Expanded form: writing numbers as a sum of place values
| Standard form | Expanded form | Word form |
|---|---|---|
| 2,615 | 2,000 + 600 + 10 + 5 | two thousand six hundred fifteen |
| 3,040 | 3,000 + 40 | three thousand forty |
| 90,007 | 90,000 + 7 | ninety thousand seven |
Expanded form takes each digit and writes what it is worth. Places with a zero are left out of the sum, but they still matter in standard form.
A routine that works
- Say the number aloud and count its digits.
- Write the place name above each digit, starting from the ones on the right.
- For each digit that is not zero, write the digit followed by the right number of zeros.
- Join them with plus signs, then add them back up to check you get the original number.
Going the other way
Expanded form sometimes arrives jumbled, for example 5 + 400 + 20,000. Sort the parts by size first: 20,000 + 400 + 5. Then fill the empty places with zeros: 20,405.
Expanded form is also how column addition works underneath. 324 + 152 is really (300 + 100) + (20 + 50) + (4 + 2).
Printable practice
Write each number in the form asked for.
- Write 4,382 in expanded form.
- Write 7,009 in expanded form.
- Write 60,000 + 500 + 3 in standard form.
- Write 8 + 300 + 4,000 in standard form.
- What is the value of the 9 in 19,240?
Show answers
- 4,000 + 300 + 80 + 2
- 7,000 + 9
- 60,503
- 4,308
- 9,000
Keep learning
Number bonds to 10 and 100What number bonds are, how to practise them with ten-frames and blocks, and how bonds to 10 lead straight into bonds to 100 and mental subtraction.Skip counting and multiples: patterns to look forSkip counting by 2, 5, 10, 3 and 9, the digit patterns each one makes, and how skip counting turns into the times tables.Comparing and ordering numbers with < and >A step-by-step method for comparing whole numbers of any size, how to remember the inequality signs, and ordering practice with answers.