NZ Level 4
Order decimal numbers with thousandths
Lesson

## Ordering numbers with thousandths

When we compared decimals with thousandths, we looked at how to work out which numbers were bigger or smaller. Now we are going to look at how to put our numbers in order. When we are ordering numbers that include decimals up to thousandths, we follow a similar process to ordering decimals up to hundredths. A thousandth means $\frac{1}{1000}$11000 of a whole. The grey cube in the picture below shows one thousandth or $0.001$0.001.

Let's start by looking at how to order numbers that have digits in the thousandths place only.

Remember!
• Ascending order means smallest to largest.
• Descending order means largest to smallest.

## Using place value to order decimals

Sometimes we have numbers with digits in the tenths place and we need to compare them to numbers with thousandths. To order them, we follow the rules of place value. In the table below, the units column has the largest value and the thousandths column has the smallest value.

Units (Ones) . Tenths Hundredths Thousandths

By remembering that thousandths are worth less than hundredths or tenths, we can start from the left to compare the digits in the largest place value column and work to the right. Let's look at how we can do this now and how we can double-check our answer.

Remember!
• If our numbers are not all expressed as thousandths, starting from the left of our number is one way to compare them.
• We can rename our numbers so they are all expressed as thousandths, which also helps us place them in order.

### Outcomes

#### NA4-6

Know the relative size and place value structure of positive and negative integers and decimals to three places.