Students practice comparing large numbers by rewriting lists of six-digit integers in ascending order.

Let’s solve each part step by step. We need to order the numbers from least to greatest — that means starting with the smallest number and ending with the largest.

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Part a:

Numbers: 340,034 | 304,043 | 340,340 | 430,040 | 430,004

Step 1: Look at the hundred thousands place (first digit).
- 304,043 → starts with 3
- 340,034 → starts with 3
- 340,340 → starts with 3
- 430,040 → starts with 4
- 430,004 → starts with 4

So the two 4xx,xxx numbers are bigger than the three 3xx,xxx numbers.

Now compare the 3xx,xxx group:
- 304,043 → ten thousands digit is 0 → smallest so far
- 340,034 → ten thousands digit is 4
- 340,340 → ten thousands digit is 4 → same as above, now check hundreds place: 0 vs 3 → 340,034 < 340,340

So among 3xx,xxx:
304,043 < 340,034 < 340,340

Now compare the 4xx,xxx group:
- 430,004 vs 430,040 → both have 430, then look at last three digits: 004 vs 040 → 004 is smaller

So 430,004 < 430,040

Final order for part a:
304,043; 340,034; 340,340; 430,004; 430,040

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Part b:

Numbers: 609,229 | 69,929 | 609,292 | 690,229 | 69,292

Note: Some numbers have only 5 digits! That means they’re less than 100,000.

List them clearly:

- 69,292 → 5 digits → smallest possible? Let’s see.
- 69,929 → also 5 digits
- 609,229 → 6 digits
- 609,292 → 6 digits
- 690,229 → 6 digits

First, separate 5-digit and 6-digit numbers.

5-digit numbers: 69,292 and 69,929
→ Compare: 69,292 < 69,929 (because 292 < 929)

6-digit numbers: 609,229 | 609,292 | 690,229

Compare first: 609,229 vs 609,292 → same up to “609,” then 229 vs 292 → 229 < 292 → so 609,229 < 609,292

Then 690,229 → starts with 690, which is bigger than 609 → so it’s the largest of the 6-digit ones.

So full order:
69,292 < 69,929 < 609,229 < 609,292 < 690,229

Final answer for part b:
69,292; 69,929; 609,229; 609,292; 690,229

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Part c:

Numbers: 733,533 | 735,553 | 733,353 | 735,535 | 735,335

All start with 73x, so let’s break them down.

Group by first three digits:

Group 1: 733,xxx → 733,533 and 733,353
→ Compare: 733,353 < 733,533 (because 353 < 533)

Group 2: 735,xxx → 735,553 | 735,535 | 735,335
→ All start with 735, so compare last three digits:

735,335 → 335
735,535 → 535
735,553 → 553

So order within group: 735,335 < 735,535 < 735,553

Now combine both groups:
733,353 < 733,533 < 735,335 < 735,535 < 735,553

Final answer for part c:
733,353; 733,533; 735,335; 735,535; 735,553

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Part d:

Numbers: 980,001 | 99,800 | 988,101 | 980,010 | 980,100

Again, note: 99,800 is only 5 digits → so it’s the smallest!

Rest are 6-digit numbers starting with 98x or 988.

Breakdown:

- 99,800 → 5 digits → smallest

Now 6-digit numbers:

980,001
980,010
980,100
988,101

Compare the 980,xxx group:

980,001 → ends with 001
980,010 → ends with 010
980,100 → ends with 100

So: 980,001 < 980,010 < 980,100

Then 988,101 → starts with 988, which is bigger than 980 → so it’s the largest.

Full order:
99,800 < 980,001 < 980,010 < 980,100 < 988,101

Final answer for part d:
99,800; 980,001; 980,010; 980,100; 988,101

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Final Challenge Box:

You can write any five 6-digit numbers here. For example:
123,456 | 234,567 | 345,678 | 456,789 | 567,890

But since this is for a friend to reorder, you don’t need to solve it — just pick any five 6-digit numbers.

Example set:
100,000; 200,000; 300,000; 400,000; 500,000

(Your friend would put them in order: 100,000; 200,000; 300,000; 400,000; 500,000 — already ordered!)

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Final Answer:

a. 304,043; 340,034; 340,340; 430,004; 430,040
b. 69,292; 69,929; 609,229; 609,292; 690,229
c. 733,353; 733,533; 735,335; 735,535; 735,553
d. 99,800; 980,001; 980,010; 980,100; 988,101
Challenge box (example): 100,000; 200,000; 300,000; 400,000; 500,000