How do we find the smallest number that rounds to 600 when rounded to the nearest hundred?

Answer 1

600

Answer 2

We realize that 549 rounds down to 500, so 550 must be the smallest whole number that rounds to 600.

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When rounding to the nearest whatever, half of the numbers between two multiples of the whatever round down and half round up. BY convention any number exactly halfway between two multiples rounds up.

Half of 100 = ½ × 100 = 50

Therefore the numbers 600 ± 50 will round to 600. This will be inclusive of 600 - 50 = 550 but exclusive of 600 + 50 = 650 (as 600 + 50 = 650 is exactly halfway between 600 + 50 and 700 - 50, and so would round up to 700).

Ie all the numbers greater than or equal to 550 and less than 650 will round to 600 to the nearest 100.

Mathematically this is written as all numbers x such that 550 ≤ x < 650 will round to 600 when rounded to the nearest 100.

Therefore 550 is the smallest number that will round [up] to 600 to the nearest 100.