Ants per human = (2 × 1016) ÷ (8 × 109) = 0.25 × 107 = 2.5 × 106 ants per person
That is about 25 lakh ants for each of us. Using the sharper figure 8.2 × 109 for the human population gives 2.4 × 106 — the same to one significant figure, which is all the data deserves.
Why it happens: 0.25 × 107 is a correct value but not standard form, since the coefficient must be at least 1. Moving the decimal point one place right multiplies by 10, so the exponent must drop by 1: 0.25 × 107 = 2.5 × 106. Watch for this whenever the top coefficient is smaller than the bottom one.
Q2.
Calculate and write the answer using scientific notation: (ii) If a flock of starlings contains 10,000 birds, how many flocks could there be in the world?
Number of flocks = (1.3 × 109) ÷ 104 = 1.3 × 109–4 = 1.3 × 105 flocks (about 1,30,000)
Why it happens: dividing by a pure power of 10 leaves the coefficient untouched and only lowers the exponent — the fastest kind of division there is. It also shows why the answer is already in standard form: 1.3 was between 1 and 10 to begin with and nothing changed it.
Q3.
Calculate and write the answer using scientific notation: (iii) If each tree had about 10⁴ leaves, find the total number of leaves on all the trees in the world.
Answer
Trees ≈ 30 kharab / 3 trillion = 3 × 1012 Leaves per tree = 104
That is 30 padma leaves — about the same order as the number of ants on Earth (2 × 1016), which is a pleasant thing to notice.
Why it happens: multiplying in standard form is the mirror of dividing — multiply the coefficients, add the exponents. Here the coefficient stays 3 because the other factor is a bare power of 10.
Q4.
Calculate and write the answer using scientific notation: (iv) If you stacked sheets of paper on top of each other, how many would you need to reach the Moon?
Answer
Distance to the Moon = 3,84,400 km = 3.844 × 1010 cm Thickness of one sheet = 0.001 cm = 10–3 cm
About 38 lakh crore sheets — and yet a single sheet folded 46 times covers the same distance, because 246 ≈ 7 × 1013.
Why it happens: dividing by 10–3 is the same as multiplying by 103, which is why the exponent went up. Subtracting a negative number adds, and this is where that rule earns its keep. It is also the neatest summary of the whole chapter: stacking 3.8 × 1013 sheets is linear, folding one sheet 46 times is exponential, and both end at the Moon.