This grade 4 place value lesson explains place value to one million in one printable page, with definitions, a method and a worked example.
Place value means the value of a digit depends on where it sits in a number. Each place is worth ten times the place to its right, so in 345,678 the digit 3 stands for 300,000. Grade 4 students use place value to read, write, and compare whole numbers up to 1,000,000.
Grade 4 Place Value Lesson: key facts
- A digit in any place is worth 10 times as much as the same digit one place to its right.
- The places from right to left are ones, tens, hundreds, thousands, ten thousands, hundred thousands, and millions.
- A number can be written as a numeral, as a number name, and in expanded form.
- To compare two numbers, find the first place from the left where the digits differ.
- Ten hundred thousands make one million, written 1,000,000.
What is place value?
Every digit in a number has a value that depends on its place. Look at 345,678. The digit 3 sits in the hundred thousands place, so it is worth 300,000. The digit 4 is in the ten thousands place, so it is worth 40,000.
Place value is the value of a digit because of where it sits in a number. The places, from right to left, are ones, tens, hundreds, thousands, ten thousands, hundred thousands, and millions. A group of three places is a period: the ones period, the thousands period, and the millions period.
How does each place compare with the place next to it?
A digit in one place is worth 10 times as much as the same digit one place to its right. Three ones is 3. Move the 3 one place left and it becomes 3 tens, or 30. Move it again and it becomes 300.
The same rule works inside one number. In 7,700 the left 7 is worth 7,000 and the right 7 is worth 700. Since \(700 \times 10 = 7{,}000\), the left 7 is 10 times as much as the right 7.
How do you read and write a multi-digit number?
A number can be written in three ways. Take 46,305.
| Form | Example |
|---|---|
| Base-ten numeral | 46,305 |
| Number name | forty-six thousand three hundred five |
| Expanded form | \(40{,}000 + 6{,}000 + 300 + 5\) |
Say the number in each period, then say the name of the period. A zero in a place means that place adds nothing, so it is skipped in the expanded form.
How do you compare two numbers?
- Line up the two numbers by place value.
- Start at the left, with the greatest place.
- Find the first place where the digits are different.
- The number with the greater digit in that place is the greater number.
Example. Compare 58,423 and 58,342. The ten thousands digits match (5 and 5) and the thousands digits match (8 and 8). In the hundreds place, 4 is greater than 3. So \(58{,}423 > 58{,}342\).
A whole number with more digits is greater, because its leftmost digit is not zero. For example, 124,500 has six digits and 99,999 has five, so \(124{,}500 > 99{,}999\). Use \(>\), \(< \), or \(=\) to write the comparison.
Place Value to One Million: frequently asked questions
What is the value of a digit?
The value of a digit is the digit times its place. In 52,430, the 5 is in the ten thousands place, so its value is 50,000. The 3 is in the tens place, so its value is 30.
Why is each place worth ten times the place to its right?
Our number system groups by tens. Ten ones make one ten, ten tens make one hundred, and ten hundreds make one thousand. The pattern keeps going up to millions.
What is expanded form?
Expanded form writes a number as the sum of the value of each digit. For 8,206 it is 8,000 + 200 + 6. A zero digit is left out because it adds nothing.
How do you compare numbers with different numbers of digits?
The number with more digits is greater, as long as neither starts with a zero. For example, 10,000 is greater than 9,999 because it has five digits and 9,999 has four.
How many hundred thousands make one million?
Ten hundred thousands make one million. In the same way, ten ten thousands make one hundred thousand, and ten thousands make ten thousand.
How to use this grade 4 place value lesson
Use this grade 4 place value lesson before the worksheet, then check what you learned with the quiz.
See every chapter on the Grade 4 math page.
