Rounding

When we calculate or measure something, we can calculate an answer with an unnecessary amount of accuracy.

For example, the distance between London and New York in a straight line, as the bird flies, is 3458.8 miles. This is accurate but if you were just having a conversation and someone asked how far it is from London to New York, it would be too accurate. It would be a little odd to say it is 3458.8 miles, though it might be quite impressive if you actually knew that.

So how far would you say it is?

Let’s make it less accurate until it feels like it is about the right accuracy.

4558.8 is a number that is accurate to 1 decimal place. Numbers can be more accurate, to 2 decimal places or 3 decimal places or more but I think your friends really aren’t going to want to ask you how far it is to anywhere if you start telling them answers to 4 decimal places. Unless you are doing it as a joke. You are funny.

Here is our number line again

In the decimal system, between each pair of numbers on the number line there are nine divisions

These divisions are the numbers to one decimal place. Reading the number line above to one decimal place, we have 4558.0, 4558.1, 4558.2, 4558.3, and so on up to 4558.9 and 4559.0

The zero is added to the whole numbers to show that it is accurate to one decimal place.

As we move right along the number line from 4558.0 to 4559.0 through all of the one decimal place numbers, we get closer to 4559.0.

If we were to round the number 4558.1 to zero decimal places, we would round it to 4558 because it is closer to 4558 than 4559.

We would do the same for the other one decimal place numbers up to 4558.4

4558.5 is exactly in the middle of 4558.0 and 4559.0 so would we round it down to 4558 or up to 4559?

The convention is to round up for 5

We would round 4558.5 and above to 4559

So, the distance from London to New York of 4558.8 would be rounded, to the nearest whole number, to 4559

I still think saying it is 4559 miles from London to New York in a conversation is too accurate. We can round it further even though there are no more decimal places.