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 to 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
