Question 4

We can break down numbers using place values in different ways.

Step 1 — First way for 8300

We want to make the number 8300. First, we take the digit 8. It is in the thousands place. We multiply 8 by 1000. $8 \times 1000 = 8000$ Next, we take the digit 3. It is in the hundreds place. We multiply 3 by 100. $3 \times 100 = 300$ We add these two results. $8000 + 300$

$\boxed{\mathbf{8300}}$

Step 2 — Second way for 8300

Let us find another way for 8300. We can group the first two digits. This gives us the number 83. The number 83 is followed by two zeros. So, it represents 83 hundreds. We multiply 83 by 100. $83 \times 100$

$\boxed{\mathbf{8300}}$

Step 3 — First way for 40629

We want to make the number 40629. First, we take the digit 4. It is in the ten thousands place. We multiply 4 by 10000. $4 \times 10000 = 40000$ Next, we take the digit 6. It is in the hundreds place. We multiply 6 by 100. $6 \times 100 = 600$ Then, we take the digit 2. It is in the tens place. We multiply 2 by 10. $2 \times 10 = 20$ Finally, we take the digit 9. It is in the ones place. We multiply 9 by 1. $9 \times 1 = 9$ We add all these results. $40000 + 600 + 20 + 9$

$\boxed{\mathbf{40629}}$

Step 4 — Second way for 40629

Let us find another way for 40629. We can group the first two digits. This gives us the number 40. The number 40 is in the thousands place. We multiply 40 by 1000. $40 \times 1000 = 40000$ Next, we take the digit 6. It is in the hundreds place. We multiply 6 by 100. $6 \times 100 = 600$ Then, we group the last two digits. This gives us the number 29. The number 29 is in the ones place. We multiply 29 by 1. $29 \times 1 = 29$ We add all these results. $40000 + 600 + 29$

$\boxed{\mathbf{40629}}$

Step 5 — First way for 56354

We want to make the number 56354. First, we take the digit 5. It is in the ten thousands place. We multiply 5 by 10000. $5 \times 10000 = 50000$ Next, we take the digit 6. It is in the thousands place. We multiply 6 by 1000. $6 \times 1000 = 6000$ Then, we take the digit 3. It is in the hundreds place. We multiply 3 by 100. $3 \times 100 = 300$ Finally, we group the last two digits. This gives us the number 54. The number 54 is in the ones place. We multiply 54 by 1. $54 \times 1 = 54$ We add all these results. $50000 + 6000 + 300 + 54$

$\boxed{\mathbf{56354}}$

Step 6 — Second way for 56354

Let us find another way for 56354. We can group the first two digits. This gives us the number 56. The number 56 is in the thousands place. We multiply 56 by 1000. $56 \times 1000 = 56000$ Next, we group the middle two digits. This gives us the number 35. The number 35 is in the tens place. We multiply 35 by 10. $35 \times 10 = 350$ Finally, we take the digit 4. It is in the ones place. We multiply 4 by 1. $4 \times 1 = 4$ We add all these results. $56000 + 350 + 4$

$\boxed{\mathbf{56354}}$

Step 7 — First way for 66666

We want to make the number 66666. First, we take the digit 6. It is in the ten thousands place. We multiply 6 by 10000. $6 \times 10000 = 60000$ Next, we take the digit 6. It is in the thousands place. We multiply 6 by 1000. $6 \times 1000 = 6000$ Then, we take the digit 6. It is in the hundreds place. We multiply 6 by 100. $6 \times 100 = 600$ Finally, we group the last two digits. This gives us the number 66. The number 66 is in the ones place. We multiply 66 by 1. $66 \times 1 = 66$ We add all these results. $60000 + 6000 + 600 + 66$

$\boxed{\mathbf{66666}}$

Step 8 — Second way for 66666

Let us find another way for 66666. We can group the first two digits. This gives us the number 66. The number 66 is in the thousands place. We multiply 66 by 1000. $66 \times 1000 = 66000$ Next, we group the next two digits. This gives us the number 66. The number 66 is in the tens place. We multiply 66 by 10. $66 \times 10 = 660$ Finally, we take the digit 6. It is in the ones place. We multiply 6 by 1. $6 \times 1 = 6$ We add all these results. $66000 + 660 + 6$

$\boxed{\mathbf{66666}}$

Step 9 — First way for 367813

We want to make the number 367813. First, we take the digit 3. It is in the hundred thousands place. We multiply 3 by 100000. $3 \times 100000 = 300000$ Next, we take the digit 6. It is in the ten thousands place. We multiply 6 by 10000. $6 \times 10000 = 60000$ Then, we take the digit 7. It is in the thousands place. We multiply 7 by 1000. $7 \times 1000 = 7000$ Next, we take the digit 8. It is in the hundreds place. We multiply 8 by 100. $8 \times 100 = 800$ Finally, we group the last two digits. This gives us the number 13. The number 13 is in the ones place. We multiply 13 by 1. $13 \times 1 = 13$ We add all these results. $300000 + 60000 + 7000 + 800 + 13$

$\boxed{\mathbf{367813}}$

Step 10 — Second way for 367813

Let us find another way for 367813. We can group the first two digits. This gives us the number 36. The number 36 is in the ten thousands place. We multiply 36 by 10000. $36 \times 10000 = 360000$ Next, we group the remaining digits. This gives us the number 7813. The number 7813 is in the ones place. We multiply 7813 by 1. $7813 \times 1 = 7813$ We add these two results. $360000 + 7813$

$\boxed{\mathbf{367813}}$

Answer

(a) 8300: (i) $(8 \times 1000) + (3 \times 100) = 8300$ (ii) $(83 \times 100) = 8300$

(b) 40629: (i) $(4 \times 10000) + (6 \times 100) + (2 \times 10) + (9 \times 1) = 40629$ (ii) $(40 \times 1000) + (6 \times 100) + (29 \times 1) = 40629$

(c) 56354: (i) $(5 \times 10000) + (6 \times 1000) + (3 \times 100) + (54 \times 1) = 56354$ (ii) $(56 \times 1000) + (35 \times 10) + (4 \times 1) = 56354$

(d) 66666: (i) $(6 \times 10000) + (6 \times 1000) + (6 \times 100) + (66 \times 1) = 66666$ (ii) $(66 \times 1000) + (66 \times 10) + (6 \times 1) = 66666$

(e) 367813: (i) $(3 \times 100000) + (6 \times 10000) + (7 \times 1000) + (8 \times 100) + (13 \times 1) = 367813$ (ii) $(36 \times 10000) + (7813 \times 1) = 367813$