Place Value to Millions
Learn to read, write, compare and order whole numbers up to millions. Understand the value of each digit in large numbers.
Understanding Place Value
Every digit in a number has a place value based on its position. As we move to the left, each place is ten times larger than the one before it. In Year 6, we work with numbers into the millions.
| Millions | Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|---|---|
| 3 | 4 | 5 | 2 | 1 | 6 | 8 |
| 3 000 000 | 400 000 | 50 000 | 2 000 | 100 | 60 | 8 |
The number above is 3 452 168 (three million, four hundred and fifty-two thousand, one hundred and sixty-eight).
Reading and Writing Large Numbers
When reading or writing large numbers, we group digits in threes from the right. In Australia, we separate groups with a space (not a comma). This makes big numbers much easier to read.
Writing Tips
- 1 250 000 — one million, two hundred and fifty thousand
- 405 072 — four hundred and five thousand and seventy-two
- 7 000 300 — seven million and three hundred
Watch Out!
- A zero in a place means that place has no value, but we still write it.
- 3 040 000 has zero hundred-thousands and zero ones.
Comparing and Ordering Large Numbers
To compare large numbers, start from the leftmost digit (the highest place value) and compare digit by digit. Use the symbols < (less than), > (greater than), and = (equal to).
Example: Compare 2 456 300 and 2 461 000
Step 1: Both start with 2 (millions) — same so far.
Step 2: Both have 4 (hundred thousands) — still the same.
Step 3: Compare ten thousands: 5 vs 6. Since 5 < 6...
Answer: 2 456 300 < 2 461 000
Real-World Example
Australia's population is about 27 000 000 and New Zealand's is about 5 200 000. Which country has more people?
Compare the millions: 27 > 5, so 27 000 000 > 5 200 000. Australia has more people.
Expanded Notation
Expanded notation shows the value of each digit in a number. It helps us understand exactly what each digit is worth.
Example: Expand 5 207 430
5 207 430 =
5 000 000 + 200 000 + 7 000 + 400 + 30
Notice there are no ten-thousands and no ones — those digits are 0.
Key Vocabulary
Place Value
The value of a digit based on its position in a number (e.g. the 5 in 5 000 000 is worth five million).
Expanded Notation
Writing a number as the sum of each digit's value (e.g. 3 200 = 3 000 + 200).
Ascending
Ordering numbers from smallest to largest.
Descending
Ordering numbers from largest to smallest.
Worked Examples
What is the value of the digit 6 in 1 603 200?
Step 1: Identify the position: 6 is in the hundred-thousands place.
Answer: The 6 is worth 600 000 (six hundred thousand).
Write four million, thirty-five thousand and twelve in digits.
Step 1: Four million = 4 000 000
Step 2: Thirty-five thousand = 35 000
Step 3: Twelve = 12
Answer: 4 035 012
Order these from smallest to largest: 3 200 100, 3 020 100, 3 200 010
Step 1: All start with 3 million. Compare hundred-thousands: 0, 2, 2.
Step 2: 3 020 100 is smallest (0 hundred-thousands).
Step 3: For the other two, compare hundreds: 100 vs 010. 010 < 100.
Answer: 3 020 100, 3 200 010, 3 200 100
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What is the value of the digit 7 in 2 700 451?
Question 2
How do you write "six million, four hundred and eight thousand" in digits?
Question 3
Which symbol makes this true? 4 520 300 ___ 4 502 300
Question 4
What is 2 350 000 in expanded notation?
Question 5
Which of these is the largest number?
Key Concepts Summary
- ●Each digit in a number has a place value that is 10 times greater than the place to its right.
- ●In Australia, we use spaces (not commas) to separate groups of three digits.
- ●To compare numbers, work from the leftmost digit to the right.
- ●Expanded notation shows what each digit is worth in a number.
- ●A number with more digits is always larger than one with fewer digits.