Numbers — Important Questions

10 million

Step 1: We know 1 crore = 1,00,00,000 (8-digit number with 1 in crores place). Step 2: In the International system, 1 million = 10,00,000 (10 lakh). Step 3: So 1 crore = 10 × 10 lakh = 10 × 1 million = 10 million. Step 4: Therefore, 1 crore = 10 million. This is a key conversion: 10 lakh = 1 million, and 1 crore = 10 million.

10,23,578

Step 1: Digits given: 0, 1, 2, 3, 5, 7, 8. Since 0 is present, we cannot put 0 first. Step 2: The smallest non-zero digit is 1, so put 1 in the first (leftmost) place. Step 3: Put 0 in the second place, then arrange remaining digits 2, 3, 5, 7, 8 in ascending order. Step 4: Result = 1, 0, 2, 3, 5, 7, 8 → 10,23,578. Common mistake: Students arrange all digits in ascending order, getting 01,23,578 which is only a 6-digit number.

8,564,321

Step 1: The number is 85,64,321 which has 7 digits. Step 2: In the International system, we group from right: first 3 digits (Ones period) = 321, next 3 digits (Thousands period) = 564, remaining digits (Millions period) = 8. Step 3: So the commas go after every 3 digits from the right: 8,564,321. Step 4: In Indian system it was 85,64,321 but International grouping gives 8,564,321. Common mistake: Using Indian grouping (2-2-3) instead of International grouping (3-3-3).

1,00,00,000

Step 1: We need the number that is greater than 99,99,999 and less than 1,00,00,001. Step 2: One more than 99,99,999 = 1,00,00,000. Step 3: One less than 1,00,00,001 = 1,00,00,000. Step 4: So 1,00,00,000 is the only number between them. This is 1 crore — the smallest 8-digit number. Common mistake: Confusing 7-digit and 8-digit number boundaries.