Concept: 1 Mark
Application: 1 Mark
Solution: 1 Mark
The smallest number Aashu arrived at using 8734 is 3478.
He did so by following the below steps:

(a) The smallest digit is placed at one's place.

(b) The next greater digit is placed at ten's place.

(c) The next greater digit is placed at hundred's place and so on.

(d) The greatest digit is placed at the highest place of the number.
Sum  = 8734 + 3478 = 12221

Concept: 1 Mark
Solution: 1 Mark
Shweta has more money than Rahul. If we compare both the numbers, then the number with the greater valued digit on the extreme left will be greater. If the digits on the extreme left of the numbers are equal, then the digits to the right of the extreme left digits are compared and so on. Therefore, Rs.1501 is greater than Rs.1001.

Now,1501-1001 = 500
$\therefore$ Shweta has Rs 500 more than Rahul.

Concept: 1 Mark
Steps: 1 Mark
Answer: 1 Mark
1km = 1000m
Distance between Ranchi and Kolkata = 420 km= 420 $\times$1000 = 420000m
Distance between Bangalore and Kolkata = 400 km = 400 $\times$1000 = 400000m
The total distance travelled by David = 400000 + 420000 = 820000m

Concept: 1 Mark
Solution: 1 Mark
If we want to find the greatest 5 digit number, we will use the greatest digit, which is 9, in each place value, of all the five digits.
Hence, the price of the lehenga is 99,999, which is the largest five digit number. 

Concept: 1 Mark
Application: 2 Marks
If a symbol of smaller value is written between the symbols of greater value, then its value is subtracted from the symbol of the greater value which is written immediately after the symbol of the smaller value. For example the value of XIV is 10 + (5 - 1) i.e. 14.

Steps: 2 Marks
Example: 2 Marks
(i) If a symbol of smaller value is written to the right of a symbol of greater value, its value gets added to the value of the greater symbol.
For example, let us take VI. Here, the value of V in decimal value = 5
And the value of I in decimal value = 1
Now, 5 > 1, the left part is greater than the right part.
So we will add the value of the smaller value of the greater one.
$\therefore$ The decimal value of VI = 5 + 1 = 6
(ii) If a symbol of smaller value is written to the left of a symbol of greater value, its value is subtracted from the value of the greater symbol.
For example, let us take IX.
Here, the decimal value X = 10
While the decimal value if I = 1
10>1, the value on the left is greater than the value on the right.
So the decimal value of IX = 10 - 1 = 9.
But we need to be a little careful while using this rule.
The symbols, V, L, and D are never written to the left of a symbol of greater value, i.e. V, L, and D are never subtracted.

Concept: 1 Mark
Steps: 2 Marks
Answer: 1 Mark
Given that
We have to estimate 4689 + 19316
Clearly, 19316 > 4689 
we shall round off the numbers to the nearest thousands.
19316 is rounded off to 19000
4689 is rounded off to 5000
Estimated sum is: 
19000 + 5000 = 24000
 We also have to estimate: 
108 + 24999
Now, 24999 > 108
We shall round off the number to nearest hundred.
108 can be rounded off to 100.
24999 can be rounded off to 25000.
The estimated sum of the numbers = 100 + 25000 = 25100.
 

Concept: 1 Mark
Steps: 2 Marks
Answer: 1 Mark
To find the greatest number, we will arrange the digits in descending order.
Greatest 5 – digit number in which 5 appears at ten’s place = 98756
To find the smallest number, we will arrange the digits in an ascending order. But we need to be careful here, as 0 is the smallest digit and it will be the first digit when we arrange it in ascending order.
However, if we put '0' as the first number then the number becomes a 4 digit number. As 01253 is a 4 digit number.

Concept: 1 Mark
Steps: 2 Marks
Solution: 1 Mark
Anshul has to pay ₹ (94 $\times$ 576).
The first number, 94, can be rounded off to the nearest ten as 90.
The second number, 576, can be rounded off to the nearest hundred as 600.
Hence, the estimated price of the product = 90 $\times$ 600 = ₹ 54,000
The actual price=94$\times$576 = (90+4)$\times$(600-24) = (90$\times$600-90$\times$24 + 4$\times$600-4$\times$24) = (54000-2160+2400-96) = ₹ 54144
Prakash has to pay ₹ (49$\times$499).
The first number 49 can be rounded off to the nearest ten as 50.
The second number 499 can be rounded off to the nearest hundred as 500.
The estimated price of the product is 50$\times$500 = ₹ 25000
The actual price= 49$\times$499 = (50-1)$\times$(500-1) = (50$\times$500-50$\times$1 -1$\times$500+1$\times$1) = (25000 - 50 - 500 + 1) = ₹ 24451

Whole numbers start from 0 and it is the number system which starts with the predecessor of 1.