4th Grade Place Value to One Million Lesson: Notes and Examples (Free PDF)

Q: What is the value of a digit?

The value of a digit is the digit times its place. In 6,482 the 4 is in the hundreds place, so its value is 400.

Q: How many times greater is a digit one place to the left?

It is 10 times greater. For example, the 3 in 30 is worth ten times the 3 in 3, and the 3 in 300 is worth ten times the 3 in 30.

Q: How do you write a number in word form?

Say the number in each period and add the period name. The number 52,014 is written fifty-two thousand, fourteen. Use hyphens for 21 through 99.

Q: What does expanded form mean?

Expanded form shows a number as a sum of the value of each digit. The number 8,060 in expanded form is 8,000 + 60.

Q: Which symbol do you use to compare numbers?

Use > when the first number is greater, < when it is less, and = when the numbers are the same. The symbol opens toward the greater number.

Q: What is the difference between digit value and place value?

A digit is one of the symbols 0 to 9, and its place value is the worth that comes from where it sits. In 5,400, the digit 4 sits in the hundreds place, so its value is 400. The same digit in a different place has a different value.

Q: How do you compare numbers with the same number of digits?

Compare digit by digit from the left, and stop at the first place where they differ. For 120,364 and 120,346, the first four digits match, and then 6 is greater than 4 in the tens place, so 120,364 is greater.

Q: How do you write 406,015 in words?

Say four hundred six thousand, fifteen. Read the part before the comma as a number of thousands, then read the rest. A zero in the middle of a group is simply not said, but it must be written in standard form.

4th grade place value lesson – Maths PDF

Cover of the book Grade 4 Math Lessons (PDF)

Download as a PDFThe Grade 4 math lessons bookPrintable PDFSee the book ›

Sommaire

This 4th grade place value lesson covers place value to one million (Common Core 4.NBT.A.1, 4.NBT.A.2), with a free PDF to print.

Key takeaway: This lesson helps fourth grade students read, write, compare, and order whole numbers up to one million using place value.

Topic: Place Value to One Million (4th grade)
Content: One-page lesson with a definition, a worked example and key facts
Standards: 4.NBT.A.1, 4.NBT.A.2
Answers: Explanations included
Format: Free printable PDF, US Letter, black and white

Place value tells how much a digit is worth based on where it sits in a number. Each digit is worth ten times the digit to its right. In 305,718, the 5 is in the thousands place, so it means 5,000. You can write numbers up to 1,000,000 three ways and compare them with <, >, or =.

This lesson helps fourth grade students read, write, compare, and order whole numbers up to one million using place value. Also, it shows that each digit is worth ten times as much as the same digit one place to its right, which explains how large numbers are built.

Students learn the place names from ones to hundred thousands, how to write numbers in standard, word, and expanded form, and how to compare numbers by looking at the leftmost digits that differ. Then, the lesson uses a place value chart to make each idea visible. Also, plan about 20 minutes, and write each example in a chart as you read.

Grade 4 · Common Core State Standards: 4.NBT.A.1, 4.NBT.A.2

Key facts in this 4th grade place value lesson

Key facts

A digit in any place is worth 10 times the same digit one place to its right.
Places from the right: ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions.
Expanded form adds the value of each digit: 4,203 = 4,000 + 200 + 3.
Then, compare numbers from the left, place by place, and use the symbols <, >, or =.
1,000,000 is ten times as much as 100,000.

What is place value?

Every digit has a job, and its job depends on where it sits in the number. The same digit can be worth a little or a lot.

Place value

The place value of a digit is the worth that comes from its position. Digits are grouped in periods of three: ones, thousands, and millions.

The digit 5 sits in the thousands place of 305,718, so it is worth 5,000.

In \(305,718\) the digit 5 is in the thousands place. It stands for \(5,000\), not for 5.

Why is a digit worth ten times the digit to its right?

Moving one place to the left makes a digit ten times as large. Ten tens make one hundred, and ten hundreds make one thousand.

Ten bars of 70 make one bar of 700. The 7 in 700 is worth ten times the 7 in 70.

So \(700 = 10 \times 70\), and \(7{,}000 = 10 \times 700\).

How do you write a number in three ways?

Form	Example
Standard form	\(305,718\)
Word form	three hundred five thousand, seven hundred eighteen
Expanded form	\(300{,}000 + 5{,}000 + 700 + 10 + 8\)

Expanded form of 305,718 adds the value of each digit.

Zeros matter. In 40,005 the thousands, hundreds, and tens places hold 0, so they add nothing to expanded form: \(40{,}000 + 5\). Always keep the 0s in standard form, because they hold the other digits in the correct places. Say each period out loud, such as “forty thousand, five,” to write the word form.

How do you compare two numbers?

Use the symbols \(<\), \(>\), and \(=\). The open side of the symbol faces the greater number.

Farther right on the number line means greater: 350,000 > 305,718.

A number with more digits is always greater when it has no leading zeros. So a six-digit number beats any five-digit number. When two numbers have the same number of digits, use the steps below.

Line up the digits by place value.
Start at the left and find the first place where the digits differ.
The number with the greater digit in that place is greater.

Example: Compare \(48,305\) and \(48,350\). The digits match in the ten thousands, thousands, and hundreds places. In the tens place, 0 is less than 5, so \(48{,}305 < 48{,}350\).

4th grade place value lesson: questions and answers

What is the value of a digit?

The value of a digit is the digit times its place. In 6,482 the 4 is in the hundreds place, so its value is 400.

How many times greater is a digit one place to the left?

It is 10 times greater. For example, the 3 in 30 is worth ten times the 3 in 3, and the 3 in 300 is worth ten times the 3 in 30.

How do you write a number in word form?

Say the number in each period and add the period name. The number 52,014 is written fifty-two thousand, fourteen. Use hyphens for 21 through 99.

What does expanded form mean?

Expanded form shows a number as a sum of the value of each digit. The number 8,060 in expanded form is 8,000 + 60.

Which symbol do you use to compare numbers?

Use > when the first number is greater, < when it is less, and = when the numbers are the same. The symbol opens toward the greater number.

Common mistakes with this 4th grade place value lesson

Students read a digit by its face value instead of its place value. Also, the 4 in 4,000 is worth four thousand, not four.
Students leave out a zero when writing a number from words. Instead, in three hundred six thousand, forty, the empty places must be held with zeros: 306,040.
Students compare numbers by length of digits alone, even when lengths match. Also, when two numbers have the same number of digits, compare from the left.

How to study this chapter

Use a place value chart with commas separating thousands. Writing numbers in the chart keeps zeros in the right places.
Say each number aloud in words as you write it. Hearing three hundred six thousand helps place the commas and zeros.
Parents can use play money or a car odometer. Watching 99,999 change to 100,000 shows how each place rolls over to the next.

Download the 4th grade place value lesson as a PDF with the button below and keep it with your notes.