2 Rounding

The world population in April 2021 was estimated to be 7.86 billion. That is not an exact value but it does give you an indication of the world’s population at the time. This is an example of a rounded or estimated number.

In newspapers and elsewhere, numbers are often rounded so that people can get a rough idea of the size, without getting lost in details. You may use rounding yourself, such as prices in a supermarket (£2.99 is about £3) or distances (18.2 miles is about 20 miles).

Using approximate values is also useful if you want to get a rough idea of an answer before you get out scrap paper or a calculator. This estimation acts as a check on your calculation and may help you to catch any errors you may have.

The general rules for rounding are:

• Locate the place value to be rounded.
• Look at the next digit to the right.
• If that digit is a 5 or greater, ‘round up’ the previous place value digit – which means increase it by one.
• If that digit is a 4 or less, leave the previous place value digit unchanged.
• Replace all digits after the place value digit with 0, but only if these are to the left of the decimal point.

This last rule may be a little harder to understand, so here’s an example.

With decimals we often refer to the number of decimal places to round to rather than a digit’s place value. So, instead of asking you to round to the nearest tenth, you might see instructions to ‘round to 1 decimal place’ (1 d.p.). The decimal places are numbered consecutively from the right of the decimal point. So, 1.54 has 2 decimal places, and 34.8942 has 4 decimal places.

Whether you are rounding using place value or decimal places, the general rules remain the same.

Before you have a look at some examples, you might like to view this video on rounding.

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Transcript

Narrator

Round 24 259 to the nearest hundred. You're going to find that doing these problems are pretty straightforward, but what I want to do is just think about what it means to round to the nearest hundred. So what I'm going to do is I'm going to draw a number line. Let me draw a number line here, and I'm just going to mark off the hundreds on the number line. So maybe we have 24 100, and then we go to 24 200, then we go to 24 300, and then we go to 24 400. I think you see what I mean when I'm only marking off the hundreds. I'm going up by increments of 100. Now, on this number line, where is 24 259? So if we look at the number line, it's more than 24 200 and it's less than 24,300. And it's 259, so if this distance right here is 10, 059 is right about there, so that is where our number is. That is 24 259. So when someone asks you to round to the nearest hundred, they're literally saying round to one of these increments of 100 or round to whichever increment of 100 that it is closest to. And if you look at it right like this, if you just eyeball it, you'll actually see that it is closer to 24 300 than it is to 24 200. So when you round it, you round to 24 300. So if you round to the nearest hundred, the answer literally is 24 300. Now that's kind of the conceptual understanding of why it's even called the nearest hundred.

The nearest hundred is 24 300. But every time you do a problem like this, you don't have to draw a number line and go through this whole process, although you might want to think about it. An easier process, or maybe a more mechanical process, is you literally look at the number 24 259. We want to round to the nearest hundred, so you look at the hundreds place. This is the hundreds place right here, and when we round, that means we don't want any digits. We only want zeros after the hundreds place. So what you do is you look at the place one less than the place you're rounding to. This is the hundreds place so you look at the 5 right there, and if this number is 5 or greater, if it's 5, 6, 7, 8, or 9, you round up. So 5 or greater, you round up.

And so rounding up in this situation, it is 5. It is 5 or greater, so rounding up means that we go to 24,000, and since we're rounding up, we make the 2 into a 3. We increment it by one, so rounding up, so 24,300. That's what we mean by rounding up. And just as kind of a counterexample, if I had 24 249 and I wanted to round to the nearest hundred, I would say, OK, I want to round to the nearest hundred. Let me look at the tens place, this place one level to the right. It is not 5 or greater, so I will round down.

And when you round down, be careful. It doesn't mean you decreases this 2. It literally means you just only have the 2. Just get rid of everything after it. So it becomes 24 200. That's the process where you round down. If you round up, it becomes 24 300. And it makes sense. 24 249 is going to be sitting right over here someplace, so it's going to be closer to 24 200. 24 200 would be the nearest hundred when we round down in this case. For the case of the problem, 24 259, the nearest hundred is 24 300. We round up.

End transcript

 

Here are a few more examples to have a look at before you have a go yourself.

Now complete Activity 3.

You’re now going to take some time to get to know your calculator. Calculators can save you a lot of time, but it’s important to know how to get the most from them.