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Mathematics

Exploring Numbers and Numeration Systems Worksheet

Large Numbers, Numeration Systems, and Estimation
Date: May 31, 2026  •  Questions: 40  •  Estimated time: 35 minutes
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Instructions: Read each question carefully and answer to the best of your ability. Show all working for word problems.
1. The number 9999989 is less than 9999999. (1 pt)
True
False
2. Adding 1 to the greatest 7-digit number results in an 8-digit number. (1 pt)
True
False
3. The Indian and International systems of numeration use the same comma placements. (1 pt)
True
False
4. Rounding off a number to the nearest hundreds always increases its value. (1 pt)
True
False
5. The Roman numeral MCMXI represents the year 1911. (1 pt)
True
False
6. The face value of a digit is always equal to its place value in the number. (1 pt)
True
False
7. Zero acts as a placeholder in large numbers. (1 pt)
True
False
8. Rounding off can sometimes lead to a result greater than the actual sum. (1 pt)
True
False
9. The predecessor of the smallest 7-digit number, when added with 1, gives the smallest 7-digit number. (1 pt)
True
False
10. Round-off estimation is not useful in everyday calculations. (1 pt)
True
False

11. What is the smallest 7-digit number? (2 pts)
A. 1000000
B. 999999
C. 10000000
D. 9999999
12. What is the greatest 7-digit number? (2 pts)
A. 9999999
B. 10000000
C. 8999999
D. 7999999
13. In the Indian numeral system, 1,00,00,000 is commonly known as: (2 pts)
A. One crore
B. Ten million
C. One hundred lakh
D. Both A and C
14. According to the chapter, what is the predecessor of 100000? (2 pts)
A. 99999
B. 999999
C. 100001
D. 1000000
15. What is the place value of 5 in 10506? (2 pts)
A. 50
B. 500
C. 5000
D. 5
16. Adding 1 to the greatest 7-digit number gives you the smallest _____-digit number. (2 pts)
A. 7
B. 8
C. 9
D. 10
17. In Roman numerals, the numeral IX represents: (2 pts)
A. 1
B. 9
C. 10
D. 11
18. Rounding 535674 to the nearest hundred results in: (2 pts)
A. 535700
B. 535600
C. 535674
D. 536000
19. Which of the following best describes the process of estimating large numbers by rounding? (2 pts)
A. Exact calculation
B. Approximation
C. Overestimation
D. Underestimation
20. What does the process of converting a Roman numeral to its numeric form involve? (2 pts)
A. Addition only
B. Subtraction only
C. Both addition and subtraction
D. Multiplication

21. The number obtained by adding 1 to the greatest 7-digit number is   . (2 pts)
22. The smallest 8-digit number is   . (2 pts)
23. The smallest 9-digit number is   . (2 pts)
24. In the Indian numbering system, 1,00,00,000 is called   . (2 pts)
25. The place value of 5 in 10506 is   . (2 pts)
26. The Roman numeral for 1911 is   . (2 pts)
27. In rounding off numbers, if the digit to the right is 5 or more, you round   . (2 pts)
28. Writing numbers in   order helps in identifying the smallest and largest numbers. (2 pts)
29. Rounding 535674 to the nearest hundred gives   . (2 pts)
30. In the international numeral system, 1000000 is known as   . (2 pts)

31. Add 7834567, 893600678, and 1035678. Show your working. (5 pts)
Working:
Answer:
32. Find the sum of the greatest 8-digit number and the smallest 5-digit number. Show your working. (5 pts)
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Answer:
33. Estimate the difference between 89567 and 34589 when both are rounded to the nearest hundreds. Show your working. (5 pts)
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Answer:
34. A man travels from a hotel to Varkala beach 850 m away and returns. Calculate the total distance traveled in 10 days if he makes one round trip per day. Show your working. (5 pts)
Working:
Answer:
35. A house priced at ₹32,56,358 increases by 20 times the next year. Find its new price. Show your working. (5 pts)
Working:
Answer:
36. A businessman invested ₹1,20,00,000 and earned a profit of ₹1,20,000. If he reinvests the profit, what is his total investment? Show your working. (5 pts)
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Answer:
37. Vanaja completed a 1 km race in 96 seconds and Sunantha in 188 seconds. By how many seconds was Vanaja ahead? Show your working. (5 pts)
Working:
Answer:
38. Roy rounded 3567 and 935 to the nearest hundreds and multiplied them. What is the estimated product? Show your working. (5 pts)
Working:
Answer:
39. Verify the place value calculation for the digit 5 in 21865734. Show your working. (5 pts)
Working:
Answer:
40. Convert the Roman numeral 'MCMXI' to its numeric value. Show your working. (5 pts)
Working:
Answer: