Arrange From Least to Greatest
Introduction
Arranging numbers into a series from least to greatest can be tricky, particularly if you have lots of numbers, each of which has lots of digits. However, to work it out, you need to organize the numbers, and then you'll be able to determine which is the smallest and which is the largest.
Terms
Lesson
When you're arranging numbers like this, the first step is to write them in a table based to help you align the digits. You can use a table like the one below:
| Hundred-Thousands | Ten-Thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|---|
Let's say we want to arrange the following numbers from least to greatest:
- 387
- 5,190,
- 4,899,
- 287,431,
- 28,431
We can first put them into a number table. Fill them in from the right, so that you make sure the ones column is aligned.
| Hundred-Thousands | Ten-Thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|---|
| 3 | 8 | 7 | |||
| 5 | 1 | 9 | 0 | ||
| 4 | 8 | 9 | 9 | ||
| 2 | 8 | 7 | 4 | 3 | 1 |
| 2 | 8 | 4 | 3 | 1 |
This allows us to easily compare the numbers. We're looking for the smallest number first, so we can eliminate numbers that have values in columns on the left. For example, 287,431 has a value in the hundred-thousands column, so we can eliminate that. 28,431 has a number in the ten-thousands column, so it's not that either. 5,190 and 4,890 both have their first number in the thousands column, but 387 doesn't have a number until the hundreds column, so that is our lowest. We can scratch that out of the table since it's now our least. We can now write this outside of our table.
| Hundred-Thousands | Ten-Thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|---|
| 5 | 1 | 9 | 0 | ||
| 4 | 8 | 9 | 9 | ||
| 2 | 8 | 7 | 4 | 3 | 1 |
| 2 | 8 | 4 | 3 | 1 |
Lowest
- 387
To find the next lowest number, we follow the same tactics; since 5,190 and 4,899 both have their first digit in the thousands column, they are the next least. Looking at the thousands column, 4 is less than 5, so 4,899 is less. We can scratch them from the table and add them (in order) to our list.
| Hundred-Thousands | Ten-Thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|---|
| 2 | 8 | 7 | 4 | 3 | 1 |
| 2 | 8 | 4 | 3 | 1 |
Lowest
- 387
- 4,899
- 5,190
Next, we go back to our table and repeat the exercise. 28,431 has its highest number in the ten-thousands column, so is smaller than 287,431. We can, therefore, complete our list:
Lowest
- 387
- 4,899
- 5,190
- 28,431
- 287,431
Highest
You can follow this approach with any set of numbers. If you have decimals, you need to add additional columns to the left, and if you have fractions, you will need to convert them into non-fractions.