Long division continued past the ones place

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What to assume they know

Extending Indian place value to the right of the point — the place-value system continuing to the right of the point, so Tenths, Hundredths and Thousandths are already named places
Whole-number long division with a remainder, including the regrouping that turns a leftover Hundred into ten Tens
Finding an equivalent fraction by multiplying numerator and denominator by the same number
Reciprocals, and Brahmagupta's rule for dividing fractions — division of fractions, and the reciprocal
Knowing which small numbers divide 10, 100 and 1000

What they should be able to do

Turn a fraction into a decimal by finding an equivalent fraction whose denominator is a power of ten, and say when that is possible
Explain why ten divided by three cannot be handled that way
Carry out whole-number long division as a sequence of regroupings, naming the place at every step
Continue the same procedure past the Ones, regrouping Ones into Tenths and Tenths into Hundredths
State where the decimal point goes in the quotient, and why it goes there
Verify a decimal quotient by the equivalent-fraction route
Divide a three-digit number by a one-digit divisor to three decimal places
Recognise the same quotient obtained by two independent methods as a check, not as duplicated work

Where it usually goes wrong

"Division stops when you run out of digits." It stops when the remainder reaches zero, and those are different events. 1324 and 1325 differ by one and the second needs two more places.
"You put a decimal point in the answer and then bring down a zero." That is the mechanical version of the rule, and it is what students forget under pressure. The chapter's version is that a leftover One is traded for ten Tenths, exactly as a leftover Hundred is traded for ten Tens. The zero appears because ten Tenths is written 10 in the Tenths column, not because a rule said to write one.
"The remainder 1 means the answer is 331 remainder 1." True if you stop there. The chapter's move is to refuse to stop, and to say what the leftover One is worth once it is broken up.
"Every fraction can be turned into a decimal by finding the right equivalent fraction." Ten over three cannot, and the chapter says so on Part II p.76. That is the reason the place-value method is introduced at all.
"The two methods are alternatives, so learn the easier one." They are alternatives only where both work. The equivalent-fraction route is quick and limited; long division is slower and always available. The chapter runs both on 1325 over 4 precisely so the reader can see them agree.
"The decimal point goes wherever it looks right." In the layout the book uses, it goes at exactly one place — between the last Ones digit and the first Tenths digit — and the reader can always find it by asking which step regrouped Ones. Q2(b) on Part II p.83 is built from exactly this error: every option there carries the same digits and only the point moves. Q2(a) mixes in two distractors that change the digit string as well, so an explanation that tells the student only the point ever moves will mis-teach that item.

Questions to check understanding

Rewrite a fraction as a decimal by finding an equivalent fraction whose denominator is a power of ten, then verify it by long division (the shape of Q1 on Part II p.83)
Choose the correct decimal quotient from options that share their digits and differ only in where the point sits (the shape of Q2(b) on Part II p.83)
Divide a three- or four-digit number by a single-digit divisor, giving the quotient to three decimal places
State the value of the remainder at a named step, in the units of its place
Explain why a stated fraction cannot be written with a denominator of 10, 100 or 1000
Word problems that end in an exact division: a length cut into equal pieces, a weight packed into equal bags
The SUMMARY bullet on Part II p.95 states the regrouping rule and the point-placement rule together and is the likely source of a recall question

Examples worth working on the board

Example 7, the red ribbon (Part II, §4.3, pp.75–76). Checked against the printed page. 29 metres shared between two, then the same 29 metres shared between four. The margin picture on p.75 is a speech bubble holding a red ribbon marked 29 m across the top and split underneath into 14 m, 14 m and 1 m — the leftover metre is drawn, and it is the leftover metre that forces the decimal. The book then rewrites one-half as five-tenths, and later multiplies 29 over 4 above and below by 25.
The impossibility on p.76 (Part II, §4.3). Ten over three. The book asks whether an equivalent fraction over 1, 10, 100 or 1000 can be found and answers that it cannot. That refusal is what motivates everything after it, so give it attention rather than passing over it.
Example 8, 1324 divided by 4 (Part II, §4.3, pp.77–78). Checked against the printed page. The page is built from four-box diagrams: a label at the top naming what is being shared, arrows fanning down into four rounded boxes, and the running contents of each box printed inside it — first 3 Hundreds, then 3 Hundreds and 3 Tens, then 3 Hundreds, 3 Tens and 1 One. Beside each diagram the same step appears in the Indian long-division layout, with the column heads Th, H, T and O set in colour above the quotient and the quotient itself written as a sum of place contributions rather than as a run of digits.
1325 divided by 4 (Part II, §4.3, pp.78–80). Checked against the printed page. The same four-box diagrams continue below the Ones: after each box holds 3 Hundreds, 3 Tens and 1 One, a dotted line is drawn inside every box and 2 Tenths written below it, then a second dotted line and 5 Hundredths below that. The long-division layout beside them grows two new colour-coded column labels, Tenths and then Hundredths, written vertically.
The verification (Part II, §4.3, p.80). The book multiplies 1325 and 4 by 25 to get a denominator of 100. Inputs: 1325, 4, 25.
Example 9, 237 divided by 8 (Part II, §4.3, pp.81–82). Checked against the printed page. No four-box diagrams here — only the long-division layout, grown step by step across two pages until five colour-coded column labels stand over it: Tens, Ones, Tenths, Hundredths, Thousandths. A margin cartoon on p.81 carries a reminder that the quotient gets its point at the moment Ones are regrouped into Tenths, and the chapter does not leave it there: the same reminder is set in bold body type immediately above that cartoon on p.81, again in the body of p.82, again in the body of Example 11 on p.83, and once more in a second margin cartoon beside Q2 on p.83.
"Figure it Out" Q1 (Part II, §4.3, p.83). Four fractions to be turned into decimals by the equivalent-fraction route and then checked by long division: 18 over 5, 415 over 4, 1217 over 2, 4827 over 8. Every denominator here divides some power of ten, which is why both routes are available.
"Figure it Out" Q2 (Part II, §4.3, p.83). Checked against the printed page. Two multiple-choice items, 1526 over 4 and 3567 over 8, and the two option lists do not work the same way. Under (b) all four options carry the digits 445875 and differ only in where the point sits — 4458.75, 44.5875, 445.875 and 4458.75, which means (i) and (iv) are the same number printed twice, so there are three distinct options and not four. Under (a) the options are 38.15, 380.15, 381.5 and 381.05: only two of those share a digit string, because the other two carry an extra zero.

Figures to have open

The four-box regrouping diagram: a labelled quantity at the top, four arrows, four boxes whose contents accumulate downwards. It must support adding a dotted line and a new place below it. Redraw it; the book's own version is drawn artwork.
The Indian long-division layout — divisor, bracket, dividend, bracket, quotient to the right — with colour-coded place labels standing above the quotient digits. This is the layout the student will meet in the examination, so match it rather than substituting the Western bracket.
A red ribbon marked 29 m and split into 14, 14 and a leftover 1. Standard schematic.
No photograph and no data set from the textbook is required for this topic.

Where this sits in the book

NCERT Ganita Prakash, Class 7, Part II, printed Chapter 4 "Another Peek Beyond the Point", §4.3 "Decimal Division", pp.75–83 — Example 7 and the equivalent-fraction route (pp.75–76), the subheading "Division Using Place Value" and Example 8 (pp.76–78), the subheading "Division with a Decimal Quotient", 1325 divided by 4 and its verification (pp.78–80), and Example 9 (pp.81–82)
Same part, same chapter, §4.3, "Figure it Out", p.83 — questions 1 and 2
Same part, same chapter, SUMMARY, p.95, bullet 3
Backward pointers: Extending Indian place value to the right of the point and Reciprocals, and Brahmagupta's rule for dividing fractions
Forward pointers: Dividing when the dividend has a decimal for a dividend that already carries a point, and Divisions that never end for what happens when the remainder never reaches zero