[2 Mark Question Answer]

Question 12 Marks

Check whether the square of the following is rational or irrational$:\frac{3 \sqrt{2}}{2}$

Answer

$\left(\frac{3 \sqrt{2}}{2}\right)^2$
$=\frac{9 \times 2}{4}$
$=\frac{9}{2}$,
which is rational

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Question 22 Marks

Check whether the square of the following is rational or irrational$:3 \sqrt{2}$

Answer

$(3 \sqrt{2})^2 $
$=9 \times 2$
$ =18,$ which is rational

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Question 32 Marks

State whether the following number is rational or irrational$:\left(\frac{\sqrt{5}}{3 \sqrt{2}}\right)^2$

Answer

$\left(\frac{\sqrt{5}}{3 \sqrt{2}}\right)^2 $
$=\frac{5}{9 \times 2} $
$=\frac{5}{18},$
which is rational

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Question 42 Marks

Insert a rational number between$:101$ and $102$

Answer

A rational number lying between $101$ and $102$
$=\frac{101+102}{2}$
$=\frac{203}{2}$
$=101.5$

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Question 52 Marks

Insert a rational number between$:8$ and $8.04$

Answer

A rational number lying between $8$ and $8.04$
$=\frac{8+8.04}{2} $
$=\frac{16.04}{2} $
$=8.02$

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Question 62 Marks

Insert a rational number between:$7.6$ and $7.7$

Answer

A rational number lying between $7.6$ and $7.7$
$=\frac{7.6+7.7}{2}$
$=\frac{15.3}{2} $
$=7.65$

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Question 72 Marks

Insert a rational number between$:3$ and $4$

Answer

A rational number lying between $3$ and $4$
$=\frac{3+4}{^2} $
$=\frac{7}{2}$
$=3.5$

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Question 82 Marks

Convert the following fraction into a decimal $:\frac{12}{21}$

Answer

$\frac{12}{21} $
$ =0.571428571428 \ldots $
$ =0 . \overline{571428}$

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Question 92 Marks

Convert the following fraction into a decimal $:\frac{-2}{7}$

Answer

$\frac{-2}{7} $
$=0.285714285714 \ldots$
$ =-0 . \overline{285714}$

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Question 102 Marks

Convert the following fraction into a decimal $:\frac{8}{11}$

Answer

$\frac{8}{11}$
$=0.72727272 \ldots$
$=0 . \overline{72}$

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Question 112 Marks

Express the following decimal as a rational number$.4.56$

Answer

$4.56$
$ =\frac{456}{100} $
$=\frac{456 \div 4}{100 \div 4} $
$ =\frac{114}{25}$

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Question 122 Marks

State if the following fraction has a terminating decimal$.\frac{147}{160}$

Answer

$\frac{147}{160} $
$ 160=2 \times 2 \times 2 \times 2 \times 2 \times 5=2^5 \times 5^1$
i.e. $160$ can be expressed as $2^{ m } \times 5^{ n } \text {. }$
Hence, $\frac{147}{160}$ has terminating decimal representation.

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Question 132 Marks

State if the following fraction has a terminating decimal$.\frac{125}{213}$

Answer

$\frac{125}{213} $
$213=3 \times 71$
i.e. $213$ cannot be expressed as $2^m \times 5^n$.
Hence, $\frac{125}{213}$ does not have terminating decimal representation.

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Question 142 Marks

State if the following fraction has a terminating decimal$.\frac{89}{125}$

Answer

$\frac{89}{125} $
$125=5 \times 5 \times 5=2^0 \times 5^3$
i.e. $125$ can be expressed as $2^m \times 5^n$.
Hence, $\frac{89}{125}$ has terminating decimal representation.

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Question 152 Marks

State if the following fraction has a terminating decimal$.\frac{59}{75}$

Answer

$\frac{59}{75}$
$75=5 \times 5 \times 3=2^2 \times 3^1$
i.e. $75$ can not be expressed as $2^m \times 5^n$.
Hence, $\frac{59}{75}$ does not have terminating decimal representation.

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Question 162 Marks

State if the following fraction has a terminating decimal.$\frac{57}{64}$

Answer

$\frac{57}{64} $
$64=2 \times 2 \times 2 \times 2 \times 2 \times 2=2^6 \times 5^0$
i.e. $64$ can be expressed as $2^m \times 5^n$.
Hence, $\frac{57}{64}$ has terminating decimal representation.

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Question 172 Marks

State if the following fraction has a terminating decimal.$\frac{37}{40}$

Answer

$\frac{37}{40} $
$40=2 \times 2 \times 2 \times 5=2^3 \times 5^1$
i.e. $40$ can be expressed as $2^m \times 5^n$.
Hence, $\frac{37}{40}$ has terminating decimal representation.

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Question 182 Marks

State if the following fraction has a terminating decimal.$\frac{25}{49}$

Answer

$\frac{25}{49} $
$49=7 \times 7$
i.e. $49$ can not be expressed as $2^m \times 5^n$.
Hence, $\frac{25}{49}$ does not have terminating decimal representation.

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Question 192 Marks

State if the following fraction has a terminating decimal.$\frac{5}{7}$

Answer

$\frac{5}{7} $
$ 7=1 \times 7 $
i.e.,$ 7$ can not be expressed as $2^m \times 5^n$.
$\therefore \frac{5}{7}$ does not have terminating decimal representation.

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Question 202 Marks

State if the following fraction has a terminating decimal.$\frac{3}{5}$

Answer

$\frac{3}{5} $
$5=1 \times 5=2^0 \times 5^1$
i.e., $5$ can be expressed as $2^m \times 5^n$.
$\therefore \frac{3}{5}$ has terminating decimal representation.

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MATHEMATICS [2 Mark Question Answer]

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