how do you round off numbers?

Question

I am learning how to round off numbers--how do you round off numbers?...is there a basic formula or technique I can apply to all rounding off of numbers?

Answer 1

I assume you are just referring to simple rounding, and in that case, you need to know two things:

1. Are we rounding up or down?

2. What place are we rounding to?

The answer to the first question is one that is easily answered. Generally, unless stated otherwise, we round numbers that are lower than five down, and numbers that are five or greater up. For instance:

Imagine we have a number, 10.1, and you are told to round it to the nearest whole number. Since the 1 in 10.1 is lower than 5, we round this value down to 10. 

Now Imagine we have a number 10.7, and you are told to round it to the nearest whole number. Since the 7 in 10.7 is greater than 5, we round this value up to 11.

Now, my examples bring up another question. I said "round to the nearest whole number." What does that mean? To answer the second part of what you need to know, the problem itself usually tells you how to round the number. Let's look at an example:

Say I have a number: 9.72991. This number has five decimal places. Let's explore some rounding options.

If I were to instruct you to round this number to the hundredths place(2nd decimal), you would begin by looking at the next decimal place, or in this case, the third decimal place. So we would take a  look at this nine: 9.72991. After finding which number we will be working with, we can drop everything off of the end behind it, so now it looks more like this: 9.729. Now, we need to determine if this number is less than five. In this case, it is not. So, we will be rounding up. Now we jump forward and look at the decimal place that we are rounding to(the second decimal place). So now we are looking at this two: 9.729. Because we determined that we are rounding up, we will drop of the 9 and increase the 2 to a 3. So when told to round 9.72991 to the hundredths place, we come out with a value of 9.73.

 

Now imagine that same number, 9.72991, but now we are rounding it to the tenths place(first decimal place). We go through the same exact process. We look at the number behind the first decimal place, and in this case, it is this two: 9.72991. Just like before, we drop off everything behind it, so we are now looking at 9.72. Next we determine if that value is less than five, and this time it is, so we round down. After that we go back to the decimal place we are rounding to and look at it. In this instance, it is 7. Because we are rounding down, we simply drop the 2, and we are done. So when told to round 9.72991 to the tenths place, or first decimal place, we end up with a value of 9.7.

So rounding to the first whole number simply means rounding all of the decimal places off for example: rounding 10.4 goes down to 10, or 5.9 goes up to 6.

I'm not quite sure what you were asking for, so if you have a question, feel free to ask!