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Place Value Tables Up to 999

This lesson explains how to build and read a place value table for numbers up to 999. It covers the hundreds, tens, and ones columns, shows how to place digits correctly, and walks through worked examples so you can convert between a table and standard form with confidence.

Introduction

A place value table is a simple grid that sorts the digits of a number into columns so you can see exactly what each digit is worth. For numbers up to 999, every table has three columns: hundreds, tens, and ones. Once a number is placed correctly into a table, it becomes much easier to read, compare, and rebuild.

What the three columns mean

Every three-digit number can be written as a sum of hundreds, tens, and ones. If a number has \(h\) hundreds, \(t\) tens, and \(o\) ones, then the number itself is

\( N = 100h + 10t + o \)

The hundreds column tells you how many groups of 100 are inside the number, the tens column tells you how many groups of 10 are left over, and the ones column tells you what remains after that. This idea connects directly to identifying hundred, tens, & ones, which is worth reviewing if the column names still feel unfamiliar.

Building a place value table

To fill in a table for a number like 347, work from left to right:

1. Write the digit 3 in the hundreds column, because 3 hundred is 300.
2. Write the digit 4 in the tens column, because 4 tens is 40.
3. Write the digit 7 in the ones column, because 7 ones is 7.

Adding those back together gives \( 300 + 40 + 7 = 347 \), which matches the original number.

The digits of 347 placed into a hundreds, tens, and ones table.

Reading a table back into a number

The same process works in reverse. If a table shows 9 in the hundreds column, 2 in the tens column, and 6 in the ones column, then the number is

\( 900 + 20 + 6 = 926 \)

The digits of 926 placed into a hundreds, tens, and ones table.

Notice that this is exactly the same idea used when you write a number in expanded form. If you want more practice turning a number into a sum of hundreds, tens, and ones, see numeral expanding up to 999.

Comparing numbers with a place value table

Place value tables also make it quick to compare two numbers. Line up two numbers by column and compare the hundreds first. Whichever number has more hundreds is larger, no matter what the tens and ones digits say. If the hundreds digits match, move to the tens column, and only compare ones if both the hundreds and tens digits are equal.

For example, compare 452 and 461:

Both have 4 hundreds, so the hundreds column does not decide it. Move to the tens column: 461 has 6 tens while 452 has 5 tens, so \( 461 > 452 \).

Why the columns sometimes need adjusting

Sometimes an amount in one column adds up to 10 or more, and it has to be traded for a group in the next column over, such as 10 ones becoming 1 ten. This process is called regrouping, and it is covered in detail in regrouping place values up to 999, which is a natural next step once you are comfortable reading and building basic tables.

Quick checklist for using a place value table

1. Find the ones digit first, then the tens digit, then the hundreds digit.
2. Keep each digit in its own column; never let a digit cross into the wrong place.
3. Multiply the hundreds digit by 100, the tens digit by 10, and keep the ones digit as is.
4. Add the three results to check your table matches the original number.

Related lessons

Math 2