Scientific notation, and why the standard form is 1 ≤ x < 10

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What to assume they know

Powers of 10, and place value written out for whole numbers and decimals — powers of 10, and expanded form written with exponents
Zero and negative exponents: extending the rule rather than inventing a meaning — negative exponents, since the exponent here may be any integer
Reading large numbers in the Indian grouping, up to crores and beyond
Multiplying and dividing a decimal by a power of ten
Rounding a number to a stated number of leading digits

What they should be able to do

Convert a large whole number into scientific notation, and back
State the condition on the coefficient and say why the notation needs it
Show that a given number has many coefficient-and-power forms but only one standard form
Compare two numbers in standard form by comparing exponents first
Explain why a change in the exponent matters more than a change in the coefficient
Read the number of digits kept in a coefficient as a statement about how well a quantity is known
Decide which of several quantities in standard form is smallest, without computing
Place a quantity on a number line whose far end is another quantity in standard form

Where it usually goes wrong

"0.59 × 10⁴ is wrong." It is arithmetically correct and the chapter prints it. It is simply not in standard form. Separate "false" from "not in the agreed form" — students who conflate them cannot follow the argument for the rule.
"The rule is 1 to 10, so 10 × 10³ is allowed." The upper end is excluded; the coefficient must stay below 10. If 10 were allowed, 10000 would have two standard forms, 10 × 10³ and 1 × 10⁴, and the exponent would stop being unique.
"The exponent counts the zeros." It counts the places you moved the point. For 5.9 × 10³ there are no zeros at all in the coefficient, and 20800 has three zeros but an exponent of 4.
"More digits in the coefficient is more accurate." More digits is a stronger claim about accuracy. Writing 1.42395 × 10⁵ for a population you know to the nearest thousand is not precision, it is a false statement about what you know.
"A larger coefficient means a larger number." Only within one exponent. 9.9 × 10¹¹ is smaller than 1.1 × 10¹². Check the exponent first, every time.
"Two numbers with the same exponent are about the same size." They can differ by nearly ten times. The chapter's Sun–Saturn and Saturn–Uranus distances share an exponent and are genuinely close; that is a fact about those two numbers, not a rule.
"Standard form is for large numbers." The exponent may be negative, which the definition says outright. A small quantity is written the same way.

Questions to check understanding

Convert a given large number to standard form, and a standard form back to digits
Identify which of several offered forms of one number is the standard one, and say what is wrong with the others
Order three or four quantities given in standard form
Given a quantity known only to a stated accuracy, write it with the right number of coefficient digits
Multiply or divide two quantities in standard form and report the result in standard form
Say by what factor a quantity changes when its exponent is altered by 1
Mark a quantity on a number line whose end point is another quantity
Explain why the coefficient is restricted — the reasoning-style question this section is built around

Examples worth working on the board

The three opening facts (Part I p.31), all printed with Indian grouping and no scientific form — converting them is the student's task:
The distance from the Sun to the centre of the Milky Way, given as 30,00,00,00,00,00,00,00,00,000 m.
The count of stars in our galaxy, given as 1,00,00,00,00,000.
The mass of the Earth, given as 59,76,00,00,00,00,00,00,00,00,00,000 kg.
The money illustration (Part I p.31): misreading zeros is like being handed ₹5,000 when ₹50,000 was owed. One digit, one order of size, ten times the money.
5900, four ways (Part I p.31), all printed as a chain: 590 × 10¹; then 59 × 10²; then 5.9 × 10³; then 0.59 × 10⁴. Four correct products, one number. This is the section's key example — it is what forces the coefficient rule.
Three numbers in the chosen form (Part I p.31): 5900 = 5.9 × 10³; 20800 = 2.08 × 10⁴; 80,00,000 = 8 × 10⁶.
The definition as printed (Part I p.31): a number is written as x × 10ʸ, where the coefficient x is at least 1 and less than 10, and the exponent y may be any integer.
The Mumbai comparison (Part I p.31), the argument for why the exponent matters more. A population of 2 crore is written 2 × 10⁷. Change the 2 to a 3 and the population rises by half. Change the 7 to an 8 and it rises tenfold — from 2 crore to 20 crore. Both are single-character edits.
The Kohima sequence (Part I p.31), the argument about precision. Quoting a population as 1,42,395 claims certainty down to the last person. If the quantity is only known to be about 1 lakh 42 thousand, write 1.42 × 10⁵; if only to about 1 lakh 40 thousand, write 1.4 × 10⁵. The chapter's own reading of this: the exponent matters most, the coefficient's leading digit next, and every digit beyond that is a small correction.
The dinosaur cartoon (Part I p.32, artwork). A visitor asks the age of a skeleton; a museum worker answers that it is seventy million and fifteen years old, because it was seventy million years old when he started working there. The joke is arithmetic: fifteen years cannot survive alongside a quantity known only to its leading digit.
Three planetary distances (Part I p.32), each printed in both forms:
Sun to Saturn, 14,33,50,00,00,000 m, that is 1.4335 × 10¹² m.
Saturn to Uranus, 14,39,00,00,00,000 m, that is 1.439 × 10¹² m.
Sun to Earth, 1,49,60,00,00,000 m, that is 1.496 × 10¹¹ m.
The question on those three (Part I p.32): which is smallest? Left open, and it is the whole point — two of the three share an exponent so the coefficients decide, while the third is settled by the exponent alone.
The solar-system strip (Part I p.32, artwork). A dark band with the Sun at the left, Saturn in the middle and a small blue-green planet at the right. Decorative and not to scale; do not use it as the number line.
The number-line task (Part I p.32). A plain horizontal line is printed with two ticks, labelled Sun at the left end and Saturn at the right. The student must mark where the Earth falls, given the Sun–Earth distance. The line carries no scale, no intermediate ticks and no numbers. Verified on the printed page. The route is the ratio of the two distances, which is about one to ten — so the Earth sits close to the left end, and that surprise is the exercise.
Four to convert (Part I p.32), left open: 59,853; 65,950; 34,30,000; and 70,04,00,00,000.

Figures to have open

A coefficient-and-exponent card — two boxes, one holding a number between 1 and 10 and one holding an integer, with the value updating as either changes. This carries sections 4, 5 and 6, and section 6 is unanswerable without it. An added figure.
The Sun-to-Saturn number line (Part I p.32), redrawn with a real scale so the Earth can be marked. The chapter's line is deliberately unscaled; the explanation's version should start unscaled, take the mark, then reveal the scale.
A four-way equality panel for 5900, showing that the coefficient and the exponent trade against each other. Standard schematic.
A digit-count strip for the three opening facts, so the exponent can be seen being counted rather than asserted. Not in the book.
No photograph is needed. The chapter's dinosaur cartoon and solar-system band are decorative, and the band is not to scale.

Where this sits in the book

NCERT Ganita Prakash Class 8, Part I, printed Chapter 2, "Power Play", §2.4 "Powers of 10", the unnumbered subheading "Scientific Notation", Part I pp.31–32, running to the end of §2.4.
The chapter's SUMMARY (Part I p.46) gives one further worked case — 308100000 as 3.081 × 10⁸ — and restates the coefficient condition.
Scientific notation is then used as a working tool, not taught again, at Part I pp.36–42 (Why the nearest power of ten is the only handle on a quantity too big to picture).
Chapter-end exercises touching scientific notation: "Figure it Out" at Part I p.45. Only item 13 actually instructs that the answer be given in scientific notation; item 12 offers six candidate forms to choose among, and item 9 asks for a count of digits, not a notation.