### Comparing Two Numbers of the Same Length

When asked to put a group of numbers in to **order of size** you need to know the **value** of each digit in the number.

If you need to remind yourself what value each digit in a number has please take a look at the **Place Value** lesson.

Let’s compare these two numbers:

527 and 438

Both these numbers have **three digits**, so it is easy to see which is bigger. We just compare the **first digit** of each number which in this case is in the **hundreds** column:

527 and 438

We can see **527** is **bigger** as it has a **5** in the hundreds column where as **438** has a **4** in the **same column**.

How about ordering these two numbers:

3221 and 3389

In this case the numbers have the **same number of digits** and they have the **same first digit** in the thousands column (both have 3).

So we simply need to look at the **next column** along to the right and compare those digits.

In this case the next column is the **hundreds** column.

3221 and 3389

**3389** has a **3** in the **hundreds** column where as **3221** has a **2**.

So **3389** is the bigger number.

Here are two very similar numbers:

22471 and 22482

When comparing **similar numbers** you repeat the process of comparing digits **moving right** along the columns until you find one number with a **bigger digit**, and then you know this is the **bigger number**.

In this case we move all the way down to the the tens column where **22482** has an **8** and **22471** has a **7**. So **22482** is the **bigger** number.

### Ordering Several Numbers of the Same Length

**more than two**numbers that have the same number of digits, for example:

489, 423, 128 and 212.

- You must take the
**first digit**in each number and order the numbers according to this. - When 2 or more numbers have the
**same digit**in a column you move on to the**next digit**and order the numbers according to this.

So with the numbers given above we can start by comparing their **first digits **and write them down in a list based on how **big** it is.

When numbers have the **same first digit** we can just write them in a group next to each other for now:

128, 212, 489, 423

The last two numbers both have **4** as their **first digit**, so we need to check the **second digit** to find their size order and rewrite the list with them in size order:

128, 212, 423, 489

### Ordering Numbers of Different Lengths

When asked to compare **whole numbers** with a **different number of digits**, for example:

3449, 204, 12, 3299, 2288

You can tell straight away that the numbers with **more digits** are **bigger** than the numbers with **less** (when dealing with decimals this is not true but with whole numbers like we have here it is).

With the numbers above, the numbers with **4 digits** are **bigger** than the ones with **3 and 2 digits** as they have a digit in the thousands column. You can see also that the** 3 digit** number is **bigger** than the **2 digit** number as it has a digit in the hundreds column.

So we can straight away roughly order the numbers based on the number of digits they have:

12, 204, (3449, 3299, 2288)

I have grouped some of the numbers in **brackets** as they have the **same number of digits** and have not yet been ordered amongst themselves but they are in the **correct place as a group**.

Next we can order the numbers in the group by comparing their first digits:

12, 204, (2288, 3449, 3299)

As two numbers have the same first digit we can order them by **moving one column right** and comparing the digits there:

12, 204, 2288, 3299, 3449

### Important Symbols

When comparing the size of numbers there are three symbols that you need to understand:

=

<

>

The first one ‘**=**‘ is easy, it is the **equals** sign meaning that **the values on either side of it are equal**, for example:

10 + 4 = 14

‘<‘ means **less than**. The value on the **left** of the symbol is **less than** the value on the **right**.

For example 4 is ‘less than’ 10 looks like:

4 < 10

‘>’ means **greater than**. The value on the **left** is **greater than** the value on the **right**.

For example 12 is ‘greater than’ 3 looks like:

12 > 3

- A good way to
**remember**the difference between the two symbols ‘**less than**‘ and ‘**greater than**‘, is to look carefully at the**shape**of each symbol. - The ‘
**less than**‘ symbol looks like this:**<**. It goes from a**small point**on the**left**to a**big opening**on the**right**. So we know the**smaller value**is on the**left**by the**small point**and it is ‘**less than**‘ the**bigger value**on the**right**by the**big opening**. - The ‘
**greater than**‘ symbol is the opposite, it looks like this:**>**. It goes from a**big opening**on the**left**to a**small point**on the**right**. So we know the**bigger value**is on the**left**of the symbol next to the**big opening**and it is ‘**greater than**‘ the**smaller value**on the**right**by the**small point**.