NCERT Solutions Ganita Prakash (Part 1) Chapter 2 .4 Powers of 10 · Scientific Notation — In-text Questions

Book page 322 Updated on2026-09-05

Q1.

Can you say which of the three distances is the smallest?

Answer

The Sun–Earth distance, 1.496 × 10¹¹ m.

Distance	Standard form	Exponent
Sun to Saturn	1.4335 × 10¹² m	12
Saturn to Uranus	1.439 × 10¹² m	12
Sun to Earth	1.496 × 10¹¹ m	11

10¹¹ is 10 times smaller than 10¹²
1.496 × 10¹¹ ≈ 0.15 × 10¹², which is less than 1.4335 × 10¹²

Why it happens: compare exponents first. All three coefficients are close to 1.4, so the coefficients decide nothing — the exponent does everything. Written in full the three numbers are 14,33,50,00,00,000 m, 14,39,00,00,00,000 m and 1,49,60,00,00,000 m, and you would have to count commas to see which is shortest. That counting is exactly what the exponent does for you.

Did you know? Of the first two, Saturn–Uranus (1.439 × 10¹²) is very slightly the larger — here the coefficients do decide, because the exponents tie.

Q2.

The number line below shows the distance between the Sun and Saturn (1.4335 × 10¹² m). On the number line below, mark the relative position of the Earth. The distance between the Sun and the Earth is 1.496 × 10¹¹ m.

Answer

Find what fraction of the Sun–Saturn distance the Earth sits at.

Earth's distance ÷ Saturn's distance
= (1.496 × 10¹¹) ÷ (1.4335 × 10¹²)
= (1.496 ÷ 1.4335) × 10^11–12
= 1.0436 × 10^–1
≈ 0.104, that is about one-tenth of the way along

So the Earth's mark goes very close to the Sun — about a tenth of the line from the left end.

The whole line is 1.4335 × 10¹² m. The Earth mark is roughly one-tenth of the way from the Sun.

Why it happens: dividing two numbers in standard form is easy — divide the coefficients and subtract the exponents. The subtraction 11 – 12 = –1 immediately says "about a tenth", before you touch the coefficients at all. That is the practical value of the notation: the rough answer arrives first, the precision afterwards.

Q3.

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

Answer

Move the decimal point so that exactly one non-zero digit stands before it; the number of places moved is the exponent.

	Number	Places moved	Standard form
(i)	59,853	4	5.9853 × 10⁴
(ii)	65,950	4	6.595 × 10⁴
(iii)	34,30,000	6	3.43 × 10⁶
(iv)	70,04,00,00,000	10	7.004 × 10¹⁰

Why it happens: moving the decimal point one place to the left divides the number by 10, so it must be balanced by multiplying by 10¹. Moving it k places left therefore costs a factor 10^k. Trailing zeros are dropped from the coefficient but the internal zeros are not: in (iv) the 0s of 7.004 are between significant digits and carry information, while the ten trailing zeros are wholly accounted for by 10¹⁰.

Check it yourself: the exponent is always one less than the number of digits in a whole number. 59,853 has 5 digits, so the exponent is 4; 70,04,00,00,000 has 11 digits, so the exponent is 10.

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