Chapter - 2 | Numbers In Indian and International System | Class 6 Mathematics | Selina Concise Mathematics - Middle School.
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📂 Chapter 2 - Numbers In Indian and International System.
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# Let's Discuss :
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A numeral is a symbol representing a given number and numeration represents that number in words.
The following two types of numeration systems are used in general :
(i) Indian (Hindu-Arabic) system of Numeration.
(ii) International system of Numeration.
# Indian (Hindu-Arabic) system of Numeration :
In Indian number system (also known as denary system), the ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are used to write a numeral (number). Each of these ten symbols is called a digit. Out of these digits :
(i) 0, 2, 4, 6 and 8 are even numerals.
(ii) 1, 3, 5, 7 and 9 are odd numerals.
In Indian System, also called Hindu-Arabic System, groups are made with certain periods to read and write large quantities with ease. Here we use ones, tens, hundreds, thousands and then lakhs and crores. Commas are used to mark thousands, lakhs and crores.
| Ten Crores (TC) | Crores (C) | Ten Lakhs (TL) | Lakhs (L) | Ten Thousands (TTh) | Thousands (Th) | Hundreds (H) | Tens (T) | Ones (o) |
|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
| 7 | 4 | 7 | 6 | 2 | 4 | 5 | 8 | 1 |
Using Commas :
Counting from the right hand-side towards the left hand-side, we use commas to mark thousands, lakhs and crores.
Numerals :
- 12,34,56,789
- 98,76,54,321
- 74,76,24,581
Numeration :
- Twelve crore thirty four lakh fifty six thousand seven hundred eighty nine.
- Ninety eight crore seventy six lakh fifty four thousand three hundred twenty one.
- Seventy four crore seventy six lakh twenty four thousand five hundred eighty one.
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# International system of Numeration :
In International System of numeration, groups are made with certain periods to read and write large quantities with ease. Here we use ones, tens, hundreds, thousands and millions and billions. Commas are used to mark thousands, millions and billions.
| Hundred Billion (H B) | Ten Billion (T B) | Billion (B) | Hundred Millions (H M) | Ten Millions (T M) | Million (M) | Hundred Thousands (H Th) | Ten Thousands (T Th) | Thousand (Th) | Hundred (H) | Tens (T) | Ones (o) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 4 | 3 | 6 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 1 | 6 | 5 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
| 3 | 7 | 4 | 9 | 4 | 7 | 6 | 2 | 4 | 5 | 8 | 1 |
Using Commas :
Counting from the right hand-side towards the left hand-side, we use commas to mark one's, thousand's, million's and billion's.
Numerals :
- 143,623,456,789
- 165,987,654,321
- 374,947,624,581
Numeration :
- One hundred forty three billion six hundred twenty three million four hundred fifty six thousand seven hundred eighty nine.
- One hundred sixty five billion nine hundred eight seven million six hundred fifty four thousand three hundred twenty one.
- Three hundred seventy four billion nine hundred forty seven million six hundred twenty four thousand five hundred eighty one.
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📌 Rules :
01. Do not write the periods in plural. Never write 5493 as
- Five thousands four hundreds ninety three. ❌
- Five thousand four hundred ninety three. ✅
02. Do not use the word 'and' before tens and ones. Do not read 5493 as
- Five thousand four hundred and ninety three. ❌
- Five thousand four hundred ninety three. ✅
03. Do not put commas when writing the numeral. Never write 5493 as
- Five thousand, four hundred, ninety three. ❌
- Five thousand four hundred ninety three. ✅
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-- EXERCISE - 2 (A) --
Q1. Write the following numerals using the Indian System or International system (as required) in words :
(i) 4,35,342 = Four lakh thirty five thousand three hundred forty two.
(ii) 36,71,430 = Thirty six lakh seventy one thousand four hundred thirty.
(iii) 4,28,30,004 = Four crore twenty eight lakh thirty thousand four.
(iv) 75,132,684 = Seventy five million one hundred thirty two thousand six hundred eighty four.
(v) 815,906 = Eight hundred fifteen thousand nine hundred six.
(vi) 5,420,700 = Five million four hundred twenty thousand seven hundred.
Q2. Write the following numbers, placing the commas, according to the Indian system :
(i) 835629 = 8,35,629
(ii) 35640254 = 3,56,40,254
(iii) 2826040 = 28,26,040
Q3. Write the following numbers, by placing the commas, according to the International system :
(i) 6509820 = 6,509,820
(ii) 428140584 = 428,140,584
(iii) 63560981 = 63,560,981
Q4. Fill in the blanks as indicated :
(i) Four lakh sixty seven thousand three hundred six.
= 4,67,306 (In Indian numeral form)
= 467,306 (In International numeral form)
= Four hundred sixty seven thousand three hundred six. (In International numeration)
(ii) Thirteen lakh forty five.
= 13,00,045 (In Indian numeral form)
= 1,300,045 (In International numeral form)
= One million Three hundred thousand forty five (In International numeration)
Q5. Fill in the blanks :
(i) Six hundred four thousand eight hundred forty seven.
= 604,847 (In International numeral form)
= 6,04,847 (In Indian numeral form)
= Six lakh four thousand eight hundred forty seven (In Indian numeration)
(ii) Two million three hundred ten thousand one hundred four.
= 2,310,104 (In International numeral form)
= 23,10,104 (In Indian numeral form)
= Twenty three lakh ten thousand one hundred four (In Indian numeration)
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-- Multiple Choice Type --
# Choose the correct answer from the options given below.
Q1. Seventeen lakh ninety five is equal to :
(i) 1,795
(ii) 17,00,095 ✅
(iii) 17,095
(iv) 170095
Q2. Five million five hundred fifty five thousand five hundred fifty five is equal to :
(i) 5,000,555
(ii) 5,000,55
(iii) 5,555,555 ✅
(iii) 5,550,055
Q3. In international place value system, we write 10-million for :
(i) One crore ✅
(ii) Ten Lakh
(iii) Ten crore
(iv) Hundred thousand
Q4. One million is equal to :
(i) One crore
(ii) Ten lakh ✅
(iii) One lakh
(iv) Hundred thousand
Q5. Nine crore five lakh forty one is equal to :
(i) 945,410
(ii) 9,05,00,041 ✅
(iii) 9,050,041
(iv) 9,005,041
Q6. 1 Million is equal to …… ten thousand.
(i) Ten
(ii) Hundred ✅
(iii) one
(iv) none of these
Q7. Forty five lakh thirteen in Indian numeral form is :
(i) 4500013
(ii) 45,00,013 ✅
(iii) 4,500,013
(iv) Both (ii) and (iii)
Q8. Four hundred six thousand seven hundred forty eight in International numeral form is :
(i) 406,748 ✅
(ii) 406748
(iii) 4,06,748
(iv) Both (i) and (iii)
Q9.
Statement 1 : As per 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.
Which of the following options is correct?
(i) Both the statements are true.
(ii) Both the statements are false.
(iii) Statement 1 is true, and statement 2 is false.✅
(iv) Statement 1 is false, and statement 2 is true.
Explanation :
For statement 1 : In Hindu Arabic system of numeration 5762983 = 57,62,983.
[Given statement is false]
[Given statement is false]
For statement 2 : In International system of numeration 5762983 = 5,762,983
[Given statement is true]
[Given statement is true]
Ans.(iv) statement 1 is false and statement 2 is true.
Q10.
Statement 1 : In Hindu Arabic system of numeration 515006200 is read as : Five hundred fifteen million and six thousand two hundred.
Statement 2 : In International system of numeration 515006200 is read as : Fifty one crore fifty lakh six thousand two hundred.
Which of the following options is correct ?
(i) Both the statements are true.
(ii) Both the statements are false. ✅
(iii) Statement 1 is true, and statement 2 is false.
(iv) Statement 1 is false, and statement 2 is true
Q11. Assertion (A) : In Hindu Arabic system of numeration 9365217 = Ninty three lakh sixty five thousand and two hundred seventeen.
Reason (R) : In Hindu Arabic system counting from right hand side towards left first three digits form one's period next two digits form thousand's period and next two digits form lakh's period.
∴ 9365217 = 93,65,217
(i) (1)
(ii)(2)
(iii)(3) ✅
(iv)(4)
Q12. Assertion (A) : In International system of numeration 638452179 = Six hundred thirty eight million four hundred fifty two thousand one hundred seventy nine.
Reason (R) : In International system of numeration counting from right hand side towards left first three digits form one's period, next three digits form thousand's period and next three digits form million's period.
∴ 638452179 = 638,452,179
(i) (1)
(ii)(2)
(iii)(3) ✅
(iv)(4)
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