# Rounding Numbers - What and Why?

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## Description

This is an introductory tutorial outlining what it means to "round a number" and why we do it. The associated video tutorial is to come.

## What does it mean to 'round' a number?

Rounding a number up or down is a way of giving an **approximate** answer to a question, rather than a strictly accurate number.

## Why do we round numbers?

There are four reasons why we might round a number.

#### 1. To make things simple (and quick).

This is probably the most common reason cited for rounding a number. For example, if you were asked to add 2,413 + 2,657 off the top of your head, you could quickly get an approximate answer by simplifying the numbers to 2,410 and 2,660. You could do it even quicker if your round the numbers to 2,400 and 2,600 - but the answer would be less accurate.

Importantly, it doesn't always matter if the answer isn't the most accurate - which brings us to #2.

#### 2. It's not always necessary to have an accurate figure.

For example, if you wanted to get an estimate of the size of the Levi Stadium, you might ask someone *'how many people can be seated in the Levi Stadium?'*

Unless you are working in the office that sells the stadium's tickets, it's not necessary to know exactly how many seats it has in order to get a feel for its size; an estimate is all you'd need. In this case, the answer is 68,500 seats, and roughly 77,000 when you add the club and luxury seats.

#### 3. There is uncertainty.

For example, if you were to ask *how many species of animals are there in the world?*, the answer would be approximately 7,770,000. The answer is an estimate because we don't actually know exactly how many different animal species there are in the world; we only know how many we've catalogued, and the rest is a guestimate (albeit an educated guestimate).

#### 4. The answer varies.

Sometimes the answer to a question is a range. For example, if you were to ask what the distance is between the earth and the moon, the answer would be '*well it depends*'. This is because the moon does not orbit the earth in a perfect circle. Instead, it follows an elliptical orbit, as shown below.

More often than not, rather than answering the question with a range (363,105 to 405,696 km), people with give an average of the two numbers i.e. 384,401 km. Although not strictly necessary, in most cases this answer would be rounded down to 384,400 km; this is because it is only an estimate, not an exact number.

Imagine you'd eaten 4 pieces of cake one afternoon while watching TV. If someone was to ask you how much of the whole cake you ate in that sitting, you wouldn't get a scale out, or your calculator and protractor. Instead, you'd make an estimate of what proportion those four slices made of the cake. Time can pass really quickly when you're watching TV. If a friend was to ask you how long the movie was that you watched last Saturday night, you probably wouldn't be able to give them an accurate answer without conferring with Google - instead, you'd give them an estimate. We use numbers to count things. For example, we can use numbers to tell someone how many slices of cake we've eaten, or how many hours of TV we've watched that day. In these cases, the answer is likely to be between 1 and say 10, maximum, and you'd be able to answer it quickly and accurately.Sometimes though, we'll round the answer up or down. Sometimes though, we'll round the answer up or down.