Rival ways of splitting off the fractional part, and why the point won

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What the video covers, what to say before it, where a class usually goes wrong, and what to set afterwards. An account is free, and it opens every chapter of every book.

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What to assume they know

Extending Indian place value to the right of the point — why a separator is needed at all, and what 705 could otherwise mean (Part I, §3.4)
A hundredth part, and continuing the split — fractions whose denominators are ten, a hundred and a thousand (Part I, §3.3)
Reading a large number written with Indian digit grouping, such as 1,000
Crores and millions: one number, two naming systems — that one number can be written under more than one naming convention (Part I, Chapter 1)
The idea that a mathematical notation is agreed rather than discovered

What they should be able to do

Distinguish decimal fractions themselves from decimal notation for them, and say which came first in the chapter's account
Place the chapter's five named figures and their contributions in order
Describe each of the rival fifteenth-century devices for marking off the whole part
Rewrite a given number in one of those rival notations, and back
Explain why more than one notation for the same quantity is a problem in practice
Say what is still not settled today, and give the two forms a number may take
Argue which parts of decimal notation are forced by the mathematics and which are chosen by agreement

Where it usually goes wrong

"Decimals were invented when the decimal point was invented." The chapter separates the two by centuries, and puts the fractions first. Getting this the wrong way round is the standard error and the section exists to correct it.
"al-Uqlīdisī used a decimal point." He used an upright stroke over a digit, and the page prints the number so the reader can see it. Show the mark.
"Napier invented the decimal point." The chapter names two mathematicians for the point in the same sentence, and a third for a rival mark at the same time. Naming one alone misreports the page.
"The comma is a mistake." It is a different convention in current use, and the chapter says so without judgement. It is also the reason a number copied from a foreign document can be read wrongly.
"1,000.5 and 1 000,5 are different numbers." They are the same number under two agreements about which mark does which job.
"Notation is arbitrary, so none of it matters." The opposite conclusion is the right one: because the mark is agreed rather than forced, everyone using it has to agree, and the cost of disagreement is exactly the sort of failure the previous two topics of this module describe.
"Everything in decimal notation is a convention." No. Splitting the unit by ten follows from the place value system already in use, as Part I, §3.4, p.59 argues, and the order of the places follows from the splitting. What is chosen is the mark. Keep the line between the two clear; it is the topic's whole payload.

Questions to check understanding

Place the chapter's named figures and their contributions in order on a timeline
Write a given number in the stroke notation and in the raised-count notation, and read one back
Given a number written with a comma separator and spaced grouping, write it in the form used here
Explain why a separator is needed, using a number that is ambiguous without one
Say which features of decimal notation are consequences of the ten-split and which are conventions
Answer, with a reason, whether decimal fractions could exist without a decimal point

Examples worth working on the board

What came first (Part I, §3.8, p.78). Fractions with denominators of ten, a hundred and a thousand appear in the work of Indian astronomers and mathematicians, the chapter naming Śhrīdharāchārya in the eighth century for work on arithmetic and algebra.
The tenth-century account (Part I, §3.8, p.78). Abūl Ḥassan al-Uqlīdisī, described on the page as an Arab mathematician, set decimal notation out in something very close to the shape it has now, around 950 CE, inside a work titled Kitāb al-Fuṣūl — the title runs on with fī al-Ḥisāb and closes on al Hindī — and the page glosses the whole as a book of chapters on Indian arithmetic.
His notation (Part I, §3.8, p.78). Checked, because the mark itself is typeset artwork and comes through the extraction detached from the digit it sits on. The number 0.059375 is printed as the seven digits 0059375 with a small upright stroke above the first of them — the final digit before the fraction starts.
The three fifteenth-century devices (Part I, §3.8, p.78). A stroke over the last whole-number digit, as above; different colours for the two parts of the number; and a small raised numeral giving how many fractional places there are, under which 0.36 becomes the two digits 36 with a raised 2 above them.
The sixteenth century (Part I, §3.8, p.78). John Napier, described as Scottish, and Christopher Clavius, described as German, used the point; François Viète, described as French, used the comma.
Today (Part I, §3.8, p.78). Several countries still separate the two parts with a comma. The chapter's own worked case: what appears here as 1,000.5 turns up in those countries as 1 000,5, with a space standing where the grouping comma would be.
The chapter's verdict (Part I, §3.8, p.78). The point has lasted as the most widely used of these forms wherever a number carrying a fraction is written the Indian way.
The ambiguity this all exists to solve (Part I, §3.4, p.61). The digits 705 standing for three different quantities, and 42 for two. Bring this back; the history is otherwise a list of names rather than an argument.

Figures to have open

A single timeline carrying the eighth century, around 950 CE, the fifteenth century and the sixteenth. It should be built once and advanced, not redrawn. Standard schematic.
One number written four ways: with a stroke over a digit, in two colours, with a raised place-count, and with a point. Standard schematic; the printed page shows the first and the third only, and the stroke must be redrawn from the printed page because it does not survive extraction.
1,000.5 and 1 000,5 set one above the other with their marks labelled. Standard schematic.
The digits 705 with three interchangeable sets of place labels. Reuse the graphic built for Extending Indian place value to the right of the point.
No photograph or portrait is required, and none is printed.

Where this sits in the book

NCERT Ganita Prakash, Class 7, Part I, printed Chapter 3 "A Peek Beyond the Point", §3.8 More on the Decimal System, and its third unnumbered subheading A Pinch of History – Decimal Notation Over Time, printed entirely on p.78. The chapter's closing practice set follows on pp.78–80 and the summary is on p.80.
Backward pointers: Part I, §3.4, p.59, for why ten; Part I, §3.4, pp.61–62, for the ambiguity the separator resolves; Part I, Chapter 1, for two naming systems applied to one number.
The same series runs A Pinch of History boxes in other chapters of both parts; Part I, Chapter 8, carries two of them.