Unit 1 · Topic 10 · Number System & Notation
Ms. Rao filled a place-value table with 853 and 835.
Both have 8 hundreds — tied. At tens, 5 beats 3, so 853 is greater.
Same comparisons, reversed order list: that is descending.
Ms. Rao compared 853 and 835 in a hundreds-tens-ones table. Hundreds tied at 8; at tens, 5 > 3, so 853 wins without looking at ones.
647 and 476: at hundreds, 6 > 4, so 647 is greater immediately.
853 and 835 again showed why you compare left to right: when a higher place is equal, drop to the next place until one digit differs.
For four-digit numbers 2357 and 1457 she compared from thousands — equal at 7, equal at 5, then 3 > 1, so 2357 is greater.
Two five-digit numbers 54087 and 54078: equal through ten-thousands, thousands, and hundreds; at tens 8 > 7, so 54087 is greater.
Two six-digit numbers followed the same rule — compare at the highest period, move left to right, stop at the first difference.
She gave six large numbers and asked for ascending order — smallest first. Anaya filled a place-value table, found the number missing a lakhs digit as smallest, then compared lakhs digits for the rest.
One number without a lakhs digit was clearly smallest. Among the rest she compared lakhs, then ten-thousands, then hundreds until the full ascending list was written.
Descending order puts the largest first using the same left-to-right comparisons — just read the sorted list the other way.
Kabir's rule: compare from the highest place; stop at the first difference; sort once; then every rank question is easy without rescanning a jumbled list.
Compare two numbers using a place-value table from the highest column leftward; the first unequal digit decides.
More digits means a larger whole number when lengths differ.
Ascending order: smallest to largest; descending: largest to smallest — same pairwise comparisons.
For many large numbers, fill a place-value table and sort period by period (lakhs, ten-thousands, …).
Write down five test scores from memory, then arrange them in both ascending and descending order.
Take any ascending list you've made and reverse it. Check it now reads correctly in descending order.
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