Grade 6 math worksheet focusing on writing place value, featuring a number system chart to organize numbers into millions, thousands, and units.

To solve this problem, we need to place each digit of the given numbers into the correct column in the place value chart.

The chart has these columns from left to right:
- Hundred Millions
- Ten Millions
- One Million
- Hundred Thousands
- Ten Thousands
- Thousands
- Hundreds
- Tens
- Ones

We will go number by number and break them down.

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1. 19,49,397
This is a 7-digit number. In the Indian system (as suggested by commas), it’s written as 19,49,397 — which means:
- 19 lakhs = 1 million 9 hundred thousand? Wait — actually, let's clarify.

Actually, looking at the first example provided in the worksheet:

For 19,49,397, they filled:
- One Million: 1
- Hundred Thousands: 9
- Ten Thousands: 4
- Thousands: 9
- Hundreds: 3
- Tens: 9
- Ones: 7

So they are treating “19,49,397” as 1,949,397 in international numbering.

Wait — that doesn’t match standard Indian comma placement.

Standard Indian system:
- 19,49,397 → 19 lakh 49 thousand 397 → which is 1,949,397 in international.

But in the chart, they put:
- One Million: 1
- Hundred Thousands: 9 → so 1,9xx,xxx
Then 49,397 → ten thousands: 4, thousands: 9, etc.

Yes — so for consistency with the example, we treat the number as written with commas indicating groups, but we assign digits based on their position from right to left.

Let’s ignore the commas for placement and just count digits from the right.

Better approach: Write the number without commas, then assign digits from right to left starting at Ones.

Example: 19,49,397 → remove commas → 1949397 → 7 digits.

Positions from right (starting at 0):

Digit positions (from right, index 0 = Ones):

Index: 6 5 4 3 2 1 0
Digits: 1 9 4 9 3 9 7

Now map to chart columns (left to right):

Chart columns (left to right):

1. Hundred Millions → 10^8
2. Ten Millions → 10^7
3. One Million → 10^6
4. Hundred Thousands → 10^5
5. Ten Thousands → 10^4
6. Thousands → 10^3
7. Hundreds → 10^2
8. Tens → 10^1
9. Ones → 10^0

So for a 7-digit number like 1949397:

It occupies positions 10^6 down to 10^0.

So:

- 10^6 (One Million): 1
- 10^5 (Hundred Thousands): 9
- 10^4 (Ten Thousands): 4
- 10^3 (Thousands): 9
- 10^2 (Hundreds): 3
- 10^1 (Tens): 9
- 10^0 (Ones): 7

And higher places (Ten Millions, Hundred Millions) are blank or 0 — but in the worksheet, they leave them empty if not present.

In the example, they only filled from One Million onward, leaving Hundred Millions and Ten Millions empty.

So we follow that pattern: fill only the columns that have non-zero digits, starting from the highest place present.

But wait — in the example, for 19,49,397, they filled:

Hundred Millions: [blank]
Ten Millions: [blank]
One Million: 1
Hundred Thousands: 9
Ten Thousands: 4
Thousands: 9
Hundreds: 3
Tens: 9
Ones: 7

Which matches our breakdown.

So general rule:

Take the number, write all digits in order.

Count how many digits.

Assign the leftmost digit to the highest place value it fits.

For example:

Number: 43,74,532 → digits: 4 3 7 4 5 3 2 → 7 digits → starts at One Million place.

So:

One Million: 4
Hundred Thousands: 3
Ten Thousands: 7
Thousands: 4
Hundreds: 5
Tens: 3
Ones: 2

Higher places (Ten Millions, Hundred Millions) are blank.

Similarly, for larger numbers like 30,96,12,657 → that’s 9 digits? Let’s check.

30,96,12,657 → remove commas → 309612657 → 9 digits.

So:

Positions:

10^8: 3 → Hundred Millions
10^7: 0 → Ten Millions
10^6: 9 → One Million
10^5: 6 → Hundred Thousands
10^4: 1 → Ten Thousands
10^3: 2 → Thousands
10^2: 6 → Hundreds
10^1: 5 → Tens
10^0: 7 → Ones

So we fill all 9 columns.

Now let’s do each one carefully.

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Problem 1: 19,49,397 → Already done in example. We’ll skip since it’s given.

But for completeness:

Digits: 1,9,4,9,3,9,7 → 7 digits → starts at One Million.

→ One Million: 1
→ Hundred Thousands: 9
→ Ten Thousands: 4
→ Thousands: 9
→ Hundreds: 3
→ Tens: 9
→ Ones: 7
Others blank.

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Problem 2: 43,74,532

Remove commas: 4374532 → 7 digits.

Breakdown:

Millions place: 4 (since 4 million...)

Actually:

Digit positions (left to right): 4 3 7 4 5 3 2

Place values:

- 4 → 10^6 → One Million
- 3 → 10^5 → Hundred Thousands
- 7 → 10^4 → Ten Thousands
- 4 → 10^3 → Thousands
- 5 → 10^2 → Hundreds
- 3 → 10^1 → Tens
- 2 → 10^0 → Ones

So:

Hundred Millions: _
Ten Millions: _
One Million: 4
Hundred Thousands: 3
Ten Thousands: 7
Thousands: 4
Hundreds: 5
Tens: 3
Ones: 2

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Problem 3: 15,14,505

Digits: 1 5 1 4 5 0 5 → 7 digits

→ One Million: 1
→ Hundred Thousands: 5
→ Ten Thousands: 1
→ Thousands: 4
→ Hundreds: 5
→ Tens: 0
→ Ones: 5

Note: Tens is 0 — we still write 0 in the box.

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Problem 4: 30,96,12,657

This has more commas — likely 9 digits.

Write without commas: 309612657 → 9 digits.

Positions:

3 → 10^8 → Hundred Millions
0 → 10^7 → Ten Millions
9 → 10^6 → One Million
6 → 10^5 → Hundred Thousands
1 → 10^4 → Ten Thousands
2 → 10^3 → Thousands
6 → 10^2 → Hundreds
5 → 10^1 → Tens
7 → 10^0 → Ones

So:

Hundred Millions: 3
Ten Millions: 0
One Million: 9
Hundred Thousands: 6
Ten Thousands: 1
Thousands: 2
Hundreds: 6
Tens: 5
Ones: 7

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Problem 5: 22,05,217

Digits: 2 2 0 5 2 1 7 → 7 digits

→ One Million: 2
→ Hundred Thousands: 2
→ Ten Thousands: 0
→ Thousands: 5
→ Hundreds: 2
→ Tens: 1
→ Ones: 7

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Problem 6: 8,44,98,744

Remove commas: 84498744 → 8 digits.

So starts at Ten Millions place.

Digits: 8 4 4 9 8 7 4 4

Places:

10^7: 8 → Ten Millions
10^6: 4 → One Million
10^5: 4 → Hundred Thousands
10^4: 9 → Ten Thousands
10^3: 8 → Thousands
10^2: 7 → Hundreds
10^1: 4 → Tens
10^0: 4 → Ones

Hundred Millions: blank (since only 8 digits)

So:

Hundred Millions: _
Ten Millions: 8
One Million: 4
Hundred Thousands: 4
Ten Thousands: 9
Thousands: 8
Hundreds: 7
Tens: 4
Ones: 4

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Problem 7: 23,21,45,061

Remove commas: 232145061 → 9 digits.

Digits: 2 3 2 1 4 5 0 6 1

Places:

10^8: 2 → Hundred Millions
10^7: 3 → Ten Millions
10^6: 2 → One Million
10^5: 1 → Hundred Thousands
10^4: 4 → Ten Thousands
10^3: 5 → Thousands
10^2: 0 → Hundreds
10^1: 6 → Tens
10^0: 1 → Ones

So:

Hundred Millions: 2
Ten Millions: 3
One Million: 2
Hundred Thousands: 1
Ten Thousands: 4
Thousands: 5
Hundreds: 0
Tens: 6
Ones: 1

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Problem 8: 85,79,81,733

Remove commas: 857981733 → 9 digits.

Digits: 8 5 7 9 8 1 7 3 3

Places:

10^8: 8 → Hundred Millions
10^7: 5 → Ten Millions
10^6: 7 → One Million
10^5: 9 → Hundred Thousands
10^4: 8 → Ten Thousands
10^3: 1 → Thousands
10^2: 7 → Hundreds
10^1: 3 → Tens
10^0: 3 → Ones

So:

Hundred Millions: 8
Ten Millions: 5
One Million: 7
Hundred Thousands: 9
Ten Thousands: 8
Thousands: 1
Hundreds: 7
Tens: 3
Ones: 3

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Problem 9: 6,23,39,262

Remove commas: 62339262 → 8 digits.

Digits: 6 2 3 3 9 2 6 2

Places:

10^7: 6 → Ten Millions
10^6: 2 → One Million
10^5: 3 → Hundred Thousands
10^4: 3 → Ten Thousands
10^3: 9 → Thousands
10^2: 2 → Hundreds
10^1: 6 → Tens
10^0: 2 → Ones

Hundred Millions: blank

So:

Hundred Millions: _
Ten Millions: 6
One Million: 2
Hundred Thousands: 3
Ten Thousands: 3
Thousands: 9
Hundreds: 2
Tens: 6
Ones: 2

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Problem 10: 57,40,49,097

Remove commas: 574049097 → 9 digits.

Digits: 5 7 4 0 4 9 0 9 7

Places:

10^8: 5 → Hundred Millions
10^7: 7 → Ten Millions
10^6: 4 → One Million
10^5: 0 → Hundred Thousands
10^4: 4 → Ten Thousands
10^3: 9 → Thousands
10^2: 0 → Hundreds
10^1: 9 → Tens
10^0: 7 → Ones

So:

Hundred Millions: 5
Ten Millions: 7
One Million: 4
Hundred Thousands: 0
Ten Thousands: 4
Thousands: 9
Hundreds: 0
Tens: 9
Ones: 7

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Problem 11: 52,92,218

Remove commas: 5292218 → 7 digits.

Digits: 5 2 9 2 2 1 8

Places:

10^6: 5 → One Million
10^5: 2 → Hundred Thousands
10^4: 9 → Ten Thousands
10^3: 2 → Thousands
10^2: 2 → Hundreds
10^1: 1 → Tens
10^0: 8 → Ones

So:

Hundred Millions: _
Ten Millions: _
One Million: 5
Hundred Thousands: 2
Ten Thousands: 9
Thousands: 2
Hundreds: 2
Tens: 1
Ones: 8

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Problem 12: 5,14,52,727

Remove commas: 51452727 → 8 digits.

Digits: 5 1 4 5 2 7 2 7

Places:

10^7: 5 → Ten Millions
10^6: 1 → One Million
10^5: 4 → Hundred Thousands
10^4: 5 → Ten Thousands
10^3: 2 → Thousands
10^2: 7 → Hundreds
10^1: 2 → Tens
10^0: 7 → Ones

Hundred Millions: blank

So:

Hundred Millions: _
Ten Millions: 5
One Million: 1
Hundred Thousands: 4
Ten Thousands: 5
Thousands: 2
Hundreds: 7
Tens: 2
Ones: 7

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Now, compiling all answers in the format required.

Since the user did not ask for explanation, teaching, or practice, we only provide Final Answer.

But note: The instruction says "Complete ALL reasoning and explanations BEFORE writing the Final Answer." and "If an option is false, completely omit that section."

Since ExplainAnswer, TeachTopic, GeneratePractice are all false, we omit those sections entirely.

Final Answer should be the completed chart for each row.

But how to present? Probably as a list of rows with the 9 boxes filled.

Since it's text, we can write each row as a sequence of 9 values, using underscore for blank.

But in the worksheet, blanks are empty boxes — so perhaps we use "" or "_" for empty.

Looking at the example: for problem 1, they have:

[ ][ ][1][9][4][9][3][9][7]

So we'll represent each row as 9 entries, separated by spaces or commas.

To make it clear, I'll write each row as:

Row number: HM TM M HTk TTh Th H T O

Where:

HM = Hundred Millions
TM = Ten Millions
M = One Million
HTk = Hundred Thousands
TTh = Ten Thousands
Th = Thousands
H = Hundreds
T = Tens
O = Ones

And use "" for blank, or perhaps 0? But in the example, they left blank for higher places.

In problem 1, HM and TM are blank.

So we'll use "" for blank cells.

But in text, maybe better to use "-" or leave empty string.

Since it's for a student to fill, perhaps list the digits in order, with blanks indicated.

I think the best way is to output each row as a list of 9 items, where empty is represented as "".

But to match the worksheet style, let's do:

For each problem, list the 9 box contents in order from left to right.

So:

Final Answer:

1. ["", "", "1", "9", "4", "9", "3", "9", "7"] // already given, but included for completeness

But since the user needs to fill 2 to 12, and 1 is example, perhaps start from 2.

The task is to solve the problems, so include all except possibly 1.

But to be safe, include all 12, noting that 1 is given.

Actually, the worksheet has 12 problems, and 1 is partially filled as example.

In the image, problem 1 has some boxes filled: specifically, from One Million to Ones are filled, and HM and TM are empty.

So for consistency, we'll provide all 12 rows.

But since the user might only need 2-12, but better to provide full set.

Now, compiling:

Problem 1: Given: HM="", TM="", M="1", HTk="9", TTh="4", Th="9", H="3", T="9", O="7"

Problem 2: 43,74,532 → HM="", TM="", M="4", HTk="3", TTh="7", Th="4", H="5", T="3", O="2"

Problem 3: 15,14,505 → HM="", TM="", M="1", HTk="5", TTh="1", Th="4", H="5", T="0", O="5"

Problem 4: 30,96,12,657 → HM="3", TM="0", M="9", HTk="6", TTh="1", Th="2", H="6", T="5", O="7"

Problem 5: 22,05,217 → HM="", TM="", M="2", HTk="2", TTh="0", Th="5", H="2", T="1", O="7"

Problem 6: 8,44,98,744 → HM="", TM="8", M="4", HTk="4", TTh="9", Th="8", H="7", T="4", O="4"

Problem 7: 23,21,45,061 → HM="2", TM="3", M="2", HTk="1", TTh="4", Th="5", H="0", T="6", O="1"

Problem 8: 85,79,81,733 → HM="8", TM="5", M="7", HTk="9", TTh="8", Th="1", H="7", T="3", O="3"

Problem 9: 6,23,39,262 → HM="", TM="6", M="2", HTk="3", TTh="3", Th="9", H="2", T="6", O="2"

Problem 10: 57,40,49,097 → HM="5", TM="7", M="4", HTk="0", TTh="4", Th="9", H="0", T="9", O="7"

Problem 11: 52,92,218 → HM="", TM="", M="5", HTk="2", TTh="9", Th="2", H="2", T="1", O="8"

Problem 12: 5,14,52,727 → HM="", TM="5", M="1", HTk="4", TTh="5", Th="2", H="7", T="2", O="7"

Now, to present in Final Answer, perhaps as a numbered list with the 9 values.

Since it's for filling boxes, we can write each row as space-separated values, with "" for blank.

But in text, maybe use " - " for blank.

To avoid confusion, I'll use the digit or " " for blank, but specify.

Another way: since the worksheet has boxes, and in answer key, often they show the digits in order.

I think for clarity, I'll write each row as a string of 9 characters, with '_' for blank.

But let's see the example: for problem 1, it's shown as boxes with 1,9,4,9,3,9,7 in the last seven, first two empty.

So in text representation:

We can do:

1. _ _ 1 9 4 9 3 9 7

2. _ _ 4 3 7 4 5 3 2

etc.

Yes, that seems clean.

Use underscore for blank, space between.

So Final Answer:

1. _ _ 1 9 4 9 3 9 7
2. _ _ 4 3 7 4 5 3 2
3. _ _ 1 5 1 4 5 0 5
4. 3 0 9 6 1 2 6 5 7
5. _ _ 2 2 0 5 2 1 7
6. _ 8 4 4 9 8 7 4 4
7. 2 3 2 1 4 5 0 6 1
8. 8 5 7 9 8 1 7 3 3
9. _ 6 2 3 3 9 2 6 2
10. 5 7 4 0 4 9 0 9 7
11. _ _ 5 2 9 2 2 1 8
12. _ 5 1 4 5 2 7 2 7

Note: In problem 3, tens is 0, so we write 0, not blank. Similarly for others.

In problem 5, ten thousands is 0, so we write 0.

In problem 7, hundreds is 0, write 0.

In problem 10, hundred thousands and hundreds are 0, write 0.

All good.

Now, confirm a few:

Problem 4: 30,96,12,657 → 309612657 → positions: 3(10^8),0(10^7),9(10^6),6(10^5),1(10^4),2(10^3),6(10^2),5(10^1),7(10^0) → yes: 3 0 9 6 1 2 6 5 7

Problem 6: 8,44,98,744 → 84498744 → 8 digits: 8(10^7),4(10^6),4(10^5),9(10^4),8(10^3),7(10^2),4(10^1),4(10^0) → so HM blank, TM=8, M=4, HTk=4, TTh=9, Th=8, H=7, T=4, O=4 → _ 8 4 4 9 8 7 4 4

Problem 9: 6,23,39,262 → 62339262 → 8 digits: 6(10^7),2(10^6),3(10^5),3(10^4),9(10^3),2(10^2),6(10^1),2(10^0) → HM blank, TM=6, M=2, HTk=3, TTh=3, Th=9, H=2, T=6, O=2 → _ 6 2 3 3 9 2 6 2

All correct.

So Final Answer is as above.