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About Knowing Our Numbers — Class 6 Olympiad

Compare large numbers, estimate sums and differences, use Indian and International place value systems, and solve Olympiad-level problems on number sense. This topic is part of the Olympiad Class 6 mathematics syllabus (chapter: Module 1). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Knowing Our Numbers — solved examples for Class 6 Olympiad

Example 1easy

In the number 97,42,753, what is the difference between the place value of the two '7's?
  1. A)70,000
  2. B)69,300
  3. C)6,93,000
  4. D)69,93,000

Step-by-step solution

  1. The first '7' is in the Lakhs place (Indian system), so its place value is 7 × 1,00,000 = 7,00,000.
  2. The second '7' is in the Thousands place, so its place value is 7 × 1,000 = 7,000.
  3. The difference between their place values is 7,00,000 - 7,000 = 6,93,000.

Answer: 6,93,000

Example 2medium

Consider three 6-digit numbers: P = 5A7B3C, Q = 5B7A3C, R = 5C7B3A. If A, B, C are distinct digits from 1 to 9, and A < B < C, which of the following statements is true?
  1. A)A. P > Q > R
  2. B)B. R > Q > P
  3. C)C. P > R > Q
  4. D)D. Q > P > R

Step-by-step solution

  1. The numbers are P = 5A7B3C, Q = 5B7A3C, R = 5C7B3A. All numbers start with 5 (lakhs place), and the thousands place is 7 for all. The relationship A < B < C is given.
  2. To compare P and Q: P has 'A' at the ten thousands place and 'B' at the hundreds place. Q has 'B' at the ten thousands place and 'A' at the hundreds place. Since A < B, the digit at the ten thousands place in P (A) is smaller than that in Q (B). This means Q > P.
  3. To compare Q and R: Q has 'B' at the ten thousands place and 'A' at the hundreds place. R has 'C' at the ten thousands place and 'B' at the hundreds place. Since B < C, the digit at the ten thousands place in Q (B) is smaller than that in R (C). This means R > Q.
  4. Combining the comparisons, we get R > Q > P.

Answer: B. R > Q > P

Example 3hard

Let N be the smallest 7-digit number formed using all distinct digits from 0 to 6 exactly once. Let M be the largest 6-digit number such that the sum of its digits is 45. What is the difference between N and M?
  1. A)23466
  2. B)23456
  3. C)23566
  4. D)23366

Step-by-step solution

  1. To form the smallest 7-digit number using distinct digits 0, 1, 2, 3, 4, 5, 6, place the smallest non-zero digit at the beginning, followed by 0, then the remaining digits in ascending order. So, N = 1023456.
  2. To form the largest 6-digit number with a sum of digits equal to 45, we place as many 9s as possible from left to right. A 6-digit number with all 9s (999999) has a digit sum of 9 × 6 = 54. Since the desired sum is 45, we need to reduce the sum by 54 - 45 = 9. To keep the number largest, we reduce the rightmost digit. So, M = 999990 (5 nines and one zero).
  3. Now, calculate the difference: N - M = 1023456 - 999990 = 23466.

Answer: 23466

Practice questions on Knowing Our Numbers

  1. Q1.easy

    What is the greatest 6-digit number that can be formed using the digits 3, 0, 8, 1, 5, 7 exactly once, such that the digit '0' is always at the hundreds place?
    1. A)875301
    2. B)875031
    3. C)875310
    4. D)875103
    Show answer

    Answer: 875031

    Hint: To form the greatest number, arrange the remaining digits in descending order from the leftmost position, keeping '0' fixed at the hundreds place.

  2. Q2.easy

    A shopkeeper wants to estimate the total cost of 3 items priced at ₹478, ₹213, and ₹395. He rounds each price to the nearest hundred. What is the difference between the actual total cost and his estimated total cost?
    1. A)₹2
    2. B)₹10
    3. C)₹14
    4. D)₹24
    Show answer

    Answer: ₹14

    Hint: First, calculate the actual sum. Then, round each number to the nearest hundred and find their sum. Finally, find the difference between these two sums.

  3. Q3.easy

    Which of the following numbers is equal to 'Seventy-five million, four hundred three thousand, two hundred ten' in the Indian place value system?
    1. A)Seven crore, fifty-four lakh, three thousand, two hundred ten
    2. B)Seven crore, five lakh, forty-three thousand, two hundred ten
    3. C)Seven crore, fifty lakh, four hundred three thousand, two hundred ten
    4. D)Seven crore, five lakh, four hundred three thousand, two hundred ten
    Show answer

    Answer: Seven crore, fifty-four lakh, three thousand, two hundred ten

    Hint: Convert the given International number to digits first (75,403,210), then group the digits according to the Indian place value system.

  4. Q4.medium

    A company's annual profit is recorded as 'Fifty-three lakh forty-five thousand two hundred five' in the Indian system. If this profit is distributed equally among 100 employees, how would each employee's share be written in the International system?
    1. A)A. Five hundred thirty-four thousand five hundred twenty point five
    2. B)B. Fifty-three thousand four hundred fifty-two point zero five
    3. C)C. Five hundred thirty-four thousand five hundred two point five
    4. D)D. Five hundred thirty-four thousand five hundred twenty-five
    Show answer

    Answer: B. Fifty-three thousand four hundred fifty-two point zero five

    Hint: First, write the number in digits in the Indian system, then divide by 100, and finally convert the result to the International system.

  5. Q5.medium

    A factory produces 785 toys per day. If the factory operates for 285 days in a year, which of the following is the best estimate of the total number of toys produced in a year?
    1. A)A. 2,10,000
    2. B)B. 2,40,000
    3. C)C. 2,25,000
    4. D)D. 2,70,000
    Show answer

    Answer: B. 2,40,000

    Hint: Round off both numbers to their nearest hundreds before multiplying to get a quick estimate.

  6. Q6.medium

    Using the digits 0, 2, 3, 5, 7, 9 exactly once, form the largest possible 6-digit odd number such that the digit 3 is always at the thousands place.
    1. A)A. 975302
    2. B)B. 973205
    3. C)C. 973520
    4. D)D. 973502
    Show answer

    Answer: B. 973205

    Hint: To form the largest number, place the largest digits in the higher place values. Remember the thousands place constraint and the odd number requirement for the unit's digit.

  7. Q7.hard

    A 5-digit number, when rounded to the nearest thousand, becomes 75,000. When the same number is rounded to the nearest hundred, it becomes 74,800. What is the sum of the digits of the smallest possible original number?
    1. A)22
    2. B)23
    3. C)24
    4. D)25
    Show answer

    Answer: 23

    Hint: Establish the possible range of the original number based on each rounding condition, then find the intersection of these ranges.

  8. Q8.hard

    A number is written as 'Fifty crore fifty lakh five thousand five' in the Indian system. If this number is read in the International system, how many millions does it represent?
    1. A)50 million
    2. B)500 million
    3. C)505 million
    4. D)550 million
    Show answer

    Answer: 505 million

    Hint: First, convert the number from the Indian system to its numerical form. Then, group the digits in sets of three from the right to read it in the International system.

  9. Q9.hard

    Using each of the digits 1, 2, 3, 4, 5, 6, 7 exactly once, form the largest possible 7-digit number that is divisible by 4. What is the digit in the thousands place of this number?
    1. A)2
    2. B)3
    3. C)4
    4. D)5
    Show answer

    Answer: 4

    Hint: For a number to be divisible by 4, its last two digits must form a number divisible by 4. To make the 7-digit number largest, prioritize larger digits in the leading positions.

These are 9 of the 60 questions available for Knowing Our Numbers. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.