Question

here are the clues for a mystery number.

• the number is 760,000 when rounded to the nearest ten thousand.
• the number is 765,000 when rounded to the nearest thousand.

which number could be the mystery number?
764,981 765,321 762,321 763,981

Explanation:

Step1: Check rounding to nearest ten thousand

For each number, round to the nearest 10,000:

• $764,981$: The ten-thousands digit is 6, thousands digit is 4. Since $4 < 5$, round down to $760,000$.
• $765,321$: The ten-thousands digit is 6, thousands digit is 5. Since $5 \geq 5$, round up to $770,000$.
• $762,321$: The ten-thousands digit is 6, thousands digit is 2. Since $2 < 5$, round down to $760,000$.
• $763,981$: The ten-thousands digit is 6, thousands digit is 3. Since $3 < 5$, round down to $760,000$.

Step2: Check rounding to nearest thousand

From valid candidates ($764,981$, $762,321$, $763,981$), round to nearest 1,000:

• $764,981$: The thousands digit is 4, hundreds digit is 9. Since $9 \geq 5$, round up to $765,000$.
• $762,321$: The thousands digit is 2, hundreds digit is 3. Since $3 < 5$, round down to $762,000$.
• $763,981$: The thousands digit is 3, hundreds digit is 9. Since $9 \geq 5$, round up to $764,000$.

Answer:

764,981