# What does -3.5 round to?

Discussion in 'Mathematics' started by Elfrune, Oct 10, 2016.

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1. ### NewToTeachingOldToMathsLead commenter

That's because it doesn't actually give "different answers" to any "the same question" ... so there's no question to address.

You can see that from my formulation of the rule. For every value, it gives a unique answer. There is no question to which it gives more than one answer.

2. ### BillyBobJoeEstablished commenter

Yes there is, as has been explained by me and by others. The fact that positive and negative are arbitrary in many situations means that using your method results in different answers. That's a pretty fundamental flaw. There are no advantages to your preferred rounding method, and demonstrable disadvantages.

3. ### NewToTeachingOldToMathsLead commenter

Please don't evade the issue. My position is that it is YOUR method which is inconsistent in situations where the position of the origin (and thus positive or negative) is essentially arbitrary. You have not addressed this. My rule is consistent no matter what translations you make, or where you site the origin. Your rule requires an exception for zero, and therefore some answers under your rule will change as you translate the origin along the number line.

You have asserted that the rule of always rounding an exact 0.5 to the larger number gives different answers to "the same question". but you have not demonstrated this - you have merely asserted. I am now calling you out on that.

Kindly state what this "same question" is, to which my rounding convention gives "different answers" ... because I do not believe that you are capable of articulating it.

Last edited: Jan 2, 2017
4. ### BillyBobJoeEstablished commenter

Consider the situation of a ball projected vertically upwards from the top of a wall at 3m/s. The ball takes 2.25s to reach the ground. Taking g=9.8m/s^2, what is the velocity of the ball when it hits the ground? Give your answer to 3 sf.

Using your method, the answer could be either 25.0 or 25.1 depending on whether you take up or down to be positive.

Or consider the more simple case: Fred has £17.50 in his bank account. He takes out £20. What is his new balance? Round your answer to a whole number of pounds.

5. ### StiltskinStar commenter

Wikipedia has a nice summation on the different methods. Round half up seems to be the most common way from the people I spoke to, but round half away from zero make sense for certain situations (such as the financial ones mentioned here). Personally, I like to symmetry of this.