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NCERT Solutions Ganita Prakash (Part 1) Chapter 2 –422.5 Did You Ever Wonder? — In-text Questions

Book page 41 Updated on2026-09-05

Q1.
A fossil of Kelenken Guillermoi, a type of terror bird, is dated to 15 million years ago ( ≈_______________ seconds). [Fill in the blank.]
Answer

≈ 4.7 × 1014 seconds

1 year ≈ 3.15 × 107 seconds
15 million years = 1.5 × 107 years

Time = (1.5 × 107) × (3.15 × 107)
= (1.5 × 3.15) × 107+7
= 4.725 × 1014
≈ 4.7 × 1014 seconds

This sits in the 1014-second row, which the table gives as ≈ 3.17 million years — and 15 ÷ 3.17 ≈ 4.7, matching the coefficient exactly.

Why it happens: the row heading itself is a conversion factor. Once you know 1014 s ≈ 3.17 million years, any span in that row can be converted by a single division of coefficients, with no need to touch the exponent. Reading a table this way is much faster than multiplying out year lengths every time.
Q2.
Plants on land started 47 crore/470 million years ago ( ≈ _______________ seconds). [Fill in the blank.]
Answer

≈ 1.5 × 1016 seconds

470 million years = 4.7 × 108 years
1 year ≈ 3.15 × 107 seconds

Time = (4.7 × 108) × (3.15 × 107)
= 14.8 × 1015
= 1.48 × 1016 ≈ 1.5 × 1016 seconds

Cross-check with the row heading: 1016 s ≈ 31.7 crore years, and 47 ÷ 31.7 ≈ 1.5. ✓

Why it happens: notice the intermediate 14.8 × 1015. It is right but not standard, so the decimal point moves one place left and the exponent rises by 1. Every multiplication in standard form may need this final adjustment, because two coefficients under 10 can multiply to something over 10.
Q3.
Calculate and write the answer using scientific notation: (i) If one star is counted every second, how long would it take to count all the stars in the universe? Answer in terms of the number of seconds using scientific notation.
Answer
Stars in the observable universe ≈ 2 × 1023
Rate = 1 star per second

Time = 2 × 1023 ÷ 1
= 2 × 1023 seconds

How long is that? Convert to years:

(2 × 1023) ÷ (3.15 × 107)
≈ 0.63 × 1016 = 6.3 × 1015 years

The universe itself is about 1.38 × 1010 years old, so counting the stars one per second would take roughly 4.6 lakh times the age of the universe.

Why it happens: the number of seconds is easy — one per star — but it means nothing until it is compared with something we know. Turning 2 × 1023 seconds into "far longer than the universe has existed" is the whole purpose of this section: very large quantities are beyond experience, so we relate and compare them with quantities we are familiar with.
Q4.
Calculate and write the answer using scientific notation: (ii) If one could drink a glass of water (200 ml) every 10 seconds, how long would it take to finish the entire volume of water on Earth?
Answer
Drops of water on Earth ≈ 2 × 1025, at 16 drops per millilitre

Volume = (2 × 1025) ÷ 16 ml
= 0.125 × 1025 = 1.25 × 1024 ml

Glasses = 1.25 × 1024 ÷ 200
= 0.00625 × 1024 = 6.25 × 1021 glasses

Time = 6.25 × 1021 × 10 s
= 6.25 × 1022 seconds

In years that is about 2 × 1015 years — again far beyond the age of the universe.

Why it happens: the chain has three steps — drops to millilitres, millilitres to glasses, glasses to seconds — and each one is a division or multiplication in standard form, so the exponents simply run 25 → 24 → 21 → 22. Keeping the working in this notation is what makes a three-step calculation on 25-digit numbers something you can do on one line.
Did you know? 1018 seconds ago the universe did not exist according to modern physics, so an answer of 1022 seconds is not a length of time anyone could ever spend. These questions are thought experiments, meant to build a feel for scale.
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