5-Digit Numbers
Building Numbers
We have learned to group ones, tens, and hundreds. The pattern continues! To build even bigger numbers, we group thousands.
We group 10 thousands together to make 1 ten thousand: 
= \(10\) thousands = \(1\) ten thousand = 
Our place value table now needs a new, larger column for Ten Thousands.
We group 10 thousands together to make 1 ten thousand:
= \(10\) thousands = \(1\) ten thousand = | Ten Thousands | Thousands | Hundreds | Tens | Ones |
| 1 | 2 | 4 | 3 | 5 |
| |  |  |  |  |
Definition 5-Digit Number
In the base 10 system, the place of a digit in a number determines its value. We can show a number like \(12\,435\) in many different ways:
- With digits: $$12\,435$$
- In expanded form: $$\begin{aligned}[t] 1\text{ ten thousand }&+& 2\text{ thousands }&+& 4\text{ hundreds }&+& 3\text{ tens }&+& 5\text{ ones }\\ 10\,000 &+& 2\,000 &+& 400 &+& 30 &+& 5 \\ 1\times 10\,000 &+& 2\times 1\,000 &+& 4\times 100 &+& 3\times 10 &+& 5\times 1 \\ \end{aligned}$$
- With words: twelve thousand, four hundred thirty-five
- In a place value table:
Ten Thousands Thousands Hundreds Tens Ones 1 2 4 3 5 - With blocks:
On the Number Line
A number line helps us see numbers in order. We can use it to count by ones, or we can make bigger jumps to count faster. With large numbers, we can imagine number lines that jump by hundreds or even thousands at a time!
- Counting by tens: 0, 10, 20, 30...
- Counting by hundreds: 0, 100, 200, 300...
- Counting by thousands: 0, 1 000, 2 000, 3 000...
Definition Number Line
A number line is a line that shows numbers in order. Moving right adds by same number.