Before we begin looking at ordering numbers, and working out which numbers are the largest or smallest we need to remember how to identify the value of the digits in our number.

Examples

Example 1

State the value for the underlined digit.

This image shows the number 386 with the 8 underlined.

Worked Solution

Create a strategy

Imagine the numbers are written in a place value table to help find the value of the digit.

Apply the idea

Here is the complete table:

Hundreds	Tens	Ones
3	8	6

The 8 is in the tens column.

So the value is 8 tens which is 80.

Idea summary

We can use a place value table to find the value of each digit in a number.

Order numbers to 1000 on a number line

Let's look at how to use a number line to order numbers from smallest to largest, and largest to smallest.

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Examples

Example 2

We want to work out which of 3 numbers is the biggest.

Which of the number lines has 730,830, and 930 plotted correctly?

Worked Solution

Create a strategy

Check the values of the ticks on the number line.

Apply the idea

Each small tick corresponds to 20. So 730 should be two ticks to the left of 750, 830 should be two ticks to the left of 850, and 930 should be two ticks to the left of 930.

So the correct answer is option A.

Write the three numbers from smallest to largest on one line.

Worked Solution

Create a strategy

The smaller a number is, the further to the left on the number line it is.

Apply the idea

Since 730 is to the left of 830, and 830 is to the left of 930, then 730 is the smallest number and 930 is the largest number.

The three numbers from smallest to largest are:

730,\, 830, \, 930

Idea summary

The smaller a number is, the further to the left on the number line it is.

Order number to 1000 using place value

We can also use place value to order numbers, and this video includes an example of how we do that.

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Examples

Example 3

Order these numbers from largest to smallest.

73,\, 33, \, 37

Worked Solution

Create a strategy

We should order the tens first, then the ones.

Apply the idea

The numbers in the place value table are shown:

Tens	Ones
7	3
3	3
3	7

33 and 37 have the same smallest tens digit, so they are smaller than 73.

But 33 has the smaller ones digit, so 33 is smaller than 37.

The numbers from largest to smallest are: 73,\,37,\, 33

671,\, 167, \, 617

Worked Solution

Create a strategy

We should order the hundreds first, then the tens, then the ones.

Apply the idea

The numbers in the place value table are shown:

Hundreds	Tens	Ones
6	7	1
1	6	7
6	1	7

167 has the smallest hundreds digit so it is the smallest number.

671 and 617 have equal hundreds digits, but 617 has the smaller tens digit.

The numbers from largest to smallest are: 671,\,617,\, 167

Idea summary

When we use place value to order numbers, always start with the far left digit and think about the digit's place value.

1.07 Order 3 digit numbers

Ideas

Are you ready?

Examples

Example 1

Order numbers to 1000 on a number line

Examples

Example 2

Order number to 1000 using place value

Examples

Example 3

Outcomes

MA2-4NA

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