999 + 1 =1000
9,999 + 1 =10,000
99,999 + 1 = 1,00,000
9,99,999 + 1 = 10,00,000

83853

8000

We have, 572
(i) Divisibility by 4 

Number formed by last two digits = 72.
On dividing 72 by 4, we get
Remainder = 0
\(\because\) 72 is divisible by 4, so 572 is also divisible by 4.
(ii) Divisibility by 8
Number formed by last three digits = 572

On dividing 572 by 8, we get Remainder \(\neq\) 0
\(\therefore\) 572 is not divisible by 8.

Given number is 2936. Here, hundred digit is 9, which is more than 5 i.e. 9 > 5.
∴ The required rounded number 2936 = 3000

Here, we have 32
32 = 29 +3

Numbers after commas are as follows: 7, 52, 21, 302.

We have, 20
20 = 1 x 20; 20 = 2 x 10; 20 = 4 x 5
\(\therefore\)Factors of 20 are 1, 2, 4, 5, 10 and 20.

Given, quantity of petrol filled on Monday = 40 L
Quantity of petrol filled on the next day i.e. Tuesday = 50 L
Total quantity of petrol = 40 + 50 = 90 L
Cost of petrol = Rs 44 per litre
Total cost of petrol = Cost per litre x Total quantity of petrol
                           = 44 x 90 = Rs 3960
Hence, total cost of petrol is Rs 3960.

We have, 8937 x 648 + 8937 x 122 + 8937 x 230 = 8937 (648 + 122 + 230)
               = 8937 x 1000 = 8937000 [taking 8937 as common term].

Cloth required for 1 shirt =3 m 05 cm
Cloth required for 14 shirts = (3 m 05 cm) \(\times\) 14
=14\(\times\)3+14\(\times\)05=42 m 70 cm

(i) 5981 rounded off to nearest tens = 5980
4428 rounded off to nearest tens = 4430
∴ Estimated product = 5980 \(\times\) 4430 = 26491400
(ii) 5981 rounded off to nearest hundreds = 6000
4428 rounded off to nearest hundreds = 4400
∴ Estimated product = 6000 \(\times\) 4400 = 26400000

According to the patterns of whole number,

On checking the rounding off in respect of given numbers, we find that the rounding off of 7805, 53552 and 3499 are incorrect.
Their correct results should be 7800, 54000 and 3000, respectively.

Given, sale of books in Ist week = Rs. 2,85,891
Sale of books in IInd week = Rs. 4,00,768
Total sales of two weeks =Sale of Ist week + Sale of IInd week
= 2,85,891 + 4,00,768 = Rs. 6,86,659
Since, 4,00,768 > 2,85,891
Thus, sale in the second week is greater.
∴ Difference in the sales amount = 4,00,768 - 2,85,891
= Rs. 1,14,877
Hence, sale in the second week was greater by Rs. 1,14,877.

Given digits are 3, 0 and 4.
We can make many numbers by using these digits, five of them are as follows:
(i) 330443 (ii) 343404 (iii) 344430 (iv) 434043 (v) 344034
Using commas, these numbers can be rewritten as :
(i) 3,30,443 (ii) 3,43,404 (iii) 3,44,430 (iv) 4,34,043 (v) 3,44,034

According to Indian system of numeration, 6,17,11,682.

According to the associative law under addition,
125 + (68 + 32) = (125 + 68) + 32.

We know that,
1 million = 1000000 (in digits) = 10 \(\times\) 100000
= ten\(\times\) hundred thousands
(in number name)
∴ 1 million = ten hundred thousands

The smallest number of 7-digit = 1000000
and the largest number of 4-digit = 9999
\(\therefore\) The difference between them
= 1000000 - 9999 = 990001

Now, complete table is shown below: 

We know that a number is divisible by
2, if it has digits 0, 2, 4, 6 or 8 in one's place.
3, if the sum of the digits is a multiple 00 or it is divisible by 3.
4, if last two digits of the number is completely divisible by 4.
5, if a number has 0 or 5 in its one's place.
6, if it is divisible by 2 and 3 both.
.8, if last three digits of the number is completely divisible by 8.
9, if the sum of the digits of the number is divisible by 9.
10, if a number has 0 in its one's place.
11, if the difference of sum of the digits of even place and sum of the digits at odd place is either 0 or multiple of 11.

(a) Weight of apples sold during the last year = 2457 kg
Weight of oranges sold during the last year = 3004 kg
∴ Total weight of apples and oranges Raman sold, during the last year = 2457 + 3004= 5461 kg
(b) Total money Raman got by selling apples
=Total number of apples \(\times\) Cost per kg
= 2457 \(\times\) 40 = Rs. 98280
(c) Total money Raman got by selling oranges
=Total number of oranges \(\times\) Cost per kg
=3004 \(\times\) 30 = Rs. 90120
∴ Total money Raman got by selling apples and oranges together =98280 + 90120 = Rs. 188400
(d) Following table shows the money received from selling items:

The entries of amount of money received in descending order are as follows:
Rs. 253670 >Rs. 240012 >Rs. 160040 > Rs. 98280 > Rs. 90120 >Rs. 68280 > Rs. 38350
The item, which brought him the highest amount is tooth brushes. This amount is Rs. 253670.

From the given figure,
(i) Total distance covered by bus from A to D
= AB + BC + CD =4170 +3410 + 2160 =9740 km
(ii) Total distance covered by bus from D to G
= DE + EF + FG = 8140 + 4830 + 2550 = 15520 km
(iii) Total distance covered by bus = Distance from A to D + Distance from D to G + Distance from G to A
=9740+15520+1290 [from (i) and (ii) parts)
=26550 km
(iv) Distance from C to D = 2160 km
Distance from D to E = 8140 km
∴ Difference of distances from C to D and D to E
=8140 - 2160 = 5980 km
(v) To find out the time for individual places, we will use the formula of time i.e.
\(Time=\frac { Distance }{ Speed } \)
(a) Time taken by bus to reach from A to B
\(=\frac { Distance\quad from\quad AtoB }{ Speed } =\frac { 4170 }{ 60 } =\frac { 139 }{ 2 } =69\frac { 1 }{ 2 } h\)
(b) Time taken by bus to reach from C to D
\(=\frac { Distance\quad from\quad CtoD }{ Speed } =\frac { 2160 }{ 60 } =36h\)
(c) Time taken by bus to reach from E to G
\(=\frac { Distance\quad from\quad EtoG }{ Speed } =\frac { 4830+2550 }{ 60 } =\frac { 7380 }{ 60 } =123h\)
(d) Time taken by bus for total journey
\(=\frac { Total\quad distance\quad covered }{ Speed } =\frac { 26550 }{ 60 } =\frac { 885 }{ 2 } =442\frac { 1 }{ 2 } h\).

100 x 89 = 8900
100 x 79 = 7900
8900 - 7900 = 1000