Express the following rational numbers as decimals

Solution:

(i) Given rational number is  

 

Now we have to express this rational number in decimal form. So we will use the long division method 

Therefore $\frac{2}{3}=0.6666$

$\Rightarrow \frac{2}{3}=0 . \overline{6}$

Hence, $\frac{2}{3}=0 . \overline{6}$

 

(ii) Given rational number is  

 

Now we have to express this rational number into decimal form. So we will use long division method

Therefore, $\frac{4}{9}=0.444$

$\Rightarrow-\frac{4}{9}=-0 . \overline{4}$

Hence, $-\frac{4}{9}=-0 . \overline{4}$

 

(iii) Given rational number is  

 

Now we have to express this rational number into decimal form. So we will use long division method

Therefore $\frac{2}{15}=0.1333$

$\Rightarrow \frac{2}{15}=0.1 \overline{3}$

Hence, $-\frac{2}{15}-0.1 \overline{3}$

 

(iv) Given rational number is  

 

Now we have to express this rational number into decimal form. So we will use long division method

Therefore $\frac{22}{13}=1.692307 \ldots$

$\Rightarrow \frac{22}{13}=1 . \overline{692307}$

Hence, $-\frac{22}{13}=-1 . \overline{692307}$

 

(v) Given rational number is  

 

Now we have to express this rational number into decimal form. So we will use long division method

$\Rightarrow \frac{437}{999}=0 . \overline{437}$

Hence, $\frac{437}{999}=0 . \overline{437}$

 

(vi) Given rational number is  

 

Now we have to express this rational number into decimal form. So we will use long division method

Therefore $\frac{33}{26}=1.2 \overline{692307} \ldots$

Hence, $\frac{33}{26}=1.2 \overline{692307}$