Exercise 2.8 - Chapter 2 Real Numbers 9th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Ex $2.8$
Question $1 .$
Represent the following numbers in the scientific notation:
(i) 569430000000
(ii) $2000.57$
(iii) $0.0000006000$
(iv) $0.0009000002$
Solution:
(i) $569430000000=5.6943 \times 10^{11}$
(ii) $2000.57=2.00057 \times 10^{13}$
(iii) $0.0000006000=6.0 \times 10^{-7}$
(iv) $0.0009000002=9.000002 \times 10^{-4}$
 

Question 2.
Write the following numbers in decimal form:
(i) $3.459 \times 10^{6}$
(ii) $5.678 \times 10^{4}$
(iii) $1.00005 \times 10^{-5}$
(iv) $2.530009 \times 10^{-7}$
Solution:
(i) $3.459 \times 10^{6}=3459000$
(ii) $5.678 \times 10^{4}=56780$
(iii) $1.00005 \times 10^{-5}=0.0000100005$
(iv) $2.530009 \times 10^{-7}=0.0000002530009$

Question $3 .$
Represent the following numbers in scientific notation:
(i) $(300000)^{2} \times(20000)^{4}$
(ii) $(0.000001)^{11} \div(0.005)^{3}$
(iii) $\left\{(0.00003)^{6} \times(0.00005)^{4}\right\} \div\left\{(0.009)^{3} \times(0.05)^{2}\right\}$
Solution:
$\begin{aligned}
&\text { (i) }(300000)^{2} \times(20000)^{4}=\left(3.0 \times 10^{5}\right)^{2} \times\left(2.0 \times 10^{4}\right)^{4} \\
&=3^{2} \times 10^{10} \times 2^{4} \times 10^{16} \\
&=9 \times 16 \times 10^{10+16} \\
&=144 \times 10^{26}=1.44 \times 10^{28}
\end{aligned}$

$\begin{aligned}
&\text { (ii) }(0.000001)^{11} \div(0.005)^{3} \\
&\frac{(0.000001)^{11}}{(0.005)^{3}}=\frac{\left(1.0 \times 10^{-6}\right)^{11}}{\left(5.0 \times 10^{-3}\right)^{3}}=\frac{(1.0)^{11} \times 10^{-66}}{(5.0)^{3} \times 10^{-9}} \\
&=1 \times \times 10^{-66+9} \times 5^{3} \\
&=125 \times 10^{-57} \\
&=1.25 \times 10^{2} \times 10^{-57} \\
&=1.25 \times 10^{(-57+2)} \\
&=1.25 \times 10^{-55} \\
&\text { (iii) }\left\{(0.00003)^{6} \times(0.00005)^{4}\right\} \div\left\{(0.009)^{3} \times(0.05)^{2}\right\} \\
&=\frac{\left(3.0 \times 10^{-5}\right)^{6} \times\left(5.0 \times 10^{-5}\right)^{4}}{\left(9.0 \times 10^{-3}\right)^{3} \times\left(5.0 \times 10^{-2}\right)^{2}} \\
&=\frac{3^{6} \times 10^{-30} \times 5^{4} \times 10^{-20}}{9^{3} \times 10^{-9} \times 5^{2} \times 10^{-4}}=\frac{3^{6} \times 5^{4} \times 10^{-30-20}}{\left(3^{2}\right)^{3} \times 10^{-9-4} \times 5^{2}}=\frac{3^{6} \times 5^{4} \times 10^{-50}}{z^{6} \times 5^{2} \times 10^{-13}} \\
&=5^{4-2} \times 10^{-50+13} \\
&=5^{2} \times 10^{-37}=25 \times 10^{-37}=2.5 \times 10^{1} \times 10^{-37}=2.5 \times 10^{-36}
\end{aligned}$

Question 4 .
Represent the following information in scientific notation:
(i) The world population is nearly $7000,000,000$.
(ii) One light year means the distance $9460528400000000 \mathrm{~km}$.
(iii) Mass of an electron is $0.00000000000000000000000000000091093822 \mathrm{~kg}$.
Solution:

(i) The world population is nearly $7000,000,000=7.0 \times 10^{9}$
(ii) One light year means the distance $9460528400000000 \mathrm{~km}=9.4605284 \times 10^{15} \mathrm{~km}$
(iii) Mass of an electron is $0.00000000000000000000000000000091093822 \mathrm{~kg}$. $=$ $9.1093822 \times 10^{-31} \mathrm{~kg}$
 

Question $5 .$
Simplify:
(i) $\left(2.75 \times 10^{7}\right)+\left(1.23 \times 10^{8}\right)$
(ii) $\left(1.598 \times 10^{17}\right)-\left(4.58 \times 10^{15}\right)$
(iii) $\left(1.02 \times 10^{10}\right) \times\left(1.20 \times 10^{-3}\right)$
(iv) $\left(8.41 \times 10^{4}\right) \div\left(4.3 \times 10^{5}\right)$
Solution:
(i) $2.75 \times 10^{7}=27500000$
$1.23 \times 108-123000000$

$\begin{aligned}
&\begin{array}{rr}
\left(2.75 \times 10^{7}\right)+\left(1.23 \times 10^{8}\right)= & 27500000+ \\
& \frac{123000000}{150500000}=1.505 \times 10^{8}
\end{array}\\
&\text { (ii) }\left(1.598 \times 10^{17}\right)-\left(4.58 \times 10^{15}\right)\\
&1.598 \times 10^{17}=159800000000000000\\
&4.58 \times 10^{15}=4580000000000000\\
&\left(1.598 \times 10^{17}\right)-\left(4.58 \times 10^{15}\right)\\
&=159800000000000000\\
&\frac{(-) 4580000000000000}{155220000000000000}=1.5522 \times 10^{17}\\
&\text { (iii) }\left(1.02 \times 10^{10}\right) \times\left(1.20 \times 10^{-3}\right)=1.02 \times 10^{10} \times 1.20 \times 10^{-3}\\
&=1.02 \times 1.20 \times 10^{10-3}=1.224 \times 10^{7}
\end{aligned}$

$\begin{aligned}
&\text { (iv) }\left(8.41 \times 10^{4}\right) \div\left(4.3 \times 10^{5}\right) \\
&=\frac{8.41 \times 10^{4}}{4.3 \times 10^{5}}=\frac{841 \times 10^{-2} \times 10^{4}}{43 \times 10^{-1} \times 10^{5}} \\
&=\frac{841 \times 10^{-2+4}}{43 \times 10^{-1+5}}=\frac{841}{43} \times \frac{10^{2}}{10^{4}} \\
&=1.95581395 \times 10^{1} \times 10^{2-4} \\
&=1.95581395 \times 10^{1} \times 10^{-2} \\
&=1.95581395 \times 10^{-1} \\
&=0.195581395
\end{aligned}$