The Number System | Math | Chapter 2 | Grade 5

The Number System - Math Chapter-2, Grade 5:

Objectives:

Students will be able to:
Recognize and read numbers upto 8-digits.
Read the number in the local and international systems.
Make smallest and largest number from given digits.
Recognize face value and Place value.
Use big numbers in real life practices.

Outcomes:

Students will have learnt the place value of numbers upto 8-digits both in Nepali and International System.

Materials:

Place value chart, beads, calculator, computer with internet (if available), etc.

Things To Know:

➧ There are two number systems in use. They are Devanagari and Hindu-Arabic number systems.
➧ Positions of a digit in a number determine it's place value.
➧ In Nepali number system, each pair of digits greater than hundreds places are separated by commas (,).
➧ In International number system, each group of three digits greater than 100 places are separated by commas (,).
➧ 100 thousands = 1 lakh
➧ 10 lakhs = 1 million
➧ In Roman number system we use 7 symbols. They are, I, V, X, L, C, D and M.

2.1 The Number System/button

Question: What is a number?
Answer: A number is a mathematical symbol used in counting labeling and measuring things.

Question: What is a number system?
Answer: The writing system for expressing numbers to a given sets using digits is known as the number system.

Also Check:

We know that we use number to express how many or how much a quantity is. This means we quantify the physical objects with the help of number system.

The most popular or widely used number system throughout the world is the Hindu-Arabic Number System. Hindu-Arabic Number System was first discovered by Hindus and Arab transmitted it to the rest of the world later on. Most of the time we use Hindu-Arabic number system in our daily life.

Digits used for Hindu-Arabic Number system are:-

0	1	2	3	4	5	6	7	8	9

In Devanagari Number System, everything is same in expression but we use our own symbols for these digits.

For Devanagari number systerm, we use,

०	१	२	३	४	५	६	७	८	९

We use the digits to express any number.

Number	No. of digits
123	3 number of digits
2,567	4 number of digits
2,36,258	6 number of digits

2.2 Face value and place value/button

The Hindu-Arabic Number System is based on the group of tens. Group of tens are categorized in the form of ones, tens, hundreds, thousands and so on.

Lets see a number in the form of periods and it's place value in table as below.

This is read as sixty three crore forty seven lakh ninety two thousand one hundred eight.

2.3 Local and International number system/button

In Nepal, locally we have our own number system which is quite different than the international number system.

Nepali Number System/Local System: In Nepali number system/local number system, we have ones, tens, hundreds, thousands, ten thousands, lakhs, ten lakhs, crores, ten crores, arabs, ten arabs and so on.

International Number System: In International number system, we have ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, ten millions, hundred millions, billions, ten billions, hundred billions and so on.

Local-Nepali Number System Chart:/button

Ten Kharabs	10,00,00,00,00,000
Kharabs	1,00,00,00,00,000
Ten Arabs	10,00,00,00,000
Arabs	1,00,00,00,000
Ten Crores	10,00,00,000
Crores	1,00,00,000
Ten Lakhs	10,00,000
Lakhs	1,00,000
Ten Thousands	10,000
Thousands	1,000
Hundreds	100
Tens	10
Ones	1

International Number System Chart:/button

Trillions	1,000,000,000,000
Hundred Billions	100,000,000,000
Ten Billions	10,000,000,000
Billions	1,000,000,000
Hundred Millions	100,000,000
Ten Millions	10,000,000
Millions	1,000,000
Hundred Thousands	100,000
Ten Thousands	10,000
Thousands	1,000
Hundreds	100
Tens	10
Ones	1

Comparison of Local-Nepali System and International System/button

Let us consider a number 639512048769.

#	International System	#	Local-Nepali System
6	Hundres Billions	6	Kharabs
3	Ten Billions	3	Ten Arabs
9	Billions	9	Arabs
5	Hundred Millions	5	Ten Crores
1	Ten Millions	1	Crores
2	Millions	2	Ten Lakhs
0	Hundred Thousands	0	Lakhs
4	Ten Thousands	4	Ten Thousands
8	Thousands	8	Thousands
7	Hundreds	7	Hundreds
6	Tens	6	Tens
9	Ones	9	Ones

Here, in International number system, the number name of 639,512,048,769 is → Six hundred thirty-nine billion five hundred twelve million forty eight thousand seven hundred sixty nine.

And in Local/Nepali number system, the number name of 639,512,048,769 is → Six kharab thirty nine arab fifty one crore twenty lakh forty eight thousand seven hundred sixty nine.

Use of Commas (,) in Local Number System and International Number System:

According to Nepali/Local Number System, comma separates the last 3 digits of unit periods at first and then ten thousands, ten lakhs, ten crores, and so on.

According to International Number System, comma separates the last 3 digits of unit periods at first and then hundred thousands, hundred millions, hundred billions and so on.

Grade 5: Math Subject-Chapter:2 - The Number System: Exercise 2.1 (With Solution)/button

1. Write the number names in both Nepali and International system.

a. 2031
Solution:
Nepali/Local System number name of 2,031 = Two thousand and thirty one.
International System number name of 2,031 = Two thousand and thirty one.

b. 40035
Solution:
Nepali/Local System number name of 40,035 = Forty thousand and thirty five.
International System number name of 40,035 = Forty thousand and thirty five.

c. 756321
Solution:
Nepali/Local System number name of 7,56,321 = Seven lakh fifty six thousand three hundred and twenty one.
International System number name of 756,321 = Seven hundred fifty six thousand three hundred and twenty one.

d. 900000
Solution:
Nepali/Local System number name of 9,00,000 = Nine lakhs.
International System number name of 900,000 = Nine hundred thousands.

e. 2999999
Solution:
Nepali/Local System number name of 29,99,999 = Twenty lakh ninety nine lakh nine hundred and ninety nine.
International System number name of 2,999,999 = Two million nine hundred ninety nine thousand nine hundred and ninety nine.

f. 67054329
Solution:
Nepali/Local System number name of 6,70,54,329 = Six crore seventy lakh fifty four thousand three hundred and twenty nine.
International System number name of 67,054,329 = Sixty seven million fifty four thousand three hundred and twenty nine.

g. 445566778
Solution:
Nepali/Local System number name of 44,55,66,778 = Forty four crore fifty five lakh sixty six thousand seven hundred and seventy eight.
International System number name of 445,566,778 = Four forty five million five hundred sixty six thousand seven hundred and seventy eight.

h. 1068375328
Solution:
Nepali/Local System number name of 1,06,83,75,328 = One arab six crore eighty three lakh seventy five thousand three hundred and twenty eight.
International System number name of 1,068,375,328 = One billion sixty eight million three hundred seventy five thousand three hundred and twenty eight.

i. 3000678900
Solution:
Nepali/Local System number name of 3,00,06,78,900 = Three arab six lakh seventy eight thousand and nine hundred.
International System number name of 3,000,678,900 = Three billion six hundred seventy eight thousand and nine hundred.

j. 432156789031
Solution:
Nepali/Local System number name of 3,00,06,78,900 = Three arab six lakh seventy eight thousand and nine hundred.
International System number name of 3,000,678,900 = Three billion six hundred seventy eight thousand and nine hundred.

k. 100100010000
Solution:
Nepali/Local System number name of 1,00,10,00,10,000 = One kharab ten crore and ten thousand.
International System number name of 100,100,010,000 = One hundred billion one hundred million and ten thousand.

2. Write the following numbers into both Nepali and International place value table.

a. 63057890152
Solution:
Nepali-Local place value table:

Ten Kharab	Kharab	Ten Arab	Arab	Ten Crore	Crore	Ten Lakhs	Lakhs	Ten Thousands	Thousands	Hundreds	Tens	Ones
		6	3	0	5	7	8	9	0	1	5	2

International place value table:

Trillions	Hundred Billions	Ten Billions	Billions	Hundred Millions	Ten Millions	Millions	Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Ones
		6	3	0	5	7	8	9	0	1	5	2

b. 1357902468075

Nepali-Local place value table:

Ten Kharab	Kharab	Ten Arab	Arab	Ten Crore	Crore	Ten Lakhs	Lakhs	Ten Thousands	Thousands	Hundreds	Tens	Ones
1	3	5	7	9	0	2	4	6	8	0	7	5

International place value table:

Trillions	Hundred Billions	Ten Billions	Billions	Hundred Millions	Ten Millions	Millions	Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Ones
1	3	5	7	9	0	2	4	6	8	0	7	5

c. 465768542001

Nepali-Local place value table:

Ten Kharab	Kharab	Ten Arab	Arab	Ten Crore	Crore	Ten Lakhs	Lakhs	Ten Thousands	Thousands	Hundreds	Tens	Ones
	4	6	5	7	6	8	5	4	2	0	0	1

International place value table:

Trillions	Hundred Billions	Ten Billions	Billions	Hundred Millions	Ten Millions	Millions	Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Ones
	4	6	5	7	6	8	5	4	2	0	0	1

d. 403210550638

Nepali-Local place value table:

Ten Kharab	Kharab	Ten Arab	Arab	Ten Crore	Crore	Ten Lakhs	Lakhs	Ten Thousands	Thousands	Hundreds	Tens	Ones
	4	0	3	2	1	0	5	5	0	6	3	8

International place value table:

Trillions	Hundred Billions	Ten Billions	Billions	Hundred Millions	Ten Millions	Millions	Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Ones
	4	0	3	2	1	0	5	5	0	6	3	8

3. Express the following number names into numbers.

a. Seven thousand two hundred and thirty six. → 7,236.
b. Fourteen thousand and seven. → 14,007.
c. Nine lakh nine thousand nine hundred and nine. → 9,09,909.
d. Seven hundred thousand and thirty. → 700,030.
e. Seventy seven crores. → 77,00,00,000.
f. One million seventy nine thousand and forty. → 1,079,040.
g. Three hundred ten billions four hundred millions and six. → 310,400,000,006.
h. Nine kharab seven arab and one. → 9,07,00,00,00,001.

4. Write the place value underlined digits in Nepali system.

a. 6360894
Solution: 6 = 60,000 (Ten Thousands)

b. 44506387
Solution: 5 = 5,00,000 (Lakhs)

c. 123498765
Solution: 3 = 30,00,000 (Ten Lakhs)

d. 306345310
Solution: 6 = 60,00,000 (Ten Lakhs)

e. 5768695301
Solution: 7 = 70,00,00,000 (Ten Crores)

f. 10034006351
Solution: 1 = 10,00,00,00,000 (Ten Arabs)

5. Write the place value of the underlined digits in International system.

a. 3756432104
Solution: 4 = 400,000 (Hundred Thousands)

b. 6666667778
Solution: 6 = 60,000,000 (Ten Millions)

c. 4003765492
Solution: 3 = 3,000,000 (Millions)

d. 97531024680
Solution:7 = 7,000,000,000 (Billions)

6. Convert the following Nepali number into International number.

a. Seven lakh
Solution: Seven lakh = 7,00,000.
In international number system = 700,000 (Seven hundred thousands).

b. Seventy nine lakhs
Solution: Seven lakh = 79,00,000.
In international number system = 7,900,000 (Seven millions nine hundred thousands).

c. Two crore ninety lakh
Solution: Two crore ninety lakh = 2,90,00,000.
In international number system = 29,000,000 (Twenty nine millions).

d. Nineteen crore fifty lakh
Solution: Nineteen crore fifty lakh = 19,50,00,000.
In international number system = 195,000,000 (One hundred ninety five millions).

e. Ninety three crore sixty lakh
Solution: Nineteen three crore sixty lakh = 93,60,00,000.
In international number system = 936,000,000 (Nine hundred thirty six millions).

f. Forty one Arab thirty one crore
Solution: Forty one Arab thirty one crore = 41,31,00,00,000.
In international number system = 41,310,000,000 (Forty one billion three hundred ten millions).

g. Thirty nine kharab twenty crore one lakh
Solution: Thirty nine kharab twenty crore one lakh = 39,21,00,01,00,000.
In international number system = 3,921,000,100,000 (Three trillions nine hundred twenty one billion and one hundred thousand).

7. Write the corresponding values.

a. 1 lakh = 100 thousands.
b. 10 crores = 100 millions.
c. 100 millions = 10 crore
d. 100 billions = 1 kharab
e. 60 lakhs = 6 millions.

8. Use commas according to both Nepali and International system for the following numbers.

a. 506320
Solution:
Nepali System - 5,06,320
International System - 506,320

b. 6176400
Solution:
Nepali System - 61,76,400
International System - 6,176,400

c. 28576187
Solution:
Nepali System - 2,85,76,187
International System - 28,576,187

d. 265500007
Solution:
Nepali System - 26,55,00,007
International System - 265,500,007

e. 5467762320
Solution:
Nepali System - 5,46,77,62,320
International System - 5,467,762,320

f. 46000003701
Solution:
Nepali System - 46,00,00,03,701
International System - 46,000,003,701

Grade 5: Math Subject-Chapter:2 - The Number System: Exercise 2.2 (With Solution)/button

1. Express the following numbers into expanded forms.

a. 21
Solution: 20 + 1

b. 331
Solution: 300 + 30 + 1

c. 2000
Solution: 2000 + 000 + 00 + 0

d. 8431603
Solution: 8000000 + 400000 + 30000 + 1000 + 600 + 00 + 3

e. 85900523
Solution: 80000000 + 5000000 + 900000 + 00000 + 0000 + 500 + 20 + 3

2. Express in short form.

a. 400 + 10 + 7
Solution: 417

b. 7000 + 600 + 10 + 8
Solution: 7,618

c. 9000 + 90 + 9
Solution: 9,099

d. 20000 + 5000 + 700 + 80 + 1
Solution: 25,781

3. Write the greatest and least number of .

a. 2 - digits
Solution:
2 - digits greatest number = 99
2 - digits smallest number = 10

b. 3 - digits
Solution:
3 - digits greatest number = 999
3 - digits smallest number = 100

c. 4 - digits
Solution:
4 - digits greatest number = 9999
4 - digits smallest number = 1000

d. 5 - digits
Solution:
5 - digits greatest number = 99999
5 - digits smallest number = 10000

e. 7 - digits
Solution:
7 - digits greatest number = 9999999
7 - digits smallest number = 1000000

f. 9 - digits
Solution:
9 - digits greatest number = 999999999
9 - digits smallest number = 100000000

4. Find the difference of the greatest and least number formed by

a. 3 - digits
Solution:
3 digits greatest number = 999
3 digits smallest number = 100
∴ 999 - 100 = 899

b. 5 - digits
Solution:
5 digits greatest number = 99999
5 digits smallest number = 10000
∴ 99999 - 10000 = 89,999.

c. 8 - digits
Solution:
8 digits greatest number = 99999999
8 digits smallest number = 10000000
∴ 99999999 - 10000000 = 89,999999.

5. What is the difference of the greatest number formed by 6 - digits and greatest number formed by 5 - digits?
Solution:
The greatest number formed by 6 - digits = 999999
The greatest number formed by 5 - digits = 99999
∴ The difference of the greatest number formed by 6 - digits and greatest number formed by 5 - digits is 999999 - 99999 = 9,00,000.

6. What is the difference of the least number formed by 7 - digits and the greatest number formed by 6 - digits.
Solution:
The least number formed by 7 - digits = 1000000.
The least number formed by 6 - digits = 100000.
∴ The difference of the least number formed by 7 - digits and the greatest number formed by 6 - digits is 1000000 - 100000 = 9,00,000.

7. What is the difference between the least number and the greatest number formed by the following digits.

a. 7,6,9,2
Solution:
The least number formed by 7,6,9,2 = 2,679.
The greatest number formed by 7,6,9,2 = 9,762.
∴ The difference between the least number and the greatest number formed by 7,6,9,2 is 9,762 - 2,679 = 7,083.

b. 3,7,5,4
Solution:
The least number formed by 3,7,5,4 = 3,457.
The greatest number formed by 3,7,5,4 = 7,543.
∴ The difference between the least number and the greatest number formed by 3,7,5,4 is 7,543 - 3,457 = 4,086.

c. 3,0,6,9
Solution:
The least number formed by 3,0,6,9 = 3,069.
The greatest number formed by 3,0,6,9 = 9,630.
∴ The difference between the least number and the greatest number formed by 3,0,6,9 is 9,630 - 3,069 = 6,561.

d. 4,0,6,8
Solution:
The least number formed by 4,0,6,8 = 4,068.
The greatest number formed by 4,0,6,8 = 8,640.
∴ The difference between the least number and the greatest number formed by 4,0,6,8 is 8,640 - 4,068 = 4,572.

8. Find the difference between the greatest number formed by the digits, 7,6,0,3,9 and the smallest number formed by 1,0,9,7,6.
Solution:
The greatest number formed by the digits, 7,6,0,3,9 = 97,630.
The smallest number formed by the dgits, 1,0,9,7,6 = 10,679.
∴ The difference between the greatest number formed by the digits, 7,6,0,3,9 and the smallest number formed by 1,0,9,7,6 is 97,630 - 10,679 = 86,951.

9. Rewrite the following numbers in Devanagari and write their number names in Nepali.

a. 578
Solution:
५७८ = पाँच सय अठहत्तर।

b. 6308
Solution:
६,३०८ = छ हजार तीन सय आठ।

c. 17610
Solution:
१७,६१० = सत्र हजार छ सय दश।

d. 115300
Solution:
१,१५,३०० = एक लाख पन्ध्र हजार तीन सय।

e. 10,00,000
Solution:
१०,००,००० = दश लाख।

f. 14113609
Solution:
१,४१,१३,६०९ = एक करोड एकचालिस लाख तेह्र हजार छ सय नौ।

g. 44716500
Solution:
४,४७,१६,५०० = चार करोड सच्चालीस लाख सोह्र हजार पाँच सय।

h. 670056009
Solution:
६७,००,५६,००९ = सतसट्ठी करोड छपन्न हजार नौ।

i. 3477500699
Solution:
३,४७,७५,००,६९९ = तीन अरब सच्चालीस करोड पचहत्तर लाख छ सय उनान्सय।

10. The population of Nepal according to 2068 B.S. Census is 2,66,53,749. Express this number in Devanagari and write the number name in Nepali.
Solution:
2,66,53,749 = २,६६,५३,७४९ = दुइ करोड छैसट्ठी लाख त्रिपन्न हजार सात सय उन्पचास।

11. According to the National Budget of Nepal Rs. 5,17,24,00,00,000 is allocated. Express this number in both Hindu-Arabic and Devanagari script. Write this number in Nepali too.
Solution:
National Budget of Nepal Rs. 5,17,24,00,00,000.
Hindu-Arabic script = 517,240,000,000 = Five hundred seventeen billion two hundred forty millions.
Devanagari script = 5,17,24,00,00,000 = Five kharab seventeen arab twenty four crore.
Nepali = ५,१७,२४,००,००,००० = पाँच खरब सत्र अरब चौबीस करोड।

12. According to the data from Election commission of Nepal, one crore twenty one lakh voters casted their votes on the 2nd constituent assembly election 2070 B.S. Express the number in Devanagari script. Write this number in Nepali too.
Solution:
One crore twenty one lakh
Devanagari script = 1,21,00,000.
Nepali = १,२१,००,०००

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