Question

Match the following numbers on the left hand side with their correct $\frac{p}{q}$ form given on the right hand side.

• A. $\frac{15}{10}$
• B. $\frac{19}{100}$
• C. $\frac{59}{99}$
• D. $\frac{1}{11}$

Answer 1

$\sqrt{2.25}=$

You have to find sqauare root of 2.25.

2.25 can be expressed as$2.25=\frac{225}{100}$

Now, $225=3\times 3\times 5\times 5=15\times 15$

So, $\sqrt{225}=\sqrt{15\times 15}=15$

∴ $\sqrt{2.25}=\sqrt{\frac{225}{100}}=\sqrt{\frac{15\times 15}{10\times 10}}=\frac{15}{10}$


$0.\overline{59}$

It is a non-terminating but repeating decimals.

You can write $0.\overline{59}$ as $0.\overline{59}=0.5959595959........$

So,



Again
$0.\overline{09}$ is a non-terminating but repeating decimals.

You can write $0.\overline{09}$as $0.\overline{09}=0.0909090909........$

So, you can write



$\sqrt{0.0361}=$

You have to find sqauare root of 0.0361

0.0361 can be expressed as$0.0361=\frac{361}{10000}$

Now, $361=19\times 19$

So, $\sqrt{361}=\sqrt{19\times 19}=19$

$\therefore \sqrt{0.0361}=\sqrt{\frac{361}{10000}}=\sqrt{\frac{19\times 19}{100\times 100}}=\frac{19}{100}$