Question

Please answer.
Ex 2.2 - Page 27

Q1 - b, d

Q2 - b, d, f

Q3, 4, 5, 6

Answer 1

scientific notation means expressing numbers as the product of

(i) a *rational* decimal number with 1 digit to the left of the decimal point

(ii) an *integer* power of 10

1)

b) $1.25436 * 10^8$

c) $3.452085 * 10^5$

2)

b)

        $2.05 * 10^{-3}\\\\= \frac{2.05}{10^3}\\\\= 0.00205$

d) $345000000.0$

f) 0.000000899

3)

1 billion = 1,00,00,00,000 (1 arab in indian number system/hindu arabic system)

1 billionth = 1 / 1 billion = $10^{-9}$

so, 1 angstrom = $1*10^{-9}$ meter

4)

time per each calculation, $t=0.0000034sec=3.4*10^{-6}$

number of caculations, $n = 4000=4*10^{3}$

so, total time

$=t*n\\\\=3.4*10^{-6}*4*10^{3}\\\\=13.6*10^{-3}$

answer is $1.36*10^{4}sec$ (standard form)

5)

(( ≈ means close to, not equal to = ))

seconds in hour ≈ 60 * 60 = 3600 sec

seconds in day ≈ 3600 * 24 = 86400 sec

seconds in week ≈ 86400 * 7 = 604800 sec

(( i'll leave month and year for you as a h/w ))

seconds in week in scientific notation $= 6.048 * 10^5sec$

(( again, you should find all of the above scientific notations as an exercise ))

6)

1 hectare $=10000sq.m=(100m)^{2}$

1 meter is 100 cm, so 1 meter squared is $100^{2}$ cm

so, 1 hectare

$=(100*100cm)^{2}\\\\=(10000cm)^{2}\\\\=100000000cm^2\\\\=10^{8}cm^{2}$

or, $1*10^{8}cm^2$

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