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The two rules for rounding numbers are Round your numbers only once (in one step), and Round 5's to the nearest even digit -- up or down as needed.   Below I explain why.   In school they usually teach you to round all 5's up to the next digit. For example, 1.45 is rounded to 1.5, 1.65 is rounded to 1.7, 3.225 is rounded to 3.23, etc.   This is wrong because it introduces what we call "systematic error": an error consistently wrong in one direction. In rounding all 5's up, you end up with an average that is too high. ("Random error" goes high or low of the true value randomly, so the average is close to the real value.)   The reason is that 5 is directly in the middle of the digits we round, so we must round it up half the time, and down half the time.   To make this more clear, look at the digits we round to another number: 1, 2, 3, 4 we round down. 6, 7, 8, 9 we round up. (0 we just truncate,... read more

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