EXERCISE:4.3
Question 1
i. $530.7=5.367 \times 10^{2}$
ii) $3908 \cdot 78=3.90878 \times 10^{3}$
iii) $39087.8=3.90878 \times 10^{4}$
iv) 2.35 it is a standard form
v) $3,43,000=3.43000 \times 10^{5}$
vi) $70,00,000=7.000000 \times 10^{6}$
vii). $3,18,65,00,000=3.186500000 \times 10^{9}$
Viii) $893,000,000=8.93000000 \times 10^{8}$
ix) $70,040,000,000=7.0040000000 \times 10^{10}$
Question 2
1) $4.7 \times 10^{3}=4700$
ii) $1.205 \times 10^{5}=120500$
iii) $1.234 \times 10^{6}=1234000$
iv) $4.87 \times 10^{7}=48700000$
V) $6.05 \times 10^{8}=605000000$
vi) $9.083 \times 10^{11}=908300000000$
Question 3
i) The distance between earth and the man is 384,00,0000
= $3.84 \times 10^{8} \mathrm{~m}$
ii) The diameter of sun$=1,400,000,000$
$=1.4 \times 10^{9} \mathrm{~m}$
iii) The universe is estimated to be about 12,000,000,000 year old
$=1.2 \times 10^{10}$ years old
iv) In a galaxy there are on an average 100,000,000,000 stars
$=1.0 \times 10^{11}$ stars
v) The distance of sun from the centre of milky way is 300,000,000,000,000,000
$=3 \times 10^{10} \mathrm{~km}$
vi) A light years is about 9,467,500,000,000km
$=9.4635 \times 10^{12} \mathrm{~km}$
Question 4
i) $4.3 \times 10^{14} ; 3.01 \times 10^{17}$
The given numbers are $4.3 \times 10^{14}$ and $3.01\times 10^{17}.$ . Note that both the numbers are in Standard form
Since the power of 10 in 4.3 $\times 10^{14}$ is less than power of 10 in 3.01$\times $ $10^{17} .$
$\therefore 4.3 \times 10^{14}<3.01 \times 10^{17}$
ii) The given numbers are $1.439 \times 10^{12}$ and $1.4335 \times 10^{12}$ . Note that both the numbers are in Standard form. Also note that both the numbers have same power of 10
So, we compare their significants
The significands in $1.439 \times 10^{12}$ is 1.439 and the significand in $1.4335 \times 10^{12}$ is $1.4335 .$
As, $1.439>1.4335$, So
$\therefore \quad 1.439 \times 10^{12}>1.4335 \times 10^{12}$
Question 5
i)279404
$\begin{aligned} 279404=& 2 \times 100000+7 \times 10000+9 \times 1000+4 \times 100+0 \times 10 \\ &+4 \times 1 \\=& 2 \times 10^{5}+7 \times 10^{4}+9 \times 10^{3}+4 \times 10^{2}+0 \times 10^{1}+4 \times 10^{\circ} \\=& 2 \times 10^{5}+7 \times 10^{4}+9 \times 10^{3}+4 \times 10^{2}+4 \times 10^{1} . \end{aligned}$
ii)3006194
$\begin{aligned} 3006194=& 3 \times 1000000+0 \times 100000+0 \times 10000+6 \times 1000+1 \times 100 \\ &+9 \times 10+4 \times 1 \\=& 3 \times 10^{6}+0 \times 10^{5}+0 \times 10^{4}+6 \times 10^{3}+1 \times 10^{2}+9 \times 10^{1}+4 \times 10^{\circ} \\=& 3 \times 10^{6}+6 \times 10^{3}+1 \times 10^{2}+9 \times 10^{\prime}+4 \times 10^{\circ} \end{aligned}$
iii)28061906
$\begin{aligned}=& 2 \times 10000000+8 \times 1000000+0 \times 100000+6 \times 10000+ \\ & 1 \times 1000+9 \times 100+0 \times 10+6 \times 1 \\=& 2 \times 10^{7}+8 \times 10^{6}+0 \times 10^{5}+6 \times 10^{4}+1 \times 10^{3}+9 \times 10^{2} \\ &+0 \times 10^{1}+6 \times 10^{\circ} \\=& 2 \times 10^{\circ}+8 \times 10^{6}+6 \times 10^{4}+1 \times 10^{3}+9 \times 10^{2}+6 \times 10^{\circ} . \end{aligned}$
Question 6
i) $3 \times 10^{4}+7 \times 10^{2}+5 \times 10^{\circ}$
$=3 \times 10000+7 \times 100+5 \times 1$
$=30000+700+5$
$=30705$
ii)
$\begin{aligned} & 4 \times 10^{5}+5 \times 10^{3}+3 \times 10^{2}+2 \times 10^{\circ} \\=& 4 \times 100000+5 \times 1000+3 \times 100+2 \times 1 \\=& 400000+5000+300+2 \\=& 405302 \end{aligned}$
iii) $8 \times 10^{7}+3 \times 10^{4}+7 \times 10^{3}+5 \times 10^{2}+8 \times 10^{1}$
$=8 \times 10000000+3 \times 10000+7 \times 1000+5 \times 100+80$
$=80000000+30000+7000+500+80$
=80037580
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