# How to Round Numbers

#### Back to Foundation Maths

## Description

This is an introductory tutorial outlining how to round numbers. The associated video tutorial is to come.

## How do we Round Numbers?

When we want to round a number, we need to know what we want to round it to - the nearest two? the nearest ten? the nearest fifty?

The numerical system that we most commonly use is the *decimal system*. This system is based on the number ten, in part because we have ten fingers and ten toes (it made simple addition easy before calculators and the like came about). You're probably wondering: *why is this relevant?*

Well most commonly when we round a number, we do it to the nearest ten, or number easily divisible by ten e.g. hundred, thousand. So, this is what we'll learn to do in this tutorial.

## The necessary steps

### Step 1: Identify the 'desired place value'

We've learned that digits occupy different place values in a number. If you want to round a number to the closest ten, the second (or tens') place value will be the 'desired' one. If you want to round to the closest hundred, the third (or hundreds') place value will be the 'desired' one.

### Step 2: Inspect the next smallest place value

This will be the digit to the right of the 'desired' place value. If you're rounding to the nearest ten, this will be the digit in the ones' place value. Conversely, if you want to round to the closest hundred, you'll be inspecting the digit in the tens' place value.

### Step 3: Round the number

If the digit to the right is a 0, 1, 2, 3 or 4, then we:

- change this digit (and any to the right of it) to 0 AND
- leave the digit in the desired place value alone.
- This is called
*rounding down*.

If the digit to the right is a 5, 6, 7, 8, or 9, then we:

- change this digit (and any to the right of it) to 0 AND
- increase the digit in the desired place value by one.
- This is called
*rounding up*.

## Some examples

### Round the number 156 to the closest ten

**Step 1: Identify the 'desired place value'**

The question asks us to round to the closest *ten* i.e. the desired place value will be the tens' place value. It is a five.

**Step 2: Inspect the next smallest place value**

The next smallest place value is the ones' place value. It is a six.

**Step 3: Round the number**

We change the six to a 0 AND increase the digit in the desired place value by one. This makes the rounded number 160.

### Round the number 21,823 to the closest hundred

**Step 1: Identify the 'desired place value'**

The question asks us to round to the closest *hundred* i.e. the desired place value will be the hundreds' place value. It is an eight.

**Step 2: Inspect the next smallest place value**

The next smallest place value is the tens' place value. It is a two.

**Step 3: Round the number**

We change the two and any numbers to the right of it to a 0 AND leave the digit in the desired place value alone. This makes the rounded number 21, 800.

### Round the number 21,573 to the closest thousand

**Step 1: Identify the 'desired place value'**

The question asks us to round to the closest *thousand* i.e. the desired place value will be the thousands' place value. It is a one.

**Step 2: Inspect the next smallest place value**

The next smallest place value is the hundreds' place value. It is a five.

**Step 3: Round the number**

We change the five and any numbers to the right of it to a 0 AND increase the digit in the desired place value by one. This makes the rounded number 22,000.

## Complementary Exercises

Below are some complementary exercises for you to work through in your own time to consolidate your understanding of how to round numbers (answers are included!). You can download the document here: