Hard Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Write the smallest 7-digit number using five different digits.
Correct! Using digits 0,1,2,3,4,5,6 arranged to get the smallest number: 10,23,456.
(2) Write the largest 6-digit number divisible by 9.
Perfect! 9,99,999 has digit sum = 54, which is divisible by 9.
(3) Write the difference between the greatest and smallest 5-digit numbers.
Excellent! 99,999 - 10,000 = 89,999.
(4) Write the Roman numeral for 99.
Great! XCIX = 90 + 9 = 99.
(5) Write the number name for 9,08,050 in the International system. Nine
Short Answer Questions (2 Marks Each)
Answer each question with proper working
(1) Write the number name for 7,43,085 in both Indian and International systems.
Indian System: Seven
International System: Seven
(2) Arrange the following numbers in ascending order and find the sum of the smallest and largest: 5,43,672; 5,34,762; 5,47,326; 5,37,642.
Ascending order:
Sum:
Perfect! Sum of smallest and largest = 10,82,088.
(3) A shopkeeper has ₹2,45,860. He spends ₹1,38,975 on goods. How much money is left with him?
Correct! ₹1,06,885 is left with the shopkeeper.
(4) Write the predecessor of the largest 6-digit number and successor of the smallest 7-digit number.
Predecessor:
Successor:
(5) A farmer harvested 8,56,420 kg of wheat in a year. He sold 4,37,825 kg. How much wheat is still with him?
Excellent! 4,18,595 kg wheat is still with the farmer.
Long Answer Questions (4 Marks Each)
Note: Answer each question with complete working and clear explanations.
(1) A city has a population of 24,56,325. Out of these, 13,78,492 are males and the rest are females. Find the number of females in the city.
Perfect! There are 10,77,833 females in the city.
(2) A factory produces 56,842 bulbs in January, 68,975 bulbs in February, and 75,086 bulbs in March. Find the total production in these three months.
Excellent! Total production = 2,00,903 bulbs.
(3) Compare the numbers 9,08,050 and 9,80,005 using both the Indian and International place value systems.
(4) The school library has 2,43,678 books in English and 1,95,482 books in other languages. How many books are there in total?
Perfect! Total books in library = 4,39,160.
(5) The product of two numbers is 5,76,000. If one number is 320, find the other number.
Excellent! The other number is 1,800.
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) The smallest number divisible by both 8 and 12 is:
(a) 12 (b) 24 (c) 48 (d) 96
Correct! LCM of 8 and 12 is 24.
(2) In Roman numerals, XC stands for:
(a) 40 (b) 60 (c) 90 (d) 110
Correct! XC = 100 - 10 = 90.
(3) The difference between the greatest 6-digit number and the smallest 6-digit number is:
(a) 99,999 (b) 1,00,000 (c) 8,99,999 (d) 9,00,000
Correct! 9,99,999 - 1,00,000 = 8,99,999.
(4) The sum of place values of 7 in 7,47,372 is:
(a) 7,777 (b) 70,070 (c) 7,07,000 (d) 7,77,000
Correct! 7,00,000 + 7,000 + 0 = 7,07,000.
(5) The largest 4-digit number divisible by 15 is:
(a) 9,990 (b) 9,995 (c) 9,985 (d) 9,900
Correct! 9,990 ÷ 15 = 666, so it's divisible by 15.
(6) The successor of 9,99,999 is:
(a) 10,00,000 (b) 9,99,998 (c) 10,00,001 (d) 1,00,000
Correct! Successor means the next number: 10,00,000.
(7) Which of these is not a correct Roman numeral?
(a) IL (b) XL (c) CD (d) CM
Correct! IL is incorrect. For 49, we write XLIX, not IL.
(8) In the International system, 5,60,732 is written as:
(a) Five hundred sixty thousand seven hundred thirty-two
(b) Fifty-six thousand seven hundred thirty-two
(c) Five lakh sixty thousand seven hundred thirty-two
(d) Fifty-six lakh seven hundred thirty-two
Correct! In International system: 560,732 = Five hundred sixty thousand seven hundred thirty-two.
(9) The sum of the greatest and smallest 5-digit numbers is:
(a) 2,00,000 (b) 1,99,999 (c) 1,09,999 (d) 99,999
Correct! 99,999 + 10,000 = 1,09,999.
(10) The product of the place value of 5 in 5,84,213 and 4 in 5,84,213 is:
(a) 20,00,000 (b) 20,000 (c) 2,00,000 (d) 20,00
Correct! Place value of 5 = 5,00,000, place value of 4 = 4,000. Product = 20,00,000.
Hard Level True or False
Determine whether these statements are True or False:
Knowing Our Numbers - Hard Quiz
🎉 Outstanding Achievement! Advanced Number Mastery:
You have successfully conquered the "Knowing Our Numbers (Hard)" worksheet and mastered:
(1) Advanced Number Formation: Creating the largest and smallest numbers with multiple constraints and conditions
(2) Complex Place Value Analysis: Working with 6-digit and 7-digit numbers across Indian and International systems
(3) Multi-step Word Problems: Solving real-world scenarios involving large numbers and multiple operations
(4) Advanced Roman Numerals: Understanding complex combinations like XCIX, XC, and identifying incorrect formations
(5) Divisibility Rules: Applying rules for 8, 9, 12, and 15 to find specific numbers meeting multiple criteria
(6) Number System Conversions: Seamlessly switching between Indian and International naming conventions
(7) Complex Arithmetic: Performing addition, subtraction, multiplication, and division with large numbers
(8) Pattern Recognition: Identifying relationships between digits, place values, and mathematical operations
(9) Critical Thinking: Analyzing multi-part problems requiring logical reasoning and systematic approaches
(10) Mathematical Communication: Expressing complex numerical concepts clearly in both numeral and word forms
(11) Problem-Solving Strategies: Breaking down challenging problems into manageable steps
(12) Accuracy in Calculations: Maintaining precision while working with large numbers and multiple operations
Exceptional work! You've demonstrated advanced mastery of our number system!