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Answer :
Certainly! Let's compare each pair of numbers step-by-step using their expanded forms:
### a) Comparing:
1. Expanded Form 1: [tex]\(60 + 3000 + 500000 + 400\)[/tex]
- Add these numbers: [tex]\(60 + 3000 = 3060\)[/tex]
- [tex]\(3060 + 500000 = 503060\)[/tex]
- [tex]\(503060 + 400 = 503460\)[/tex]
2. Expanded Form 2: [tex]\(30000 + 400 + 600000 + 60\)[/tex]
- Add these numbers: [tex]\(30000 + 400 = 30400\)[/tex]
- [tex]\(30400 + 600000 = 630400\)[/tex]
- [tex]\(630400 + 60 = 630460\)[/tex]
3. Comparison:
- 503460 is less than 630460, so we have [tex]\(503460 < 630460\)[/tex].
- The symbol is [tex]\(<\)[/tex].
### b) Comparing:
1. Expanded Form 1: [tex]\(9 + 800000 + 40000\)[/tex]
- Add these numbers: [tex]\(9 + 40000 = 40009\)[/tex]
- [tex]\(40009 + 800000 = 840009\)[/tex]
2. Expanded Form 2: [tex]\(400000 + 90000 + 80\)[/tex]
- Add these numbers: [tex]\(400000 + 90000 = 490000\)[/tex]
- [tex]\(490000 + 80 = 490080\)[/tex]
3. Comparison:
- 840009 is greater than 490080, so we have [tex]\(840009 > 490080\)[/tex].
- The symbol is [tex]\(>\)[/tex].
### c) Comparing:
1. Expanded Form 1: [tex]\(50 + 400000 + 20000\)[/tex]
- Add these numbers: [tex]\(50 + 20000 = 20050\)[/tex]
- [tex]\(20050 + 400000 = 420050\)[/tex]
2. Expanded Form 2: [tex]\(400000 + 500 + 2000\)[/tex]
- Add these numbers: [tex]\(500 + 2000 = 2500\)[/tex]
- [tex]\(2500 + 400000 = 402500\)[/tex]
3. Comparison:
- 420050 is greater than 402500, so we have [tex]\(420050 > 402500\)[/tex].
- The symbol is [tex]\(>\)[/tex].
### d) Comparing:
1. Expanded Form 1: [tex]\(500 + 6000 + 30 + 400000 + 1 + 20000\)[/tex]
- Let's break it down:
- Start with: [tex]\(500 + 6000 = 6500\)[/tex]
- [tex]\(6500 + 30 = 6530\)[/tex]
- [tex]\(6530 + 1 = 6531\)[/tex]
- [tex]\(6531 + 20000 = 26531\)[/tex]
- Finally, [tex]\(26531 + 400000 = 426531\)[/tex]
2. Expanded Form 2: [tex]\(400000 + 500 + 20 + 6000 + 20000 + 1\)[/tex]
- Let's break it down:
- Start with: [tex]\(500 + 20 = 520\)[/tex]
- [tex]\(520 + 6000 = 6520\)[/tex]
- [tex]\(6520 + 1 = 6521\)[/tex]
- [tex]\(6521 + 20000 = 26521\)[/tex]
- Finally, [tex]\(26521 + 400000 = 426521\)[/tex]
3. Comparison:
- 426531 is greater than 426521, so we have [tex]\(426531 > 426521\)[/tex].
- The symbol is [tex]\(>\)[/tex].
By comparing each pair of expanded forms, we have determined the symbols for each comparison.
### a) Comparing:
1. Expanded Form 1: [tex]\(60 + 3000 + 500000 + 400\)[/tex]
- Add these numbers: [tex]\(60 + 3000 = 3060\)[/tex]
- [tex]\(3060 + 500000 = 503060\)[/tex]
- [tex]\(503060 + 400 = 503460\)[/tex]
2. Expanded Form 2: [tex]\(30000 + 400 + 600000 + 60\)[/tex]
- Add these numbers: [tex]\(30000 + 400 = 30400\)[/tex]
- [tex]\(30400 + 600000 = 630400\)[/tex]
- [tex]\(630400 + 60 = 630460\)[/tex]
3. Comparison:
- 503460 is less than 630460, so we have [tex]\(503460 < 630460\)[/tex].
- The symbol is [tex]\(<\)[/tex].
### b) Comparing:
1. Expanded Form 1: [tex]\(9 + 800000 + 40000\)[/tex]
- Add these numbers: [tex]\(9 + 40000 = 40009\)[/tex]
- [tex]\(40009 + 800000 = 840009\)[/tex]
2. Expanded Form 2: [tex]\(400000 + 90000 + 80\)[/tex]
- Add these numbers: [tex]\(400000 + 90000 = 490000\)[/tex]
- [tex]\(490000 + 80 = 490080\)[/tex]
3. Comparison:
- 840009 is greater than 490080, so we have [tex]\(840009 > 490080\)[/tex].
- The symbol is [tex]\(>\)[/tex].
### c) Comparing:
1. Expanded Form 1: [tex]\(50 + 400000 + 20000\)[/tex]
- Add these numbers: [tex]\(50 + 20000 = 20050\)[/tex]
- [tex]\(20050 + 400000 = 420050\)[/tex]
2. Expanded Form 2: [tex]\(400000 + 500 + 2000\)[/tex]
- Add these numbers: [tex]\(500 + 2000 = 2500\)[/tex]
- [tex]\(2500 + 400000 = 402500\)[/tex]
3. Comparison:
- 420050 is greater than 402500, so we have [tex]\(420050 > 402500\)[/tex].
- The symbol is [tex]\(>\)[/tex].
### d) Comparing:
1. Expanded Form 1: [tex]\(500 + 6000 + 30 + 400000 + 1 + 20000\)[/tex]
- Let's break it down:
- Start with: [tex]\(500 + 6000 = 6500\)[/tex]
- [tex]\(6500 + 30 = 6530\)[/tex]
- [tex]\(6530 + 1 = 6531\)[/tex]
- [tex]\(6531 + 20000 = 26531\)[/tex]
- Finally, [tex]\(26531 + 400000 = 426531\)[/tex]
2. Expanded Form 2: [tex]\(400000 + 500 + 20 + 6000 + 20000 + 1\)[/tex]
- Let's break it down:
- Start with: [tex]\(500 + 20 = 520\)[/tex]
- [tex]\(520 + 6000 = 6520\)[/tex]
- [tex]\(6520 + 1 = 6521\)[/tex]
- [tex]\(6521 + 20000 = 26521\)[/tex]
- Finally, [tex]\(26521 + 400000 = 426521\)[/tex]
3. Comparison:
- 426531 is greater than 426521, so we have [tex]\(426531 > 426521\)[/tex].
- The symbol is [tex]\(>\)[/tex].
By comparing each pair of expanded forms, we have determined the symbols for each comparison.
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