4 Mark Question

Question 14 Marks

Write the following numbers in standard form.
(i) 0.000000564
(ii) 0.0000021
(iii) 21600000
(iv) 15240000

Answer

(i) We have, 0.000000564
$\begin{array}{l}
=\frac{564}{1000000000} \\
=\frac{564}{10^9}=\frac{5.64 \times 100}{10^9} \\
=5.64 \times 10^2 \times 10^{-9} \\
=5.64 \times 10^{-7} \quad\left[\because a^m \times a^n=a^{m+n}\right]
\end{array}$
which is the required standard form.
(ii) Ans. $2.1 \times 10^{-6}$
(iii) We have, 21600000
$\begin{array}{l}
=216 \times 10^5 \\
=2.16 \times 10^2 \times 10^5 \\
=2.16 \times 10^7 \quad\left[\because a^m \times a^n=a^{m+n}\right]
\end{array}$
which is the required standard form.
(iv) Ans. $1.524 \times 10^7$

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Question 24 Marks

The given table shows the crop production of a state in the year 2008 and 2009. Observe, the table given below and answer the given questions.

Crop	2008 Harvest (in hectare)	Increase/Decrease in 2009 (in hectare)
Bajra	$1.4 \times 10^3$	-100
Jowar	$1.7 \times 10^6$	-440000
Rice	$3.7 \times 10^3$	-100
Wheat	$5.1 \times 10^5$	190000

(i) For which crop(s) did the production decrease?
(ii) Write the production of all the crops in 2009 in their standard form.
(iii) Assuming the same decrease in rice production each year as in 2009, how many acres will be harvested in 2015 ? Write in standard form.

Answer

(i) Production decreased for bajra, jowar and rice.
(ii) Production of bajra in $2008=14 \times 10^3$ and decrease in production of bajra in 2009
$
=100=0.1 \times 10^3
$
So, production of bajra in 2009
$
\begin{array}{l}
=14 \times 10^3-01 \times 10^3 \\
=(1.4-0.1) \times 10^3=1.3 \times 10^3
\end{array}
$
Production of jowar in $2008=1.7 \times 10^6$
and decrease in production of jowar in 2009
$
=440000=0.44 \times 10^6
$
So, production of jowar in 2009
$
\begin{array}{l}
=1.7 \times 10^6-0.44 \times 10^6 \\
=(1.7-0.44) \times 10^6=1.26 \times 10^6
\end{array}
$
Production of rice in 2008 $=37 \times 10^3$ and decrease in production of rice in 2009
$
=100=01 \times 10^3
$
So, production of rice in 2009
$
\begin{array}{l}
=3.7 \times 10^3-01 \times 10^3 \\
=(3.7-01) \times 10^3=36 \times 10^3
\end{array}
$
Production of wheat in $2008=51 \times 10^5$ and increase in production of wheat in 2009
$
=190000=1.9 \times 10^5
$
So, production of wheat in 2009
$
\begin{array}{l}
=51 \times 10^5+19 \times 10^5 \\
=(5.1+19) \times 10^5=7.0 \times 10^5
\end{array}
$
(iii) Decrease in production of rice in 2009
$
=01 \times 10^3
$
After 7 yr , decrease in production
$
=7 \times 01 \times 10^3=0.7 \times 10^3
$
So, production of rice in 2015
$
\begin{array}{l}
=3.7 \times 10^3-0.7 \times 10^3 \\
=(3.7-0.7) \times 10^3=3.0 \times 10^3 hec
\end{array}
$
Hence, $3.0 \times 10^3 hec$ will be harvested in 2015 .

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