Indian Number System

3,03,346

Step 1: Available digits are 3, 0, 6, 4 with 3 repeated 3 times. Total digits: 3, 3, 3, 0, 6, 4 - that is 6 digits. Step 2: To form the smallest number with 0 present, arrange digits in ascending order: 0, 3, 3, 3, 4, 6. Step 3: Since 0 cannot be the first digit, put the smallest non-zero digit (3) first, then place 0 second, then remaining digits in ascending order: 3, 0, 3, 3, 4, 6. Step 4: The number is 3,03,346. Step 5: Common mistake - putting 0 first gives 0,33,346 which is only a 5-digit number. The rule is: put 0 in the second position from the left when 0 is one of the digits.

53,74,812

Step 1: Count digits - 5,67,35,948 has 8 digits; 5,62,07,579 has 8 digits; 53,74,812 has 7 digits; 53,74,264 has 7 digits. Step 2: 8-digit numbers are larger than 7-digit numbers. Compare the two 8-digit numbers: 5,67,35,948 vs 5,62,07,579. At crore place: 5=5. At ten-lakh place: 6=6. At lakh place: 7 > 2. So 5,67,35,948 > 5,62,07,579. Step 3: Now compare 7-digit numbers: 53,74,812 vs 53,74,264. At ten-lakh: 5=5, lakh: 3=3, ten-thousand: 7=7, thousand: 4=4, hundred: 8 > 2. So 53,74,812 > 53,74,264. Step 4: Descending order: 5,67,35,948 > 5,62,07,579 > 53,74,812 > 53,74,264. Step 5: The THIRD n

The digit 0 is incorrect; it should be 2 in the tens place of 800.

Thirty one crore thirty eight lakh sixty two thousand eight hundred is written as 31,38,62,800. Comparing this with 31,38,62,008, the last three digits are wrong: 800 has been changed to 008. So the digit 0 is incorrectly placed in the hundreds and tens positions, and the tens place should contain 0 while the hundreds place should contain 8; the numeral should end with 800.

60,45,38,271

Step 1: Organize the digits by their positions: TC=6, C=0, TL=4, L=5, TTh=3, Th=8, H=2, T=7, O=1. Step 2: Write the digits from left to right (highest place to lowest): 6, 0, 4, 5, 3, 8, 2, 7, 1. Step 3: Now apply Indian comma placement. Starting from right, first 3 digits = 271, next 2 = 38, next 2 = 45, remaining = 60. Step 4: With commas: 60,45,38,271. Step 5: Verify each digit's position: T(6), O(0), TL(4), L(5), TTh(3), Th(8), H(2), T(7), O(1) - wait, re-reading TC=6, C=0. So 60,45,38,271 ✓. Common mistake: students mix up ten-lakh and lakh positions, writing 60,54,38,271 instead.