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Place Value Tables of Multi-Digit Numbers

A place value table organizes the digits of a multi-digit number into labeled columns such as ones, tens, hundreds, and thousands, so each digit's true value is easy to see. This page shows how to build a place value table, fill it in correctly, and use it to read and understand large numbers with confidence.

What Is a Place Value Table?

A place value table (sometimes called a place value chart) is a simple grid that sorts the digits of a multi-digit number into labeled columns, such as thousands, hundreds, tens, and ones. Instead of just looking at a long string of digits, a place value table shows exactly what each digit is worth based on where it sits.

This matters because the same digit can mean very different things depending on its position. In the number \(4,273\), the digit \(4\) is not just "4" — it sits in the thousands column, so it stands for \(4000\). A place value table makes that instantly visible.

Building a Place Value Table

To build a place value table for a multi-digit number, follow these steps:

1. Count how many digits the number has, starting from the right.
2. Draw one column for each digit, labeling columns from right to left as ones, tens, hundreds, thousands, ten thousands, and so on.
3. Write each digit of the number into its matching column, keeping the digits lined up from right to left.

Each column is exactly \(10\) times larger than the column to its right. That is why the columns are named ones, tens, hundreds, thousands: each name reflects a jump of \(10\).

Reading a Number From a Table

Once digits are placed in a table, you can read the number by going column by column, from the largest place on the left to the smallest on the right. The table above shows \(4,273\): \(4\) thousands, \(2\) hundreds, \(7\) tens, and \(3\) ones. Multiplying each digit by its column value and adding the results gives back the full number: \(4000 + 200 + 70 + 3 = 4273\).

This column-by-column view is also the foundation for writing a number in its expanded form, and for pulling out the value of just one digit, which is covered separately under identifying the place value of a digit.

Extending the Table for Larger Numbers

A place value table is not limited to four columns. For a five-digit number like \(58,914\), add a ten thousands column to the left of thousands.

The pattern never changes: every new column to the left is worth \(10\) times more than the one beside it. This same idea is what lets you convert between place values once a number gets large.

Worked Example

Place the number \(30,652\) into a table.

Step 1: Count the digits. There are \(5\) digits, so the table needs \(5\) columns: ten thousands, thousands, hundreds, tens, ones.

Step 2: Fill in the columns from right to left: ones = \(2\), tens = \(5\), hundreds = \(6\), thousands = \(0\), ten thousands = \(3\).

Step 3: Check by adding the column values: \(30000 + 0 + 600 + 50 + 2 = 30652\). Notice the \(0\) in the thousands column still needs its own column; skipping it would turn the number into \(3652\) instead of \(30,652\).

Common Mistakes to Avoid

Most place value table errors come from misaligning digits. Always line up the ones column first, then fill columns to the left. Do not skip a column just because its digit is \(0\), and do not add extra empty columns on the left of the first non-zero digit. Keeping every digit in exactly one labeled column is what makes the table reliable for reading, comparing, and writing numbers correctly.

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