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NCERT Solutions for Class 9th Science Chapter 1 Estimation, exactness and the branches of science — Pause and Ponder

Book page 6 Updated on2026-09-08

Q2.
Describe one situation where an approximate answer is good enough, and one where you would need a very exact value.
Answer

The rule that decides between them: ask how much the answer may change before your decision changes. That allowed slack is the precision you need — no more, no less.

Approximate answer is good enough — buying rice for a school picnic.

80 students × about 150 g cooked-rice serving ≈ 12 kg
buy a 15 kg bag — an error of 2 kg either way changes nothing

A 15% error here costs a little extra rice, and nothing else. Estimating is not laziness; measuring each student's appetite would be pointless work.

A very exact value is needed — the dose of a medicine for a child.

paracetamol dose = 15 mg per kg of body weight
for a 20 kg child: 15 mg kg⁻¹ × 20 kg = 300 mg exactly
double this, repeated, and the liver is damaged

Here a 100% error is dangerous, so the child's mass and the syrup's concentration must both be measured properly.

Why it happens: precision costs time, money and equipment, so science spends it only where it changes the outcome. The picnic decision is tolerant — many answers lead to the same action, buy one bag. The medicine decision is sensitive — a small change in the number changes the outcome from cure to harm. The same distinction runs through all of science: an estimate is enough to decide whether an experiment is worth doing, but the final measurement it produces must be as exact as the instrument allows.
More pairs to think about: approximate — how many buses for a school trip, how much paint for a wall, whether a bridge design is even in the right range. Exact — gold weighed at a jeweller's, the diameter of a machine part, the timing of a spacecraft's engine burn.
Q3.
Choose a real‑life object (maybe a pressure cooker or a mobile phone) or a problem (maybe a traffic jam near your school). Make a sketch listing what kind of ideas from physics, chemistry, biology, earth science, or mathematics are involved. Show how at least two branches of science connect with your example.
Answer

Sample answer — the pressure cooker. First list the ideas each branch contributes, then show the chain that links them.

BranchIdeas it contributes
PhysicsPressure of trapped steam; boiling point rises with pressure; conduction of heat through the base; the weight-valve as a force balance
ChemistryStarch grains absorb water and gelatinise; reaction rate roughly doubles for every 10 °C rise; why aluminium and steel are chosen
BiologyHeat kills bacteria and spores; softened starch is easier to digest; how much vitamin C survives the heating
Earth scienceLPG is a fossil fuel; less cooking time means less fuel burnt and less CO₂ released; water boils below 100 °C in the hills
MathematicsReading a pressure–temperature graph; calculating the fuel and time saved as a percentage

How two branches connect. Physics and chemistry are joined by a single chain, and the sketch below traces it:

PHYSICS — the lid seals the vessel, so steam pressure builds up to about 2 × 10⁵ Pa (twice the outside air). PHYSICS — at higher pressure water boils at about 120 °C instead of 100 °C, so the food gets hotter. CHEMISTRY — reaction rate roughly doubles for every 10 °C rise, so a 20 °C rise makes it about 4 times. BIOLOGY — starch gelatinises sooner and bacteria and their spores are destroyed at this temperature. MATHEMATICS and EARTH SCIENCE — about 4 times faster means roughly one-fourth the cooking time, so roughly one-fourth the LPG burnt and one-fourth the CO₂ released.
One chain, four branches: a physics idea (pressure raises the boiling point) sets up a chemistry idea (rate rises with temperature), which produces the biological and environmental result.
Why it happens: the cooker does not cook faster because steam is “under pressure” — pressure by itself does not soften rice. It cooks faster because the pressure lets the water reach 120 °C without boiling away, and the chemical reactions that soften starch speed up sharply with temperature. Take away either link and the explanation fails. That is exactly the point of the chapter: the divisions between physics, chemistry and biology are made by us to organise knowledge, and a single everyday object cuts straight across all of them.
Try this: build the same sketch for a mobile phone — physics (radio waves, battery voltage, touchscreen capacitance), chemistry (lithium-ion cells, the glass), biology (how the eye reads a 60 Hz refresh), earth science (the minerals mined for it, e-waste), mathematics (data compression, error-correcting codes). Then trace one chain across two branches, as above.
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