Math worksheet for converting large numbers into expanded form.
Worksheet for writing numbers in expanded form with 15 large numbers to convert, featuring spaces for name, teacher, score, and date at the top.
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Show Answer Key & Explanations
Step-by-step solution for: Place Value Worksheets | Place Value Worksheets for Practice
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Show Answer Key & Explanations
Step-by-step solution for: Place Value Worksheets | Place Value Worksheets for Practice
Let’s solve each problem step by step.
We are asked to write numbers in expanded form. That means breaking the number down into the value of each digit based on its place — like hundreds, thousands, millions, etc.
For example:
The number 123 in expanded form is:
100 + 20 + 3
But our numbers are much bigger — up to billions! So we’ll break them down by groups: billions, millions, thousands, and ones.
Each group has 3 digits:
- Billions: hundred billions, ten billions, billions
- Millions: hundred millions, ten millions, millions
- Thousands: hundred thousands, ten thousands, thousands
- Ones: hundreds, tens, ones
We’ll go one by one.
---
1) 456,441,814,221
Break it down:
- 400,000,000,000 (hundred billions)
- 50,000,000,000 (ten billions)
- 6,000,000,000 (billions)
- 400,000,000 (hundred millions)
- 40,000,000 (ten millions)
- 1,000,000 (millions)
- 800,000 (hundred thousands)
- 10,000 (ten thousands)
- 4,000 (thousands)
- 200 (hundreds)
- 20 (tens)
- 1 (ones)
So expanded form:
400,000,000,000 + 50,000,000,000 + 6,000,000,000 + 400,000,000 + 40,000,000 + 1,000,000 + 800,000 + 10,000 + 4,000 + 200 + 20 + 1
---
2) 865,683,897,167
Breakdown:
- 800,000,000,000
- 60,000,000,000
- 5,000,000,000
- 600,000,000
- 80,000,000
- 3,000,000
- 800,000
- 90,000
- 7,000
- 100
- 60
- 7
Expanded:
800,000,000,000 + 60,000,000,000 + 5,000,000,000 + 600,000,000 + 80,000,000 + 3,000,000 + 800,000 + 90,000 + 7,000 + 100 + 60 + 7
---
3) 255,954,346,845
Breakdown:
- 200,000,000,000
- 50,000,000,000
- 5,000,000,000
- 900,000,000
- 50,000,000
- 4,000,000
- 300,000
- 40,000
- 6,000
- 800
- 40
- 5
Expanded:
200,000,000,000 + 50,000,000,000 + 5,000,000,000 + 900,000,000 + 50,000,000 + 4,000,000 + 300,000 + 40,000 + 6,000 + 800 + 40 + 5
---
4) 861,588,634,662
Breakdown:
- 800,000,000,000
- 60,000,000,000
- 1,000,000,000
- 500,000,000
- 80,000,000
- 8,000,000
- 600,000
- 30,000
- 4,000
- 600
- 60
- 2
Expanded:
800,000,000,000 + 60,000,000,000 + 1,000,000,000 + 500,000,000 + 80,000,000 + 8,000,000 + 600,000 + 30,000 + 4,000 + 600 + 60 + 2
---
5) 144,673,746,771
Breakdown:
- 100,000,000,000
- 40,000,000,000
- 4,000,000,000
- 600,000,000
- 70,000,000
- 3,000,000
- 700,000
- 40,000
- 6,000
- 700
- 70
- 1
Expanded:
100,000,000,000 + 40,000,000,000 + 4,000,000,000 + 600,000,000 + 70,000,000 + 3,000,000 + 700,000 + 40,000 + 6,000 + 700 + 70 + 1
---
6) 962,335,344,754
Breakdown:
- 900,000,000,000
- 60,000,000,000
- 2,000,000,000
- 300,000,000
- 30,000,000
- 5,000,000
- 300,000
- 40,000
- 4,000
- 700
- 50
- 4
Expanded:
900,000,000,000 + 60,000,000,000 + 2,000,000,000 + 300,000,000 + 30,000,000 + 5,000,000 + 300,000 + 40,000 + 4,000 + 700 + 50 + 4
---
7) 569,335,118,738
Breakdown:
- 500,000,000,000
- 60,000,000,000
- 9,000,000,000
- 300,000,000
- 30,000,000
- 5,000,000
- 100,000
- 10,000
- 8,000
- 700
- 30
- 8
Expanded:
500,000,000,000 + 60,000,000,000 + 9,000,000,000 + 300,000,000 + 30,000,000 + 5,000,000 + 100,000 + 10,000 + 8,000 + 700 + 30 + 8
---
8) 864,895,242,758
Breakdown:
- 800,000,000,000
- 60,000,000,000
- 4,000,000,000
- 800,000,000
- 90,000,000
- 5,000,000
- 200,000
- 40,000
- 2,000
- 700
- 50
- 8
Expanded:
800,000,000,000 + 60,000,000,000 + 4,000,000,000 + 800,000,000 + 90,000,000 + 5,000,000 + 200,000 + 40,000 + 2,000 + 700 + 50 + 8
---
9) 427,185,896,886
Breakdown:
- 400,000,000,000
- 20,000,000,000
- 7,000,000,000
- 100,000,000
- 80,000,000
- 5,000,000
- 800,000
- 90,000
- 6,000
- 800
- 80
- 6
Expanded:
400,000,000,000 + 20,000,000,000 + 7,000,000,000 + 100,000,000 + 80,000,000 + 5,000,000 + 800,000 + 90,000 + 6,000 + 800 + 80 + 6
---
10) 252,785,931,492
Breakdown:
- 200,000,000,000
- 50,000,000,000
- 2,000,000,000
- 700,000,000
- 80,000,000
- 5,000,000
- 900,000
- 30,000
- 1,000
- 400
- 90
- 2
Expanded:
200,000,000,000 + 50,000,000,000 + 2,000,000,000 + 700,000,000 + 80,000,000 + 5,000,000 + 900,000 + 30,000 + 1,000 + 400 + 90 + 2
---
11) 346,788,814,557
Breakdown:
- 300,000,000,000
- 40,000,000,000
- 6,000,000,000
- 700,000,000
- 80,000,000
- 8,000,000
- 800,000
- 10,000
- 4,000
- 500
- 50
- 7
Expanded:
300,000,000,000 + 40,000,000,000 + 6,000,000,000 + 700,000,000 + 80,000,000 + 8,000,000 + 800,000 + 10,000 + 4,000 + 500 + 50 + 7
---
12) 793,981,513,350
Breakdown:
- 700,000,000,000
- 90,000,000,000
- 3,000,000,000
- 900,000,000
- 80,000,000
- 1,000,000
- 500,000
- 10,000
- 3,000
- 300
- 50
- 0 → skip last zero? But since it's part of the number, we can include “+ 0” or just stop at 50. Usually we don’t add +0 unless specified. Let’s check: the number ends with 350 → so 300 + 50 + 0. But in expanded form, we usually omit adding zero if it doesn't change value. However, for completeness, let’s include all places.
Actually, standard practice is to only write non-zero parts. Since the ones digit is 0, we don’t need to write "+ 0".
So:
- 700,000,000,000
- 90,000,000,000
- 3,000,000,000
- 900,000,000
- 80,000,000
- 1,000,000
- 500,000
- 10,000
- 3,000
- 300
- 50
Expanded:
700,000,000,000 + 90,000,000,000 + 3,000,000,000 + 900,000,000 + 80,000,000 + 1,000,000 + 500,000 + 10,000 + 3,000 + 300 + 50
---
13) 682,611,642,112
Breakdown:
- 600,000,000,000
- 80,000,000,000
- 2,000,000,000
- 600,000,000
- 10,000,000
- 1,000,000
- 600,000
- 40,000
- 2,000
- 100
- 10
- 2
Expanded:
600,000,000,000 + 80,000,000,000 + 2,000,000,000 + 600,000,000 + 10,000,000 + 1,000,000 + 600,000 + 40,000 + 2,000 + 100 + 10 + 2
---
14) 845,837,252,340
Breakdown:
- 800,000,000,000
- 40,000,000,000
- 5,000,000,000
- 800,000,000
- 30,000,000
- 7,000,000
- 200,000
- 50,000
- 2,000
- 300
- 40
- 0 → again, skip +0
Expanded:
800,000,000,000 + 40,000,000,000 + 5,000,000,000 + 800,000,000 + 30,000,000 + 7,000,000 + 200,000 + 50,000 + 2,000 + 300 + 40
---
15) 872,511,487,675
Breakdown:
- 800,000,000,000
- 70,000,000,000
- 2,000,000,000
- 500,000,000
- 10,000,000
- 1,000,000
- 400,000
- 80,000
- 7,000
- 600
- 70
- 5
Expanded:
800,000,000,000 + 70,000,000,000 + 2,000,000,000 + 500,000,000 + 10,000,000 + 1,000,000 + 400,000 + 80,000 + 7,000 + 600 + 70 + 5
---
Now, here are all the final answers written clearly:
Final Answer:
1) 400,000,000,000 + 50,000,000,000 + 6,000,000,000 + 400,000,000 + 40,000,000 + 1,000,000 + 800,000 + 10,000 + 4,000 + 200 + 20 + 1
2) 800,000,000,000 + 60,000,000,000 + 5,000,000,000 + 600,000,000 + 80,000,000 + 3,000,000 + 800,000 + 90,000 + 7,000 + 100 + 60 + 7
3) 200,000,000,000 + 50,000,000,000 + 5,000,000,000 + 900,000,000 + 50,000,000 + 4,000,000 + 300,000 + 40,000 + 6,000 + 800 + 40 + 5
4) 800,000,000,000 + 60,000,000,000 + 1,000,000,000 + 500,000,000 + 80,000,000 + 8,000,000 + 600,000 + 30,000 + 4,000 + 600 + 60 + 2
5) 100,000,000,000 + 40,000,000,000 + 4,000,000,000 + 600,000,000 + 70,000,000 + 3,000,000 + 700,000 + 40,000 + 6,000 + 700 + 70 + 1
6) 900,000,000,000 + 60,000,000,000 + 2,000,000,000 + 300,000,000 + 30,000,000 + 5,000,000 + 300,000 + 40,000 + 4,000 + 700 + 50 + 4
7) 500,000,000,000 + 60,000,000,000 + 9,000,000,000 + 300,000,000 + 30,000,000 + 5,000,000 + 100,000 + 10,000 + 8,000 + 700 + 30 + 8
8) 800,000,000,000 + 60,000,000,000 + 4,000,000,000 + 800,000,000 + 90,000,000 + 5,000,000 + 200,000 + 40,000 + 2,000 + 700 + 50 + 8
9) 400,000,000,000 + 20,000,000,000 + 7,000,000,000 + 100,000,000 + 80,000,000 + 5,000,000 + 800,000 + 90,000 + 6,000 + 800 + 80 + 6
10) 200,000,000,000 + 50,000,000,000 + 2,000,000,000 + 700,000,000 + 80,000,000 + 5,000,000 + 900,000 + 30,000 + 1,000 + 400 + 90 + 2
11) 300,000,000,000 + 40,000,000,000 + 6,000,000,000 + 700,000,000 + 80,000,000 + 8,000,000 + 800,000 + 10,000 + 4,000 + 500 + 50 + 7
12) 700,000,000,000 + 90,000,000,000 + 3,000,000,000 + 900,000,000 + 80,000,000 + 1,000,000 + 500,000 + 10,000 + 3,000 + 300 + 50
13) 600,000,000,000 + 80,000,000,000 + 2,000,000,000 + 600,000,000 + 10,000,000 + 1,000,000 + 600,000 + 40,000 + 2,000 + 100 + 10 + 2
14) 800,000,000,000 + 40,000,000,000 + 5,000,000,000 + 800,000,000 + 30,000,000 + 7,000,000 + 200,000 + 50,000 + 2,000 + 300 + 40
15) 800,000,000,000 + 70,000,000,000 + 2,000,000,000 + 500,000,000 + 10,000,000 + 1,000,000 + 400,000 + 80,000 + 7,000 + 600 + 70 + 5
We are asked to write numbers in expanded form. That means breaking the number down into the value of each digit based on its place — like hundreds, thousands, millions, etc.
For example:
The number 123 in expanded form is:
100 + 20 + 3
But our numbers are much bigger — up to billions! So we’ll break them down by groups: billions, millions, thousands, and ones.
Each group has 3 digits:
- Billions: hundred billions, ten billions, billions
- Millions: hundred millions, ten millions, millions
- Thousands: hundred thousands, ten thousands, thousands
- Ones: hundreds, tens, ones
We’ll go one by one.
---
1) 456,441,814,221
Break it down:
- 400,000,000,000 (hundred billions)
- 50,000,000,000 (ten billions)
- 6,000,000,000 (billions)
- 400,000,000 (hundred millions)
- 40,000,000 (ten millions)
- 1,000,000 (millions)
- 800,000 (hundred thousands)
- 10,000 (ten thousands)
- 4,000 (thousands)
- 200 (hundreds)
- 20 (tens)
- 1 (ones)
So expanded form:
400,000,000,000 + 50,000,000,000 + 6,000,000,000 + 400,000,000 + 40,000,000 + 1,000,000 + 800,000 + 10,000 + 4,000 + 200 + 20 + 1
---
2) 865,683,897,167
Breakdown:
- 800,000,000,000
- 60,000,000,000
- 5,000,000,000
- 600,000,000
- 80,000,000
- 3,000,000
- 800,000
- 90,000
- 7,000
- 100
- 60
- 7
Expanded:
800,000,000,000 + 60,000,000,000 + 5,000,000,000 + 600,000,000 + 80,000,000 + 3,000,000 + 800,000 + 90,000 + 7,000 + 100 + 60 + 7
---
3) 255,954,346,845
Breakdown:
- 200,000,000,000
- 50,000,000,000
- 5,000,000,000
- 900,000,000
- 50,000,000
- 4,000,000
- 300,000
- 40,000
- 6,000
- 800
- 40
- 5
Expanded:
200,000,000,000 + 50,000,000,000 + 5,000,000,000 + 900,000,000 + 50,000,000 + 4,000,000 + 300,000 + 40,000 + 6,000 + 800 + 40 + 5
---
4) 861,588,634,662
Breakdown:
- 800,000,000,000
- 60,000,000,000
- 1,000,000,000
- 500,000,000
- 80,000,000
- 8,000,000
- 600,000
- 30,000
- 4,000
- 600
- 60
- 2
Expanded:
800,000,000,000 + 60,000,000,000 + 1,000,000,000 + 500,000,000 + 80,000,000 + 8,000,000 + 600,000 + 30,000 + 4,000 + 600 + 60 + 2
---
5) 144,673,746,771
Breakdown:
- 100,000,000,000
- 40,000,000,000
- 4,000,000,000
- 600,000,000
- 70,000,000
- 3,000,000
- 700,000
- 40,000
- 6,000
- 700
- 70
- 1
Expanded:
100,000,000,000 + 40,000,000,000 + 4,000,000,000 + 600,000,000 + 70,000,000 + 3,000,000 + 700,000 + 40,000 + 6,000 + 700 + 70 + 1
---
6) 962,335,344,754
Breakdown:
- 900,000,000,000
- 60,000,000,000
- 2,000,000,000
- 300,000,000
- 30,000,000
- 5,000,000
- 300,000
- 40,000
- 4,000
- 700
- 50
- 4
Expanded:
900,000,000,000 + 60,000,000,000 + 2,000,000,000 + 300,000,000 + 30,000,000 + 5,000,000 + 300,000 + 40,000 + 4,000 + 700 + 50 + 4
---
7) 569,335,118,738
Breakdown:
- 500,000,000,000
- 60,000,000,000
- 9,000,000,000
- 300,000,000
- 30,000,000
- 5,000,000
- 100,000
- 10,000
- 8,000
- 700
- 30
- 8
Expanded:
500,000,000,000 + 60,000,000,000 + 9,000,000,000 + 300,000,000 + 30,000,000 + 5,000,000 + 100,000 + 10,000 + 8,000 + 700 + 30 + 8
---
8) 864,895,242,758
Breakdown:
- 800,000,000,000
- 60,000,000,000
- 4,000,000,000
- 800,000,000
- 90,000,000
- 5,000,000
- 200,000
- 40,000
- 2,000
- 700
- 50
- 8
Expanded:
800,000,000,000 + 60,000,000,000 + 4,000,000,000 + 800,000,000 + 90,000,000 + 5,000,000 + 200,000 + 40,000 + 2,000 + 700 + 50 + 8
---
9) 427,185,896,886
Breakdown:
- 400,000,000,000
- 20,000,000,000
- 7,000,000,000
- 100,000,000
- 80,000,000
- 5,000,000
- 800,000
- 90,000
- 6,000
- 800
- 80
- 6
Expanded:
400,000,000,000 + 20,000,000,000 + 7,000,000,000 + 100,000,000 + 80,000,000 + 5,000,000 + 800,000 + 90,000 + 6,000 + 800 + 80 + 6
---
10) 252,785,931,492
Breakdown:
- 200,000,000,000
- 50,000,000,000
- 2,000,000,000
- 700,000,000
- 80,000,000
- 5,000,000
- 900,000
- 30,000
- 1,000
- 400
- 90
- 2
Expanded:
200,000,000,000 + 50,000,000,000 + 2,000,000,000 + 700,000,000 + 80,000,000 + 5,000,000 + 900,000 + 30,000 + 1,000 + 400 + 90 + 2
---
11) 346,788,814,557
Breakdown:
- 300,000,000,000
- 40,000,000,000
- 6,000,000,000
- 700,000,000
- 80,000,000
- 8,000,000
- 800,000
- 10,000
- 4,000
- 500
- 50
- 7
Expanded:
300,000,000,000 + 40,000,000,000 + 6,000,000,000 + 700,000,000 + 80,000,000 + 8,000,000 + 800,000 + 10,000 + 4,000 + 500 + 50 + 7
---
12) 793,981,513,350
Breakdown:
- 700,000,000,000
- 90,000,000,000
- 3,000,000,000
- 900,000,000
- 80,000,000
- 1,000,000
- 500,000
- 10,000
- 3,000
- 300
- 50
- 0 → skip last zero? But since it's part of the number, we can include “+ 0” or just stop at 50. Usually we don’t add +0 unless specified. Let’s check: the number ends with 350 → so 300 + 50 + 0. But in expanded form, we usually omit adding zero if it doesn't change value. However, for completeness, let’s include all places.
Actually, standard practice is to only write non-zero parts. Since the ones digit is 0, we don’t need to write "+ 0".
So:
- 700,000,000,000
- 90,000,000,000
- 3,000,000,000
- 900,000,000
- 80,000,000
- 1,000,000
- 500,000
- 10,000
- 3,000
- 300
- 50
Expanded:
700,000,000,000 + 90,000,000,000 + 3,000,000,000 + 900,000,000 + 80,000,000 + 1,000,000 + 500,000 + 10,000 + 3,000 + 300 + 50
---
13) 682,611,642,112
Breakdown:
- 600,000,000,000
- 80,000,000,000
- 2,000,000,000
- 600,000,000
- 10,000,000
- 1,000,000
- 600,000
- 40,000
- 2,000
- 100
- 10
- 2
Expanded:
600,000,000,000 + 80,000,000,000 + 2,000,000,000 + 600,000,000 + 10,000,000 + 1,000,000 + 600,000 + 40,000 + 2,000 + 100 + 10 + 2
---
14) 845,837,252,340
Breakdown:
- 800,000,000,000
- 40,000,000,000
- 5,000,000,000
- 800,000,000
- 30,000,000
- 7,000,000
- 200,000
- 50,000
- 2,000
- 300
- 40
- 0 → again, skip +0
Expanded:
800,000,000,000 + 40,000,000,000 + 5,000,000,000 + 800,000,000 + 30,000,000 + 7,000,000 + 200,000 + 50,000 + 2,000 + 300 + 40
---
15) 872,511,487,675
Breakdown:
- 800,000,000,000
- 70,000,000,000
- 2,000,000,000
- 500,000,000
- 10,000,000
- 1,000,000
- 400,000
- 80,000
- 7,000
- 600
- 70
- 5
Expanded:
800,000,000,000 + 70,000,000,000 + 2,000,000,000 + 500,000,000 + 10,000,000 + 1,000,000 + 400,000 + 80,000 + 7,000 + 600 + 70 + 5
---
Now, here are all the final answers written clearly:
Final Answer:
1) 400,000,000,000 + 50,000,000,000 + 6,000,000,000 + 400,000,000 + 40,000,000 + 1,000,000 + 800,000 + 10,000 + 4,000 + 200 + 20 + 1
2) 800,000,000,000 + 60,000,000,000 + 5,000,000,000 + 600,000,000 + 80,000,000 + 3,000,000 + 800,000 + 90,000 + 7,000 + 100 + 60 + 7
3) 200,000,000,000 + 50,000,000,000 + 5,000,000,000 + 900,000,000 + 50,000,000 + 4,000,000 + 300,000 + 40,000 + 6,000 + 800 + 40 + 5
4) 800,000,000,000 + 60,000,000,000 + 1,000,000,000 + 500,000,000 + 80,000,000 + 8,000,000 + 600,000 + 30,000 + 4,000 + 600 + 60 + 2
5) 100,000,000,000 + 40,000,000,000 + 4,000,000,000 + 600,000,000 + 70,000,000 + 3,000,000 + 700,000 + 40,000 + 6,000 + 700 + 70 + 1
6) 900,000,000,000 + 60,000,000,000 + 2,000,000,000 + 300,000,000 + 30,000,000 + 5,000,000 + 300,000 + 40,000 + 4,000 + 700 + 50 + 4
7) 500,000,000,000 + 60,000,000,000 + 9,000,000,000 + 300,000,000 + 30,000,000 + 5,000,000 + 100,000 + 10,000 + 8,000 + 700 + 30 + 8
8) 800,000,000,000 + 60,000,000,000 + 4,000,000,000 + 800,000,000 + 90,000,000 + 5,000,000 + 200,000 + 40,000 + 2,000 + 700 + 50 + 8
9) 400,000,000,000 + 20,000,000,000 + 7,000,000,000 + 100,000,000 + 80,000,000 + 5,000,000 + 800,000 + 90,000 + 6,000 + 800 + 80 + 6
10) 200,000,000,000 + 50,000,000,000 + 2,000,000,000 + 700,000,000 + 80,000,000 + 5,000,000 + 900,000 + 30,000 + 1,000 + 400 + 90 + 2
11) 300,000,000,000 + 40,000,000,000 + 6,000,000,000 + 700,000,000 + 80,000,000 + 8,000,000 + 800,000 + 10,000 + 4,000 + 500 + 50 + 7
12) 700,000,000,000 + 90,000,000,000 + 3,000,000,000 + 900,000,000 + 80,000,000 + 1,000,000 + 500,000 + 10,000 + 3,000 + 300 + 50
13) 600,000,000,000 + 80,000,000,000 + 2,000,000,000 + 600,000,000 + 10,000,000 + 1,000,000 + 600,000 + 40,000 + 2,000 + 100 + 10 + 2
14) 800,000,000,000 + 40,000,000,000 + 5,000,000,000 + 800,000,000 + 30,000,000 + 7,000,000 + 200,000 + 50,000 + 2,000 + 300 + 40
15) 800,000,000,000 + 70,000,000,000 + 2,000,000,000 + 500,000,000 + 10,000,000 + 1,000,000 + 400,000 + 80,000 + 7,000 + 600 + 70 + 5
Parent Tip: Review the logic above to help your child master the concept of expanded notation worksheet grade 3.
