## Arithmetic Chapter 2 Concept Of Seven And Eight Digit Number

**Question 1. Write one perfect seven-digit number and one perfect eight-digit number.**

** Solution**: One perfect seven-digit number is 9086542 and one perfect eight-digit number is 70994312.

**Question 2. What are the actual (real) value and the place value of 4 in the number 89743201?**

** Solution**: The actual value (or real value) of 4 in the number 89743201 is 4.

**For place value of 4:**

** Read and Learn More WBBSE Solutions For Class 6 Maths**

The digit 4 is placed in Ten thousand place. The place value of Ten thousand is 10000**.**

The place value of 4

= 4 x 10000

= 40000.

Here, we have four places on the right-hand side of 4 in the place value list. So the place value of 4 (in short) is 40000.

**Question 3.** **What is the difference between the place values of 2 in two places of the number 37452129?**

** Solution**: Now,

We see that in the number 37452129, the first 2 (from left) is placed in the thousands place and its place value is 1000 and the second 2 is placed in the tens place and its place value is 10.

∴ The place value of the first 2 is 2 x 1000 = 2000

and the place value of the second 2 is 2 x 10 = 20

∴ The required difference = 2000 – 20 = 1980.

**Question 4. What is the difference between the place value and the actual value of 9 in the number 27946138?**

** Solution**: The place value of 9 in the number 27946138 is 9 x 100000 = 900000 and the actual value of 9 is 9.

The required difference = 900000 – 9

= 899991

The difference between the place value and the actual value = 899991

** Question 5. Write the following numbers using numerals ;**

**1. Seventy-eight lac eight hundred eight;**

**2. Ninety-three lac forty-four thousand six hundred five ;**

**3. Three crores three lac three thousand three hundred three ;**

**4. Forty-four core forty-four lac forty-four thousand forty-four;**

**5. Seventy-eight crore eight thousand eight ;**

**6. Two crores two lac two thousand two hundred two.**

** Solution**:

1.

∴ The required number = is 7800808.

2.

∴ The required number = is 9344605.

3.

∴ The required number = is 30303303.

4.

∴ The required number = is 444444044.

5.

∴ The required number = is 780008008.

6.

∴ The required number = is 20202202.

**Question 6. Choose the correct answer :**

**1. Twenty lac ten thousand eight**

**1. 2001008 **

**2. 2010008 **

**3. 2100008 **

**4. 20010080**

**2. One crore eleven lac eight thousand forty-one**

**1. 11018041 **

**2. 11010841 **

**3. 11108041 **

**4. 10111481**

**3. Two crores three lac sixty thousand five hundred twenty-six **

**1. 20360526 **

**2. 20365026 **

**3. 20360562 **

**4. 23065026**

** Solution **:

1.

∴ The required number is 2. 2010008.

2.

∴ The required number 3. is 11108041.

3.

∴ The required number is 1. 20360526.

**Question 7. Write in words:**

**1. 782005 **

**2. 4207029 **

**3. 30030030 **

**4. 50505005 **

**5. 42034047.**

Solution:

1.

∴ The number is seven lac eighty-two thousand five.

2.

∴ The number is forty-two lac seven thousand twenty-nine.

3.

∴ The number is three crore thirty thousand thirty.

4.

∴ The number is five crores five lac five thousand five.

5.

∴ The number is four crores twenty lac thirty-four thousand forty-seven.

**Question 8.** **Write the expanded form in place value in each of the following numbers :**

**1. 4627593 **

**2. 2213101 **

**3. 9999999**

**4. 7007007**

**5. 2406739**

** Solution **:

**1. In the number 4627593**

the place value of 4 = 4000000

the place- value of 6 = 600000

the place value of 2 = 20000

the place value of 7 = 7000

the place value of 5 = 500

the place value of 9 = 90

the place value of 3 = 3.

∴ The required expanded form of the number 4627593

= 4000000 + 600000 + 20000 + 7000 + 500 + 90 + 3

2. In the number 2213101

the place value of 2 (first from left) = 2000000

the place value of 2 (second from left) = 200000

the place value of first 1 = 10000

the place value of 3 = 3000

the place value of second 1 = 100

the place value of 0 = 0

the place value of third 1 = 1

∴ The required expanded form of the number 2213101

= 2000000 + 200000 + 10000 + 3000 + 100 + 1

2213101 = 2000000 + 200000 + 10000 + 3000 + 100 + 1

3. In the number 9999999

the place value of the first 9 (from left) = 9000000

the place value of second 9 = 900000

the place value of third 9 = 90000

the place value of fourth 9 = 9000

the place value of fifth 9 = 900

the place value of sixth 9 = 90

the place value of seventh 9 = 9

9999999 = 9000000+900000+ 90000+9000+900+90+9

4. In the number 7007007

the place value of first (from left) 7 = 7000000

the place value of first 0 = 0

the place value of second 0 = 0

the place value of second 7 = 7000

the place value of third 0 = 0

the place value of fourth 0 = 0

the place value of third 7 = 7

∴ The required expended form of 7007007 = 7000000 + 7000 + 7

Since the place value of 0 is always 0, it is not necessary to obtain the place value of 0 and so you need not put 0 in the expanded form.

5. In the number 2406739

the place value of 2 = 2000000

the place value of4 = 400000

the place value of 0 = 0

the place value of 6 = 6000

the place value of 7 = 700

the place value of 3 = 30

the place value of 9 = 9

∴ The required expanded form of the number

= 2000000 + 400000 + 6000 + 700 + 30 + 9

2406739 = 2000000 + 400000 + 6000 + 700 + 30 + 9

**Question 9. Write in words the place value of the following numbers :**

**1. 90874326 **

**2. 22222222**

**Solution:**

1. We write,

**∴** **According to the place value:** Nine crores eight lac seven ten thousand four thousand three hundred two ten six units.

2. We write,

**∴ According to the place value:** Two crores two ten lac two ten thousand two hundred two ten two units.

**Question 10: Write the greatest and least 8-digit numbers taking the digits in each of the following :**

**1. 3, 5, 7, 9, 2, 6, 5, 6 **

**2. 6, 4, 8, 5, 1, 2, 0, 3 **

**3. 7, 3, 2, 1, 9, 5, 6, 0**

**4. 8, 9, 2, 4, 7, 3, 2, 1**

** Solution **:

**1. We have the digits:** 3, 5, 7, 9, 2, 6, 5, 6.

The greatest 8-digit numbers taking above digits = 97665532

and the least number = 23556679

**2. We have the digits:** 6, 4, 8, 5, 1, 2, 0, 3

With the above digits, the greatest 8 digit numbers = 86543210 and the least 8 digit numbers = 10234568

**3. We have the digits:** 7, 3, 2, 1, 9, 5, 6, 0

With the above digits, the greatest 8-digit numbers = are 97653210, and the least 8-digit numbers = are 10235679.

**4. We have the digits:** 8, 9, 2, 4, 7, 3, 2, 1

With the above digits, the greatest 8-digit numbers = are 98743221, and the least 8-digit numbers = 12234789.

1. Special care is to be taken while writing the greatest number using the given digits, that the greater digit can not be placed after a smaller digit.

2. While writing the least number, care is to be taken that the smaller digit can riot be placed after a greater digit.

3. If the given digits contain 0 as one of the digits, then 0 is the least of the digits. While writing the least number 0 can not be placed in the first place (from left) because then the number obtained is not a perfect number. In this case, the next least digit is written first, then 0 is placed next to it.

**Question 11. Write the following numbers in ascending (increasing) order in each case :**

7525762, 7525662, 7526762, 7525652.

**8705321, 8702358, 8707341, 8703741**

**518890, 872300, 27562, 300252**

** Solution **:

**1. The given numbers are **

7525762, 7525662, 7526762, 7525652

The first three digits of the given four numbers are the same. The fourth digits of the given four numbers are 5, 5, 6, and 5.

Here 6 > 5

∴ The greatest number is 7526762

The fifth digits of the remaining 3 numbers are 7, 6, and 6.

Here 7 > 6

∴ The next i.e. second greatest integer is 1525762.

The sixth digits of the remaining 2 numbers are 6 and 5.

Here 6 > 5.

∴ The third greatest number is 7525662.

∴ 7526762 > 7525762 > 7525662 > 7525652

∴ Among the given numbers in ascending order, we get,

7525652, 7525662, 7525762, 7526762

2. The given numbers are

8705321, 8702358, 8707341, 8703741

The first 3 digits of the given four numbers are the same

The fourth digits of the given four numbers are 5, 2, 7, 3

As 7 > 5 > 3 > 2,

∴ 8707341 > 8705321 > 8703741 > 8702358

So arranging the given numbers in ascending order, we get,

8702358, 8703741, 8705321, 8707341.

**3. The given numbers are **

518890, 872300, 27562, and 300252.

Here the third number is a number containing 5 digits and the first, second, and fourth numbers are 6-digit numbers.

So the third number he., 27562 is the least number.

The first digits of the remaining 3 numbers are 5, 8, and 3.

As 8 > 5 > 3,

∴ 872300 > 518890 > 300252 > 27562

∴ Arranging the given numbers in ascending order, we get,

27562, 300252, 518890, 872300

**Question 12. Write the following numbers in descending (decreasing) order in each case :**

**1. 4503210, 4503201, 4503120, 4502210**

**2. 301516, 8640051, 302560, 6352289**

**3. 5102080, 5108200, 5100280, 5182000.**

**Solution : **

**1. The given numbers are **

4503210, 4503201, 4503120, 4502210

All the given four numbers are 7-digit numbers and the first 3 digits of all the numbers are the same.

The fourth digits of the numbers are 3, 3, 3, 2.

4502210 is the least number.

The fifth digits of the remaining 3 numbers are 2, 2, 1, and 2 > 1, we get the least of these 2 remaining numbers is 4503120.

Again the sixth digits of the remaining 2>numbers are 1 and 0. But 1 > 0 /. 4503210 > 4503201

So arranging the given numbers in descending order, we get,

4503210, 4503201, 4503120, 4502210

**2. The given numbers are **

301516, 8640051, 302560, and 6352289.

Here the first and third numbers are 6-digit numbers and the second and fourth numbers are 7-digit numbers.

The first digits of the second and fourth numbers are 8 and 6. But 8 > 6.

So, 8640051 > 6352289.

The first two. digits of the first and third numbers are the same. The third digits of these- two numbers are 1 and 2.

As 2 > 1, we get 302560 > 301516.

8640051 > 6352289 > 302560 > 301516.

Arranging the given numbers in descending orders, we get,

8640051, 6352289, 302560, 301516.

**3. The given numbers are**

5102080, 5108200, 5100280, and 5182000.

All the given four numbers are 7-digit numbers. The first two digits of all the numbers are the same.

The third digits of the given numbers are 0, 0, 0, and 8. But 8 > 0.

5182000 is the greatest number.

The fourth digits of the remaining 3 numbers are 2, 8, and 0.

But 8 > 2 > 0

∴ 5108200 > 5102080 > 5100280

So we get, 5182000 > 5108200 > 5102080 > 5100280.

∴ Arranging the given numbers in descending order, we get,

5182000, 5108200, 5102080, 5100280

**Question 13. The sum of two numbers is ****82945195****; one number is ****69100278. ****What is the other number?**

**Solution :
**

**Given:**

The sum of two numbers is 82945195; one number is 69100278.

∴ The other number is 13844917.

**Question 14. The difference between the two numbers is ****28351036; ****if the greater number is ****30529179, ****then what is the smaller number?**

**Solution:**

**Given:**

The difference between the two numbers is 28351036; if the greater number is 30529179,

∴ The smaller number is 2178143.

**Question 15. ****The difference between the two numbers is ****28351036; ****if the greater number is ****30529179, ****then what is the smaller number?**

**Solution :**

**Given:**

The difference between the two numbers is 28351036; if the greater number is 30529179

∴ The other number is 3010098.

Question 16. What least number must be added to 234567 so that the sum is divisible by 835?

**Solution:**

**Given:**

234567 And 835

835 – 767 = 68

∴ 68 is to be added to the given number 234567 so that the sum is divisible by 835.

**Question 17. A publishing organization made a profit of ₹7521200 last year and it has made a profit of ₹ 3250325 this year. How much does the total profit **make **the organization in the two years?**

**Solution :**

**Given:**

A publishing organization made a profit of ₹7521200 last year and it has made a profit of ₹ 3250325 this year.

∴ The organization has made a total profit in two years = ₹ 1,07,71,525.

**Question 18. By selling the property Sukhendubabu got ₹35629850. He gave****X** ₹**10062000 t o his wife and divided ₹**

**13050000 among his three children equally. He donated the rest of the money for constructing a village school. Then****1. how much money each child was given?**

**2. how much money did he donate to the village school?**

**Solution : **

1. Total amount of money was distributed equally among three children = ₹ 13050000.

Each child, received = ₹ (13050000 ÷ 3) = ₹ 4350000

2.

Remaining money = ₹ (35629850 – 23112000)

= ₹ 12517850

∴ Sukhendubabu donated ₹12517850 for the construction of a village school

**Question 19. The area of the country is about 3287263 sq. km. The country has a hilly area is about 754740 sq. km. and a plane area is about 2503000 sq. km. What is the area of the remaining land leaving hilly and plane areas?**

**Solution:**

**Given:**

The area of the country is about 3287263 sq. km. The country has a hilly area is about 754740 sq. km. and a plane area is about 2503000 sq. km.

Hilly area ** = **754740 sq. km.

Plane area = 2503000 sq. km.

(Adding) = 3257740 sq. km.

Total of Hilly and plane areas = 3257740 sq. km.

Area or the remaining land = (3287263 – 3257740) sq. km.

= 29523 sq. km.

The area of the remaining land leaving hilly and plane areas = 29523 sq. km.

**Question 20. The population of a city is two crore ninety-eight lac seventy-two thousand six hundred. Of them, 12500500 are men and 8872435 are women and the remaining are children. What is the number of children?**

**Solution :**

**Given:**

The population of a city is two crore ninety-eight lac seventy-two thousand six hundred. Of them, 12500500 are men and 8872435 are women and the remaining are children.

∴ Total number of men and women = 21372935

Again total population in the city = Two crores ninety-eight lac seventy-two thousand six hundred = 29872600

∴ Total number of children = 29872600 – 21372935

= 8499665.

Total number of children = 8499665.

**Question 21. In the last parliament, election Adhirbabu received 840967 votes, Asimbabu received 133545 votes and Tapanbabu received 40907 votes.**

**1. Who received less number of votes?**

**2. Who received the highest number of votes and won the election?**

**3. What was the difference between the votes cast in favor of ****Adhirbabu and Asimbabu?**

**4. If there is no other candidate, then what was the total number of casted valid votes in this center?**

**Solution:**

1. Since 840967 > 133545 > 40907,

∴ Tapanbabu received less number of votes.

2. Since 840967 > 133545 > 40907,

∴ Adhirbabu received the highest number of votes and he won the election.

3. Difference between the votes cast in favor of Adhirbabu and Asimbabu

= 840967 – 133545

= 707422

4. The total number of valid votes cast in the center

= 840967 + 133545 + 40907

= 1015419.

**Question 22. The total population in the city of Rahul is 2708724 and the total population in the city of Indra is 3878899.**

**1. Which city has less population and by how many?**

**2. What is **the**total population of the two cities?**

** Solution **:

1. ∴ 3878899 > 2708724

∴ The city of Rahul has less number of population than that of Indra.

Again, 3878899 – 2708724

= 1170175

∴ The population in the city of Rahul is 1170175 less than the city of India.

2. Total population in the two cities

= 3878899 + 2708724

= 6587623