In-text Questions — Scientific Notation — Power Play

1. 12 marksGanita Prakash Cl-8 Part 1, §2.4 (Sun-Saturn-Earth distances)

   The distance between the Sun and Saturn is 1.4335 × 10¹² m, between Saturn and Uranus is 1.439 × 10¹² m, and between the Sun and Earth is 1.496 × 10¹¹ m. Which of these three distances is the smallest?

   Hint. Compare the powers of 10 first — a smaller exponent means a much smaller number, regardless of the coefficient.

   Step 1 — Compare the exponents. Two distances have exponent 12, and one (Sun-Earth) has exponent 11 — one power of 10 smaller.

   Step 2 — Confirm this makes it smallest. Since 10¹¹ is a tenth of 10¹², the Sun-Earth distance is smallest even though its coefficient (1.496) is larger than the others' coefficients.

   ✦ Answer: The distance between the Sun and Earth (1.496 × 10¹¹ m) is the smallest.

   Where students slip. Comparing only the coefficients (1.4335 vs 1.439 vs 1.496) without checking the exponents first — a number with a smaller exponent is smaller overall, no matter how its coefficient compares.

2. 23 marksGanita Prakash Cl-8 Part 1, §2.4, Figure it Out-style prompt

   Express the following numbers in standard form: (i) 59,853 (ii) 65,950 (iii) 34,30,000 (iv) 70,04,00,00,000

   Hint. Move the decimal point until only one nonzero digit remains before it, and count how many places you moved.

   Step 1 — (i) 59853 → 5.9853 × 10⁴ (decimal moved 4 places).

   Step 2 — (ii) 65950 → 6.595 × 10⁴ (decimal moved 4 places; the trailing zero is dropped as it carries no extra precision).

   Step 3 — (iii) 3430000 → 3.43 × 10⁶ (decimal moved 6 places).

   Step 4 — (iv) 700400000000 → 7.004 × 10¹⁰ (decimal moved 10 places), since scientific notation always keeps exactly one nonzero digit before the decimal point.

   ✦ Answer: (i) 5.9853 × 10⁴ (ii) 6.595 × 10⁴ (iii) 3.43 × 10⁶ (iv) 7.004 × 10¹⁰.

   Where students slip. Counting the digit-shift incorrectly for numbers with trailing zeros, as in (iv) — count only the places actually moved to get the coefficient between 1 and 10, not the total digit count of the number.

3. 32 marksGanita Prakash Cl-8 Part 1, §2.5 thought-experiments

   If each person in the world (about 8.2 × 10⁹ people) had 30 pieces of clothing, find the total number of pieces of clothing, in scientific notation.

   Hint. Multiply the population by 30, then convert the result back into standard scientific-notation form.

   Step 1 — Set up the multiplication. 8.2 × 10⁹ × 30.

   Step 2 — Multiply the coefficients. 8.2 × 30 = 246.

   Step 3 — Convert 246 × 10⁹ into standard scientific notation. 246 = 2.46 × 10², so the total is 2.46 × 10² × 10⁹ = 2.46 × 10¹¹.

   ✦ Answer: 2.46 × 10¹¹ pieces of clothing.

   Where students slip. Leaving the answer as 246 × 10⁹ — standard scientific notation requires the coefficient to be between 1 and 10, so the extra factor of 100 must be folded into the power of 10.

4. 42 marksGanita Prakash Cl-8 Part 1, §2.5 thought-experiments

   There are about 100 million bee colonies in the world. Find the number of honeybees, in scientific notation, if each colony has about 50,000 bees.

   Hint. Write both numbers in scientific notation first, then multiply the coefficients and add the exponents.

   Step 1 — Write both quantities in scientific notation. 100 million = 10⁸; 50,000 = 5 × 10⁴.

   Step 2 — Multiply. 10⁸ × 5 × 10⁴ = 5 × 10¹².

   ✦ Answer: 5.0 × 10¹² honeybees.

   Where students slip. Forgetting to add the exponents of the two powers of 10 separately from multiplying the coefficients — the two operations (multiply coefficients, add exponents) are independent steps.

5. 52 marksGanita Prakash Cl-8 Part 1, §2.5 thought-experiments

   The human body has about 38 trillion bacterial cells, and the world population is about 8.2 × 10⁹. Find the total bacterial population residing in all humans in the world, in scientific notation.

   Hint. Write 38 trillion in scientific notation first, then multiply by the population.

   Step 1 — Write 38 trillion in scientific notation. 38 trillion = 38 × 10¹² = 3.8 × 10¹³.

   Step 2 — Multiply by the world population. 3.8 × 10¹³ × 8.2 × 10⁹ = (3.8 × 8.2) × 10²² = 31.16 × 10²², since multiplying two scientific-notation numbers multiplies their coefficients and adds their exponents separately.

   Step 3 — Convert to standard form. 31.16 × 10²² = 3.116 × 10²³.

   ✦ Answer: 3.116 × 10²³ bacterial cells.

   Where students slip. Leaving the coefficient as 31.16 instead of adjusting it back into the 1-10 range — this requires bumping the exponent up by one more, from 22 to 23.

6. 63 marksGanita Prakash Cl-8 Part 1, §2.5 thought-experiments

   Estimate the total time spent eating in a lifetime, in seconds, assuming a 70-year lifespan and 1 hour of eating per day.

   Hint. Convert 1 hour to seconds, then multiply by the number of days in 70 years.

   Step 1 — Convert the daily eating time to seconds. 1 hour = 3600 seconds.

   Step 2 — Find the total number of days in 70 years. 365 × 70 = 25550 days.

   Step 3 — Multiply. 3600 × 25550 = 91,980,000 seconds, since the daily total in seconds scales up directly with the number of days lived.

   Step 4 — Convert to scientific notation. 91,980,000 = 9.198 × 10⁷.

   ✦ Answer: About 9.198 × 10⁷ seconds.

   Where students slip. Forgetting to convert the daily time into seconds before multiplying by the number of days — mixing units (hours and days) part-way through gives a wrong final unit.

7. 72 marksGanita Prakash Cl-8 Part 1, §2.5 thought-experiments

   If you have lived for a million seconds, how old would you be?

   Hint. Convert a million seconds into days by dividing by the number of seconds in a day.

   Step 1 — Find the number of seconds in a day. 60 × 60 × 24 = 86400 seconds.

   Step 2 — Divide a million seconds by this. 1,000,000 ÷ 86400 ≈ 11.6 days.

   ✦ Answer: About 12 days old.

   Where students slip. Confusing a million seconds with a million minutes or hours — a million seconds is a surprisingly small span (under two weeks), unlike a million days or years.

8. 82 marksGanita Prakash Cl-8 Part 1, §2.5 (naming large numbers)

   The names million (10⁶), billion (10⁹), trillion (10¹²), quadrillion (10¹⁵), and so on each begin with a Latin number prefix (bi-, tri-, quad-, ...). What does the first part of each name denote?

   Hint. Compare consecutive names: a thousand million is a billion, a thousand billion is a trillion — what's counted each time a new prefix is used?

   Step 1 — Recall how each name is built. A thousand thousand is a million (1000²); a thousand million is a billion (1000³); a thousand billion is a trillion (1000⁴) — each new name multiplies the previous one by another 1000, since that is exactly how the prefix sequence bi-tri-quad was defined to work.

   Step 2 — Read off what the prefix tracks. The prefix (bi, tri, quad, ...) denotes how many times 1000 has been multiplied together to reach that number, counting from the base unit of a thousand.

   ✦ Answer: The first part of each name (bi-, tri-, quad-, ...) denotes how many times 1000 is multiplied by itself to build up to that number.

   Where students slip. Assuming the prefix directly equals the power of 10 divided by some fixed number — the prefix instead tracks how many factors of 1000 are chained together, which is why it climbs by exactly 3 in the exponent each time (10⁶, 10⁹, 10¹², ...).

Solutions written by the tuition.in editorial team and checked against the NCERT Class 8 Mathematics textbook Ganita Prakash Part 1, Reprint 2026-27 (hegp102.pdf). Questions are scattered as 'Math Talk'/'Try This' prompts through the running text, plus two formal 'Figure it Out' blocks. Every answer here is checked against the book's own printed answer key at the end of the chapter.. Questions are referenced from the NCERT textbook for identification.