Write in Expanded Notation
Introduction
Expanded notation is a way of writing large numbers to show the value of each digit. For example, for the number 629 (written in standard notation) you could expand it to be 6 x 100 + 2 x 10 + 9. Expanded notation allows you to easily see what the number is made up of.
Terms
Lesson
To write a number in expanded notation you can use a number table to help. For example, if we take the number: 48,943, we can add it to a number table. A number table is a series of columns that show you how many of each value you have. Plugging 48,943 into a number table gives us:
| 10,000 | 1,000 | 100 | 10 | 1 |
|---|---|---|---|---|
| 4 | 8 | 9 | 4 | 3 |
Once we've put a number into a number table, turning it into standard notification is simple. We simply multiply each digit in the table by the number at the head of its column. When writing in expanded notation, we start with the highest value column first (i.e. the one on the furthest left). So, multiplying the digit by the column head gives us 4 x 10,000 for the start. Repeating this for the next column gives us 8 x 1,000. Completing this for the whole table gives us:
4 x 10,000 8 x 1,000 9 x 100 4 x 10 3 (we don't multiply the ones digit by 1 because it doesn't change the value)
To complete it, we need to add all the values together. Because of PEMDAS, putting addition signs between the equations won't mess up the order, because we do the multiplying first.
So, to finish it off, we'd write:
4 x 10,000 + 8 x 1,000 + 9 x 100 + 4 x 10 + 3.
If we were to multiply all the numbers and then add them together, we'd get 48,943, which is the number written in standard notation.