Worksheet Solutions: Knowing Our Numbers- 2

Q1: Fill up the blanks:
(a) Smallest 6-digit number in Indo Arabic Numeration System is __________.
(b) Largest 8-digit number in International Numeration System is
__________.
(c) Expanded notation of 2730145 is __________ .
(d) MDCL in Hindu-Arabic form is written as __________ .
(e) 707 in Roman Numerals can be written as __________ .
Sol: (a) One lakh (100,000)
(b) Ninety nine million nine hundred ninety nine thousand nine hundred ninety nine (99,999,999).
(c) 2 × 10,00,000 + 7 × 1,00,000 + 3 × 10,000 + 0 × 1000 + 1 × 100 + 4 × 10 + 5 = 2,730,145
(d) 1650
(e) DCCVII

Explanation: 
(a) A 6‐digit number is any number from 1,00,000 to 9,99,999 in the Indo‐Arabic system. The smallest 6‐digit number is One lakh (100,000).
(b) The largest 8‐digit number in the International system is 99,999,999, written in words as ninety nine million nine hundred ninety nine thousand nine hundred ninety nine.
(c) The expanded notation shows the value contributed by each digit according to its place value. For 2,730,145 it is 2 × 10,00,000 + 7 × 1,00,000 + 3 × 10,000 + 0 × 1000 + 1 × 100 + 4 × 10 + 5, which equals 2,730,145.
(d) Convert Roman numerals by adding values: M = 1000, D = 500, C = 100, L = 50. So MDCL = 1000 + 500 + 100 + 50 = 1650.
(e) Write 707 as 500 + 100 + 100 + 7, so in Roman numerals it is DCCVII (D = 500, CC = 200, VII = 7).

​Q2: Using 2, 0, 4, 5 write largest and smallest 4-digit number (without repetition).
Sol: Largest number : 5420 Smallest number : 2045

Explanation: The largest number is formed by arranging digits in descending order: 5, 4, 2, 0 → 5420. The smallest 4‐digit number cannot begin with zero, so arrange digits in ascending order with the smallest non‐zero digit first: 2, 0, 4, 5 → 2045.

Q3: Fill up the blanks using > or < signs:
(i) 2347 ________  2437 ________  2473 ________  2734 ________  2743
(ii) 50725 ________  50572 ________  50527 ________  50275 ________  50257
Sol: 

(i) 2347 < 2437 < 2473 < 2734 < 2743
(ii) 50725 > 50572 > 50527 > 50275 > 50257

Explanation: 
(i) Compare digits from the leftmost place. The numbers are in ascending order: 2347 < 2437 < 2473 < 2734 < 2743.
(ii) Again compare from the left: 50725 is the greatest and 50257 is the smallest, so 50725 > 50572 > 50527 > 50275 > 50257.

Q4: Add 825432 and 543082 and write the sum according to Indo Arabic Numeration System.
Sol: Sum = 13,68,514 (Thirteen lakh sixty‐eight thousand five hundred and fourteen.)

Explanation: Add the two numbers:
825,432 + 543,082 = 1,368,514. In the Indo‐Arabic (Indian) grouping this is written as 13,68,514 and in words as thirteen lakh sixty‐eight thousand five hundred and fourteen.

Q5: Subtract 405235 from 995432 and write the difference according to International system of numeration.
Sol: Difference = 590,197 (Five hundred and ninety thousand one hundred and ninety‐seven)

Explanation: Subtract: 995,432 - 405,235 = 590,197. In the International system this is written as 590,197 and in words as five hundred and ninety thousand one hundred and ninety‐seven.

Q6: If in a garden there are 4592 flowering plants and 3257 fruit trees then what's the total number of plants in the garden?
Sol: Total number of plants = 7849

Explanation: Add the two counts: 4,592 + 3,257 = 7,849. So there are 7,849 plants in all.

Q7: Evaluate : 81 [15 {7 - 2 (7 - 3)}]
Sol: -1215

Explanation:
Step 1: Work inside the innermost brackets: 7 - 3 = 4
Then 2 × 4 = 8, so 7 - 8 = -1.
Step 2: Multiply by 15: 15 × (-1) = -15.
Step 3: Now multiply by 81: 81 × (-15) = -1,215.
Therefore, the value of the expression is -1,215.

Q8: A flask has 5 litres of lemonade. How many glasses, each of 200ml capacity, can it fill?
Sol: Number of glasses = 25

Explanation: Convert litres to millilitres: 5 litres = 5,000 ml. Divide by the capacity of one glass: 5,000 ÷ 200 = 25. So the flask fills 25 glasses.

Q9: Estimate each of the following using general rule:
(i) 842 + 1245
(ii) 19,643 - 13,775
(iii) 2149 × 493
(iv) 5762 ÷ 287
(v) 439 + 8325 - 387
Ans: 

(i) 2,000
(ii) 6,000
(iii) 10,00,000
(iv) 20
(v) 8,000

Explanation:
(i) 842 + 1245
Round to convenient values: 800 + 1,200 = 2,000.
(ii) 19,643 - 13,775
Round each number: 20,000 - 14,000 = 6,000.
(iii) 2149 × 493
Round 2,149 → 2,000 and 493 → 500, then 2,000 × 500 = 1,000,000, written in Indian grouping as 10,00,000.
(iv) 5762 ÷ 287
Round 5,762 → 6,000 and 287 → 300, then 6,000 ÷ 300 = 20.
(v) 439 + 8325 - 387
Round numbers: 400 + 8,000 - 400 = 8,000.

Q10: Fill up the blanks:

Ans: