(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

Given, number is 6523689.
Place value of first 6 = 6 \(\times\) 1000000 = 6000000
Place value of second 6 = 6 \(\times\) 100 = 600
∴ Difference between the place values of two 6's
= 6000000 - 600 = 5999400

We have, 1,08,734 - 47599
\(\because \begin{matrix} 1,08,734\rightarrow 1,08,700 \\ 47,599\rightarrow 47,600 \end{matrix}\} [rounding\quad off\quad to\quad nearest\quad hundreds]\)
∴  Rough estimate = 1,08,734 - 47,599
= 1,08,700 - 47,600 = 61,100
\(\because \begin{matrix} 1,08,734\rightarrow 1,08,730 \\ 47,599\rightarrow 47,600 \end{matrix}\} [rounding\quad off\quad to\quad nearest\quad tens]\)
and closer estimate = 1,08,734 - 47,599
=1,08,730 - 47,600 = 61,130

We have, 439 + 334 + 4317
\(\therefore \begin{matrix} 439\rightarrow 400 \\ 334\rightarrow 300 \\ 4317\rightarrow 4300 \end{matrix}\} [rounding\quad off\quad to\quad nearest\quad hundreds]\)
∴ Rough estimate = 439 + 334 + 4317
= 400 + 300 + 4300 = 5000
\(Again\begin{matrix} 439\rightarrow 440 \\ 334\rightarrow 330 \\ 4317\rightarrow 4320 \end{matrix}\} [rounding\quad off\quad to\quad nearest\quad tens]\)
and closer estimate = 439 +334 +4317
= 440 + 330 + 4320 = 5090

Given, capacity of vessel = 4 L 500 mL
= 4 \(\times\)1000 + 500 = 4000 + 500 = 4500 mL. [1L= 1000mL]
and capacity of one glass = 25 mL
∴ Number of glasses of curd filled out of vessel
\(=\frac { Capacity\quad of\quad a\quad vessel }{ Capacity\quad of\quad a\quad glass } =\frac { 4500 }{ 25 } =180\)
Hence, curd can be filled in 180 glasses.

Given, distance between the school and the house
= 1 km 875 m =1\(\times\)1000+875
= 1000 + 875 = 1875 m [∵ 1 km = 1000 m]
∴ Distance covered by the student in one day
= 2\(\times\) 1875 = 3750 m [∵ She walks both ways in one day]
∴ Distance covered in 6 days = 6 x 3750
= 22500 m = (22 \(\times\) 1000 + 500) m
= 22 km 500 m    [∵1 km = 1000 m]

Given, number of tickets sold on the first day = 1094
Number of tickets sold on the second day = 1812
Number of tickets sold on the third day = 2050
Number of tickets sold on the fourth day = 2751
∴ Total number of tickets sold on all the four days
= 1094 + 1812 + 2050 + 2751 = 7707
Hence, there are 7707 tickets sold on all the four days.

Given, weight of one tablet = 20 mg
Total weight of 200000 tablets in the box = 200000 \(\times\) 20 mg
=4000000 mg
Now, weight in grams =\(\frac{4000000}{1000}g=4000g\) \(​​\left[ \because \quad 1mg=\frac { 1 }{ 1000 } g \right] \)
Now, weight in kilograms =\(\frac{4000}{1000}kg=4kg\) \(​​\left[ \because \quad 1g=\frac { 1 }{ 1000 } kg \right] \).

The smallest 8-digit number = 10000000
∴ 1 st next number = 10000000 + 1 = 10000001
2nd next number = 10000000 + 2 = 10000002
3rd next number =10000000 + 3 = 10000003
4th next number =10000000 + 4 = 10000004
5th next number = 10000000 + 5 = 10000005
Now, ascending order of these numbers is as follows:
10000001 < 10000002 < 10000003 < 10000004 < 10000005.

The greatest 6-digit number = 999999
1st previous number =999999 -1 = 999998
2nd previous number = 999999 - 2 = 999997
3rd previous number = 999999 - 3 = 999996
4th previous number =999999 - 4 = 999995
5th previous number = 999999 - 5 = 999994
Now, descending order of these numbers is as follows:
999998 > 999997 > 999996 > 999995 > 999994.

The least 6-digit number is 100000 (one lakh). Now, five examples, where the number of things counted would be more than 6-digit number are as follows:
(i) The number of people in a big city.
(ii) The number of stars in a clear dark night.
(iii) The number of motorcycles in a big town.
(iv) The number of grains in a sack full of wheat.
(v) The number of pages of notebooks of all students in a big town.

Two given digits are 2 and 3. We want to make 4-digit numbers using both the digit equal number of times.
The possible 4-digit numbers are 2233, 3322, 2332, 3223, 2323 and 3232.
(i) The greatest number is 3322.
(ii) The smallest number is 2233.
(iii) We can make 6 different numbers in all.

Digits in ascending order are 0,1,2,3,4,5,6,7,8,9 and digits in descending order are 9,8,7,6,5,4,3,2,1, 0. Also, we know that 0 can never be taken at the leftmost place.
Keeping the digit 9 at hundreds place, we can fill thousands, tens and ones place by remaining digits.
Greatest number

[Keeping the greatest digit i.e. 8, 7 and 6 at thousands, tens and ones place]
Smallest number 

[Keeping the smallest digit l.e. 1, 0 and 2 at thousands, tens and ones place]

Digits in ascending order are 0,1,2,3,4,5,6,7,8,9 and digits in descending order are 9,8,7,6,5,4,3,2,1, 0. Also, we know that 0 can never be taken at the leftmost place.
Keeping the digit 4 at tens place, we can fill other places thousands, hundreds and ones place by remaining number.
Greatest number

[Keeping the greatest digits i.e. 9, 8 and 7 at thousands, hundreds and tens place]
Smallest number

[Keeping the smallest digits i.e. 9, 8 and 7 at thousands, hundreds and tens place].

Digits in ascending order are 0,1,2,3,4,5,6,7,8,9 and digits in descending order are 9,8,7,6,5,4,3,2,1, 0. Also, we know that 0 can never be taken at the leftmost place.
Keeping the digit 7 at ones place, we can fill other places tens, hundreds and thousands by remaining numbers.
Greatest number 

-[Keeping the greatest digits i.e. 9, 8 and 6 at thousands, hundreds and tens place]
Smallest number

[Keeping the smallest digits i.e. 0, 1, 2 at hundreds, thousands and tens place. If keep 0 at thousands place, then number will be equal to 3-digit number]