Year 5 Maths: Convert between standard and expanded form

Introduction to Standard and Expanded Form

Today, we are going to learn about two different ways to write numbers: standard form and expanded form. This might sound a bit tricky, but don’t worry! We will take it step by step.

What is Standard Form?

Standard form is the way we normally write numbers. For example:

• The number 2,340 is in standard form.

What is Expanded Form?

Expanded form is another way to show numbers, breaking them down into parts. It shows the value of each digit. For example:

• The number 2,340 in expanded form would be written as 2,000 + 300 + 40.

Key Rules for Converting Between Forms

1. Identify Each Digit: Look at the number and identify each digit’s place value.
2. Write in Expanded Form: Take each digit and multiply it by its place value (like thousands, hundreds, tens, and units).
3. Combine the Parts: In expanded form, you add these parts together.

Examples

Example 1: Converting from Standard to Expanded Form

Let’s take the number 5,672.

• The digit 5 is in the thousands place: 5,000
• The digit 6 is in the hundreds place: 600
• The digit 7 is in the tens place: 70
• The digit 2 is in the units place: 2

So, in expanded form, 5,672 is written as:

5,000 + 600 + 70 + 2.

Example 2: Converting from Expanded to Standard Form

Now let’s convert 3,000 + 400 + 50 + 8 back to standard form.

• We add these parts together:
  • 3,000 + 400 = 3,400
  • 3,400 + 50 = 3,450
  • 3,450 + 8 = 3,458

So, in standard form, 3,000 + 400 + 50 + 8 is written as 3,458.

Tips and Tricks

• Always start from the largest place value when writing expanded form.
• Practice breaking numbers down into their parts until it feels easy.
• Use place value charts to help you see where each digit goes.

Questions to Practice

Easy Level Questions

1. Write 1,234 in expanded form.
2. Write 2,000 + 500 + 30 + 4 in standard form.
3. Write 4,567 in expanded form.
4. Write 3,100 + 20 + 7 in standard form.
5. Write 6,890 in expanded form.
6. Write 5,000 + 600 + 90 + 2 in standard form.
7. Write 2,345 in expanded form.
8. Write 1,000 + 300 + 40 in standard form.
9. Write 9,876 in expanded form.
10. Write 8,500 + 400 + 10 + 3 in standard form.

Medium Level Questions

11. Write 7,654 in expanded form.
12. Write 5,000 + 600 + 50 + 7 in standard form.
13. Write 4,321 in expanded form.
14. Write 3,200 + 70 + 5 in standard form.
15. Write 6,783 in expanded form.
16. Write 2,000 + 900 + 80 + 1 in standard form.
17. Write 5,432 in expanded form.
18. Write 1,000 + 600 + 90 + 4 in standard form.
19. Write 3,456 in expanded form.
20. Write 2,500 + 300 + 20 + 3 in standard form.

Hard Level Questions

21. Write 9,231 in expanded form.
22. Write 7,000 + 400 + 60 + 5 in standard form.
23. Write 8,765 in expanded form.
24. Write 5,000 + 800 + 90 + 9 in standard form.
25. Write 6,543 in expanded form.
26. Write 4,000 + 300 + 10 + 2 in standard form.
27. Write 3,745 in expanded form.
28. Write 2,000 + 800 + 50 + 6 in standard form.
29. Write 1,234 in expanded form.
30. Write 9,999 in expanded form.

Answers and Explanations

Easy Level Answers

1. 1,234 = 1,000 + 200 + 30 + 4
2. 2,000 + 500 + 30 + 4 = 2,534
3. 4,567 = 4,000 + 500 + 60 + 7
4. 3,100 + 20 + 7 = 3,127
5. 6,890 = 6,000 + 800 + 90
6. 5,000 + 600 + 90 + 2 = 5,692
7. 2,345 = 2,000 + 300 + 40 + 5
8. 1,000 + 300 + 40 = 1,340
9. 9,876 = 9,000 + 800 + 70 + 6
10. 8,500 + 400 + 10 + 3 = 8,913

Medium Level Answers

11. 7,654 = 7,000 + 600 + 50 + 4
12. 5,000 + 600 + 50 + 7 = 5,657
13. 4,321 = 4,000 + 300 + 20 + 1
14. 3,200 + 70 + 5 = 3,275
15. 6,783 = 6,000 + 700 + 80 + 3
16. 2,000 + 900 + 80 + 1 = 2,981
17. 5,432 = 5,000 + 400 + 30 + 2
18. 1,000 + 600 + 90 + 4 = 1,694
19. 3,456 = 3,000 + 400 + 50 + 6
20. 2,500 + 300 + 20 + 3 = 2,823

Hard Level Answers

21. 9,231 = 9,000 + 200 + 30 + 1
22. 7,000 + 400 + 60 + 5 = 7,465
23. 8,765 = 8,000 + 700 + 60 + 5
24. 5,000 + 800 + 90 + 9 = 5,899
25. 6,543 = 6,000 + 500 + 40 + 3
26. 4,000 + 300 + 10 + 2 = 4,312
27. 3,745 = 3,000 + 700 + 40 + 5
28. 2,000 + 800 + 50 + 6 = 2,856
29. 1,234 = 1,000 + 200 + 30 + 4
30. 9,999 = 9,000 + 900 + 90 + 9

Now, give these questions a go! Remember to take your time, and have fun with numbers!