Unit 1 · Topic 08 · Number System & Notation
Ms. Rao gave Anaya and Kabir the same four digits — 7, 2, 9, 4 — and asked for the biggest possible number, no calculator allowed.
Kabir shuffled the digits until one 'looked' biggest. Anaya wrote hers down in one try and never changed it.
She hadn't guessed. She had sorted.
Ms. Rao wrote four digits on the board: 7, 2, 9, 4. "Using all four, once each, make the greatest number you can. Then make the smallest." Kabir started trying combinations — 7294, then 9274, then 9724 — swapping digits and comparing them by eye each time.
Anaya didn't try combinations. She looked at the four digits and asked herself one question: which digit deserves the biggest place, the thousands place? "The biggest digit," she said, and wrote 9 first. Then the next biggest for the hundreds place: 7. Then 4 for the tens, and 2 for the ones. 9742.
Kabir checked his best guess, 9724, against hers. 9742 was bigger — the hundreds digit made the difference, and he had only found his answer by luck, not by a rule.
"For the greatest number," said Ms. Rao, "always arrange the digits in DESCENDING order — biggest first. The biggest digit belongs in the biggest place, because that place is worth the most."
"And the smallest?" asked Anaya, already reaching for the answer. "Ascending order — smallest first: 2479."
Ms. Rao then changed the digits to 0, 5, 3, 8, and asked for the smallest number again. Anaya wrote 0538 without thinking, and Ms. Rao shook her head. "Read that number out loud." Anaya paused. "0538 is really just 538 — a three-digit number. The zero at the front doesn't count."
"Exactly. A zero can never lead. So when zero is your smallest digit, it doesn't go first — the SECOND-smallest digit goes first instead, and zero slides into the next place." Anaya corrected herself: 3, then 0, then 5, then 8 — 3058.
Kabir summed up the whole rule in one line: "Descending for the biggest, ascending for the smallest — but zero never leads, it just waits its turn."
To form the GREATEST number from a set of digits (each used once), arrange the digits in DESCENDING order — biggest digit first, then the next biggest, and so on. Each place value is worth more the further left it sits, so the biggest digit should occupy the most valuable place.
To form the SMALLEST number, arrange the digits in ASCENDING order — smallest digit first. The one exception: if the smallest digit is 0, it cannot lead the number, because a leading zero simply disappears and shortens the number. Swap 0 with the next-smallest (smallest non-zero) digit instead, and let 0 take the following place.
These two rules — descending for greatest, ascending for smallest, with the zero exception — work for any number of digits, using every given digit exactly once.
From 2, 5, 7 write greatest 752 and smallest 257.
From 9, 8, 5, 3 write greatest 9,853 and smallest 3,589.
From 7, 5, 4, 0 write greatest 7,540 and smallest 4,057 and explain the zero rule.
Loading questions…