation

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

5,000,000 + 555,000 + 555 = 5,555,555

Correct option: 3

MCQ 3

In the International place-value system, 10 million is equal to:

1. One crore
2. Ten lakh
3. Ten crore
4. Hundred thousand

Explanation

The relationship between the two systems is 1 crore = 10 million.

Correct option: 1

MCQ 4

One million is equal to:

1. One crore
2. Ten lakh
3. One lakh
4. Hundred thousand

Explanation

10 lakh = 1 million.

Correct option: 2

MCQ 5

Nine crore five lakh forty one is equal to:

1. 945,410
2. 9,05,00,041
3. 9,050,041
4. 9,005,041

Explanation

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

9,00,00,000 + 5,00,000 + 41 = 9,05,00,041

Correct option: 2

MCQ 6

1 million is equal to ______ ten thousand.

1. Ten
2. Hundred
3. One
4. None of these

Explanation

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

Number of ten-thousands in one million:

1,000,000 ÷ 10,000 = 100

Therefore, 1 million equals 100 ten-thousands.

Correct option: 2

MCQ 7

Forty five lakh thirteen in Indian numeral form is:

1. 4500013
2. 45,00,013
3. 4,500,013
4. Both 2 and 3

Explanation

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

45,00,000 + 13 = 45,00,013

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

Correct option: 2

MCQ 8

Four hundred six thousand seven hundred forty eight in International numeral form is:

1. 406,748
2. 406748
3. 4,06,748
4. Both 1 and 3

Explanation

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

406,000 + 748 = 406,748

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

Correct option: 1

5Statement I–II Type Questions

Question 9

Choose the correct option for the two statements.

Statement 1: As per the Hindu-Arabic system of numeration, 5762983 will be written as 5,762,983.

Statement 2: As per the International system of numeration, 5762983 will be written as 5,762,983.

1. Both statements are true.
2. Both statements are false.
3. Statement 1 is true and Statement 2 is false.
4. Statement 1 is false and Statement 2 is true.

Explanation

Statement 1: In the Indian system, 5762983 = 57,62,983, not 5,762,983. Therefore, Statement 1 is false.

Statement 2: In the International system, 5762983 = 5,762,983. Therefore, Statement 2 is true.

Correct option: 4

Question 10

Choose the correct option for the two statements.

Statement 1: In the Hindu-Arabic system of numeration, 515006200 is read as five hundred fifteen million and six thousand two hundred.

Statement 2: In the International system of numeration, 515006200 is read as fifty one crore fifty lakh six thousand two hundred.

1. Both statements are true.
2. Both statements are false.
3. Statement 1 is true and Statement 2 is false.
4. Statement 1 is false and Statement 2 is true.

Explanation

Statement 1: In the Indian system, 515006200 = 51,50,06,200, read as fifty one crore fifty lakh six thousand two hundred. Therefore, Statement 1 is false.

Statement 2: In the International system, 515006200 = 515,006,200, read as five hundred fifteen million six thousand two hundred. Therefore, Statement 2 is false.

Correct option: 2

6Assertion–Reason Type Questions

Question 11

Determine whether the assertion and reason are true or false.

Assertion (A): In the Hindu-Arabic system of numeration, 9365217 = Ninety three lakh sixty five thousand two hundred and seventeen.

Reason (R): Counting from right to left, the first three digits form the ones period, the next two digits form the thousands period and the next two digits form the lakhs period.

9365217 = 93,65,217

1. A is true, R is false.
2. A is false, R is true.
3. Both A and R are true.
4. Both A and R are false.

Explanation

Assertion: 9365217 = 93,65,217, read as ninety three lakh sixty five thousand two hundred seventeen. Therefore, A is true.

Reason: The Indian system uses a three-digit ones period followed by two-digit thousands and lakhs periods. Therefore, R is true.

Correct option: 3

Question 12

Determine whether the assertion and reason are true or false.

Assertion (A): In the International system of numeration, 638452179 = Six hundred thirty eight million four hundred fifty two thousand one hundred seventy nine.

Reason (R): Counting from right to left, the first three digits form the ones period, the next three digits form the thousands period and the next three digits form the millions period.

638452179 = 638,452,179

1. A is true, R is false.
2. A is false, R is true.
3. Both A and R are true.
4. Both A and R are false.

Explanation

Assertion: 638452179 = 638,452,179, read as six hundred thirty eight million four hundred fifty two thousand one hundred seventy nine. Therefore, A is true.

Reason: The International system groups digits into three-digit periods: ones, thousands and millions. Therefore, R is true.

Correct option: 3

7Frequently Asked Questions

Starting from the right, place the first comma after three digits. Then place a comma after every two digits. Example: 12345678 becomes 1,23,45,678.

Starting from the right, place a comma after every three digits. Example: 12345678 becomes 12,345,678.

Ten lakh make one million. Therefore, 10,00,000 in the Indian system is written as 1,000,000 in the International system.

Ten million make one crore. Thus, 1,00,00,000 in the Indian system equals 10,000,000 in the International system.

Look at the comma pattern. Indian commas follow 3,2,2,2 from the right, whereas International commas follow 3,3,3 from the right.

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