Place Value to 10,000
Learn to read, write and order 4-digit numbers by understanding the value of each digit's position.
What Is Place Value?
Every digit in a number has a place, and that place tells us its value. In 4-digit numbers, we have thousands, hundreds, tens and ones.
Place Value Chart for 5,382
Thousands
5
= 5,000
Hundreds
3
= 300
Tens
8
= 80
Ones
2
= 2
5,382 = 5,000 + 300 + 80 + 2
This is called expanded form.
Key Idea
A zero in any place means there are none of that value. For example, in 4,072 there are zero hundreds.
Reading and Writing Large Numbers
We use a comma to separate thousands from hundreds, making big numbers easier to read.
Australian Style
In Australia, we write 1,234 with a comma (not a space or full stop as used in some other countries).
Ordering Numbers to 10,000
To put numbers in order, compare the digits from left to right — starting with the thousands digit.
Order these numbers from smallest to largest: 4,521 4,215 4,512
Step 1: All start with 4 (thousands), so compare hundreds. 2 < 5, so 4,215 is smallest.
Step 2: Compare 4,521 and 4,512. Same thousands (4) and hundreds (5). Compare tens: 2 < 1? No — 1 < 2, so 4,512 < 4,521.
Answer: 4,215 < 4,512 < 4,521
Number line from 0 to 10,000
Partitioning Numbers
Partitioning means breaking a number into its parts. This helps us understand what each digit is worth.
6,847 partitioned:
6,000 + 800 + 40 + 7
Six thousands, eight hundreds, four tens, seven ones
2,060 partitioned:
2,000 + 0 + 60 + 0
Two thousands, zero hundreds, six tens, zero ones
Key Vocabulary
Place Value
The value a digit has because of its position in a number (e.g. the 3 in 3,400 has a value of 3,000).
Digit
Any of the single symbols 0–9 used to write numbers. The number 4,823 has four digits.
Expanded Form
Writing a number to show the value of each digit. E.g. 2,345 = 2,000 + 300 + 40 + 5.
Ordering
Arranging numbers from smallest to largest (ascending) or largest to smallest (descending).
Worked Examples
What is the value of the digit 7 in 7,483?
Step 1: Find which place the 7 is in. It is the first digit, so it is in the thousands place.
Step 2: The value of 7 in the thousands place is 7 × 1,000.
Answer: The value of 7 is 7,000.
Write 5,000 + 200 + 30 + 4 as a number.
Step 1: Place each part in its column: 5 thousands, 2 hundreds, 3 tens, 4 ones.
Answer: 5,234
Order 3,812 3,128 3,821 from largest to smallest.
Step 1: All have 3 thousands. Compare hundreds: 8, 1, 8. Two numbers have 8 hundreds.
Step 2: Compare 3,812 and 3,821. Same thousands and hundreds. Tens: 1 < 2, so 3,821 > 3,812.
Answer: 3,821 > 3,812 > 3,128
Knowledge Check
Choose the correct answer for each question and click Check Answer.
Question 1: What is the value of the digit 6 in 6,253?
Question 2: Which number equals 4,000 + 500 + 7?
Question 3: Which set of numbers is in order from smallest to largest?
Question 4: In 8,406, which digit is in the hundreds place?
Question 5: A school raises $9,450 for a fundraiser. Which number is 1,000 more than $9,450?