Lesson 1.1 · Place Value
Place value to one million
A big city might have 425,000 people living in it. To read, write and understand a number that large, you need to know what each digit is worth. That is what place value tells you.
The place value chart
In third grade you worked with ones, tens, hundreds and thousands. Now the chart keeps going. Every group of three places is called a period, and a comma separates the periods.
| Hundred thousands | Ten thousands | Thousands | , | Hundreds | Tens | Ones |
|---|---|---|---|---|---|---|
| 4 | 2 | 5 | , | 3 | 1 | 8 |
The number in the chart is 425,318. The digit 4 is in the hundred thousands place, so it is worth 400,000. The digit 2 is in the ten thousands place, so it is worth 20,000.
Definition
Value of a digit
A digit's place is where it sits in the number. Its value is how much it is worth there. In 425,318, the digit 5 is in the thousands place, and its value is 5,000.
Each place is 10 times bigger
Move one place to the left and a place is worth 10 times as much.
| Place | Worth |
|---|---|
| Ones | 1 |
| Tens | 10 |
| Hundreds | 100 |
| Thousands | 1,000 |
| Ten thousands | 10,000 |
| Hundred thousands | 100,000 |
| Millions | 1,000,000 |
Ten hundred thousands make one million, written 1,000,000. It is the first number with seven digits.
The 10 times rule
A digit in one place is worth 10 times what it would be worth in the place just to its right.
In 77,000, both digits are 7. The first 7 is worth 70,000 and the second 7 is worth 7,000. And .
Worked example: Finding the value of a digit
What is the value of the 6 in 368,012?
Count places from the right: ones (2), tens (1), hundreds (0), thousands (8), ten thousands (6). The 6 is in the ten thousands place, so its value is 60,000.
Three ways to write a number
You can write the same number in three forms.
- Standard form uses digits: 507,293
- Word form uses words: five hundred seven thousand, two hundred ninety-three
- Expanded form adds up the value of each digit:
In word form, read the first period, say "thousand" where the comma is, then read the last period.
Worked example: Word form to standard form
Write "sixty thousand, four hundred nine" in standard form.
The thousands period is sixty, so write 60 and a comma. The last period is four hundred nine, which is 409.
The answer is 60,409. Notice the zeros: there are no thousands and no tens.
Worked example: Expanded form with zeros
Write 803,050 in expanded form.
Go digit by digit: 8 hundred thousands, 0 ten thousands, 3 thousands, 0 hundreds, 5 tens, 0 ones.
Skip the zeros: .
Common mistake
Don't forget the zeros when you write a number in standard form. "Four hundred thousand, twenty" is 400,020, not 40,020 or 420. The thousands period needs three digits (400) and so does the last period (020).
Tip
To check your standard form, count the digits after the comma. There should always be exactly three.
Practice
What is the value of the digit 8 in 482,315?
Type a number.
Which digit is in the ten thousands place in 736,294?
Type a number.
Write in standard form: .
Type a number.
Write in standard form: two hundred six thousand, fifty-one.
Type a number.
Which shows 70,408 in expanded form?
In the number 55,000, the value of the first 5 is how many times the value of the second 5?
Type a number.
How many hundred thousands make one million?
Type a number.
Write the number that has 6 hundred thousands, 4 thousands, 9 hundreds, 2 ones, and zeros in every other place.
Type a number.