What you will learn
- Say the value of each digit in a number up to 9 999.
- Write a number in expanded notation, and change expanded notation back into a numeral.
- Describe the same number in different ways, such as 624 tens and 5 ones.
Every digit in a number has a job. In 7 777 all four digits are 7, but each 7 is worth a different amount. In this lesson you will find out why. You will learn to break numbers into parts and put them back together.
Place and value
The place of a digit is where it sits in the number. The value of a digit is how much it is worth in that place.
| Thousands | Hundreds | Tens | Ones |
|---|---|---|---|
| 7 | 7 | 7 | 7 |
| 7 000 | 700 | 70 | 7 |
In 7 777 the first 7 is worth 7 000. The next is worth 700, then 70, then 7. Each place is worth ten times the place to its right.
Worked example
What is the value of the digit 4 in 2 456?
Show me how
Find the place of the 4. Count from the right: ones, tens, hundreds.
The 4 is in the hundreds place.
4 hundreds = 400.
Answer: the value of the 4 is 400.
Expanded notation
Expanded notation shows a number as the sum of the values of its digits.
4 352 = 4 000 + 300 + 50 + 2
When a digit is zero, it is worth nothing, so we can leave it out: 5 060 = 5 000 + 60.
To go back to a numeral, put each part in its place. The parts can be in any order: 7 + 2 000 + 400 = 2 407.
Worked example
Write 3 000 + 40 + 5 as a numeral.
Show me how
3 000 means 3 thousands.
There is no hundreds part, so the hundreds digit is 0.
40 means 4 tens and 5 means 5 ones.
Answer: 3 045.
Watch out! A common mistake
Do not just join the digits together. 3 000 + 40 + 5 is not 345. Check each place: thousands 3, hundreds 0, tens 4, ones 5. The answer is 3 045.
One number, many ways
You can describe a number in more than one way. Look at 6 245:
6 thousands, 2 hundreds, 4 tens and 5 ones
62 hundreds and 45 ones
624 tens and 5 ones
6 245 ones
They all mean the same number! 62 hundreds is 6 thousands and 2 hundreds put together. 624 tens is all the tens in 6 245.
Worked example
How many tens are in 3 580?
Show me how
Cover the ones digit: 358 | 0.
The digits left over tell you the number of tens.
Answer: 358 tens. 358 tens = 3 580.
Try it
TRY ITPlace-value builder
Press + and − to change each column. The builder shows the expanded notation of your number.
TRY ITDigit detective
Choose a game and tap the right answer.
Let’s practise
Work out each one in your copybook. Open Hint if you are stuck, then open Show answer to check your working.
1. What is the value of the digit 8 in 3 841?
Hint
Which place is the 8 in?
Show answer
The 8 is in the hundreds place, so its value is 800.
2. Write 9 263 in expanded notation.
Hint
Write the value of each digit with + between.
Show answer
9 000 + 200 + 60 + 3
3. Write 4 000 + 500 + 7 as a numeral.
Hint
There is no tens part.
Show answer
4 507
4. Write 1 090 in expanded notation.
Hint
Leave out the zeros.
Show answer
1 000 + 90
5. Fill in the gaps: 5 372 = ____ thousands, ____ hundreds, ____ tens and ____ ones.
Hint
Read the digits from left to right.
Show answer
5 thousands, 3 hundreds, 7 tens and 2 ones.
6. How many hundreds are in 4 600?
Hint
Cover the tens and ones digits.
Show answer
46 hundreds.
7. (a) 30 + 6 000 + 2 = ____
(b) 800 + 7 000 = ____
(c) 9 + 50 + 3 000 = ____
Hint
Put the thousands first, then hundreds, tens and ones.
Show answer
(a) 6 032
(b) 7 800
(c) 3 059
8. Kiran says the 5 in 5 108 is worth 5. Is he right? Explain.
Hint
Look at the place of the 5.
Show answer
No. The 5 is in the thousands place, so it is worth 5 000.
Quiz
Lesson quiz: 10 questions
Answer every question, then press Check my answers. Score 8 or more to earn the Place Value Pro badge.
Place value and expanded notation: worksheet
Name: ____________________ Date: ______________
Part A: Let’s practise
1. What is the value of the digit 8 in 3 841?
2. Write 9 263 in expanded notation.
3. Write 4 000 + 500 + 7 as a numeral.
4. Write 1 090 in expanded notation.
5. Fill in the gaps: 5 372 = ____ thousands, ____ hundreds, ____ tens and ____ ones.
6. How many hundreds are in 4 600?
7. (a) 30 + 6 000 + 2 = ____
(b) 800 + 7 000 = ____
(c) 9 + 50 + 3 000 = ____
8. Kiran says the 5 in 5 108 is worth 5. Is he right? Explain.
Part B: Quiz
1. What is the value of the digit 6 in 4 629?
(a) 6
(b) 60
(c) 600
(d) 6 000
2. Write 2 000 + 300 + 40 + 1 as a numeral.
3. Which is 7 405 in expanded notation?
(a) 7 000 + 400 + 5
(b) 700 + 40 + 5
(c) 7 000 + 400 + 50
(d) 7 + 4 + 0 + 5
4. In 3 333, every digit has the same value.
True or False? Circle one: True / False
5. Write 5 000 + 8 as a numeral.
6. Which digit is in the tens place in 8 157?
(a) 8
(b) 1
(c) 5
(d) 7
7. 6 245 is the same as …
(a) 624 tens and 5 ones
(b) 62 tens and 45 ones
(c) 6 tens and 245 ones
(d) 624 hundreds and 5 ones
8. How many hundreds are in 3 200?
9. 600 + 4 000 + 20 = 4 620
True or False? Circle one: True / False
10. What is the value of the digit 9 in 9 014?
(a) 9
(b) 90
(c) 900
(d) 9 000
Answers (for the adult)
Part A
1. The 8 is in the hundreds place, so its value is 800.
2. 9 000 + 200 + 60 + 3
3. 4 507
4. 1 000 + 90
5. 5 thousands, 3 hundreds, 7 tens and 2 ones.
6. 46 hundreds.
7. (a) 6 032
(b) 7 800
(c) 3 059
8. No. The 5 is in the thousands place, so it is worth 5 000.
Part B
1. (c) 600
2. 2 341
3. (a) 7 000 + 400 + 5
4. False
5. 5 008
6. (c) 5
7. (a) 624 tens and 5 ones
8. 32
9. True
10. (d) 9 000
Recap
- The value of a digit depends on its place: thousands, hundreds, tens or ones.
- Expanded notation adds the values of the digits: 4 352 = 4 000 + 300 + 50 + 2.
- Zeros are left out of expanded notation, but they must be written in the numeral.
- One number can be described in many ways: 6 245 is 62 hundreds and 45 ones, or 624 tens and 5 ones.
Words to know
- place value
- The value a digit has because of its place in a number.
Example: In 2 456 the place value of 4 is hundreds. - value
- How much a digit is worth.
Example: The value of the 4 in 2 456 is 400. - expanded notation
- A way of writing a number as the sum of the values of its digits.
Example: 5 060 in expanded notation is 5 000 + 60. - base ten blocks
- Blocks that show ones, tens, hundreds and thousands.
Example: We used base ten blocks to build 1 245.
Try it at home
- Make digit cards from paper (0 to 9). Pick four cards, make a number and write it in expanded notation.
- Mini project: make a place value chart on a sheet of paper with four columns. Use beans or buttons as counters to show three different numbers, and ask an adult to read them.
Test tips
Tips for class tests
- Label the places above the digits (Th, H, T, O) before you answer.
- In expanded notation, check that each part has the right number of zeros.
- When changing expanded notation to a numeral, put a zero in any empty place.
For parents and teachers
After this lesson, your child should be able to:
- give the value of any digit in a four-digit number;
- write numbers in expanded notation and back again;
- describe a number in different ways, such as 62 hundreds and 45 ones.
Watch for children who join digits (writing 3 000 + 40 + 5 as 345). Ask them to say the value of each part aloud. A place value chart drawn on paper helps a lot.
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Previous: Numbers to 10 000: Count, Read and Write – Standard 3 Maths
Next: Compare and Order Numbers – Standard 3 Maths
Course: Standard 3 Maths
Updates
2026/11/03
– First version of this lesson.
Attributions to media used in this post:
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© 2026 Vedesh Kungebeharry. All rights reserved.
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