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Rounding a number to the nearest thousandth is finding out which multiple of 1000 is closest to the number. The only two multiples of 1000 that we need to look at are -56000 and -57000 because -56000 is greater than -56371, -57000 is less than -56271, and there are no multiples of 1000 in between them. The absolute value of the difference between -56371 and -56000 is 371. The absolute value of the difference between -56371 and -57000 is 629. Since 371 is less than 629, the multiple of 1000 that is closest to -56371 is -56000.
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