Ordering decimals is a process of arranging them in a specific order.
Read on to find out how to order decimals and an example of ordering decimals.
Steps of ordering decimals
- Use a table to line up the decimal points and compare the decimals.
- Fill in all of the numbers that you want to compare.
- If empty squares are at the end of the decimal, fill them in with zeroes.
- Start comparing the size of the decimal.
- Start on the left and keep moving across to the right.
Different types of ordering
There are different ways to order decimals, just like other types of ordering for all numbers.
If you are ordering decimals in ascending order, the smallest goes first, and the numbers get bigger.
If you are descending in descending order, the most significant decimal goes first, and the numbers get smaller until you reach the smallest.
Ordering decimals: example
Now we know a bit more about ordering, let’s look at an example of ordering decimals.
Put these decimals in ascending order: 1.73, 1.073, 0.86, 0.806.
We know that ascending order means the smallest number goes first, so bear that in mind as we go through.
- Let’s start by arranging them on a table and filling empty squares with zeroes.
| 1 | . | 7 | 3 | 0 |
| 1 | . | 0 | 7 | 3 |
| 0 | . | 8 | 6 | 0 |
| 0 | . | 8 | 0 | 6 |
Compare the first (left) column.
In this case, you can see that two numbers start with 1, which we can ignore for now because we are looking for the smallest number.
Two numbers start with 0, so let’s move across and look at the tenth column.
- Compare the tenth column.
We can ignore the 7 in the tenth column because it belongs to 1.73.
There are two 8s in the tenth column, which means we must move across again and see which decimal is the smallest.
- Compare the hundredths column.
In the hundredths column, we can ignore 3 and 7 because they belong to 1.73 and 1.073.
There is a 6, which is more significant than 0. So we know that 0.86 isn’t the smallest number. So this means that 0.806 is the smallest number.
Now that we know the smallest number, we can work our way back up to the biggest.
- Start listing the numbers from smallest to biggest.
We know that 0.806 is the smallest number and that 0.86 is the following most significant number.
So now we must look at 1.73 and 1.073 to see which comes next in the sequence. We can see that 1.73 is the biggest because it has the most significant number in the tenth column.
It allows us to slot the remaining numbers in place.
Our answer is 0.806, 0.86, 1.073, and 1.73.
