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# A number rounded to the nearest hundred thousand is 400000 the same number rounded to the nearest ten thousand is 350000 what could the number be?

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When rounding to the nearest whatever, all numbers round to a multiple of that whatever; to decide which way to round all numbers less than half of that whatever greater than a multiple round down and all numbers greater than or equal to a half of that whatever less than a multiple round up.

To the nearest hundred thousand (100,000), those numbers less than 100,000 ÷ 2 = 50,000 greater than a multiple of 100,000 round down, and those greater than 50,000 less than a multiple of 100,000 round up.

Thus those numbers which round to 400,000 are greater than or equal to 400,000 - 50,000 = 350,000 and less than 400,000 + 50,000 = 450,000; ie all numbers x such that 350,000 ≤ x < 450,000

Those numbers which round to 350,000 to the nearest 10,000 are those which are greater than or equal to 350,000 - 10,000 ÷ 2 = 350,000 - 5,000 = 345,000, and those which are less than 350,000 + 5,000 = 355,000; ie all numbers x such that 345,000 ≤ x < 355,000

The numbers in both ranges are those which are greater than or equal to 350,000 and less than 355,000, ie:

All numbers x such that 350,000 ≤ x < 355,000 will round to 400,000 to the nearest hundred thousand and 350,000 to the nearest ten thousand.

it could be anywhere in between 350000 and 450000

Any number in the range [350000, 355000).

Numbers that round to 400000 (nearest 100000) are between 350000 and 449999 inclusive.

Numbers that round to 350000 (nearest 10000) include 345000 to 354999.

Numbers in common between those two ranges would satisfy the question; 350000 to 354999.