Question:Divide :
    (i) `0.63` by `9`
    
   (ii) `0.0204` by `17`
    
   (iii) `3.1603` by `13` 

(i )`63 ÷ 9=7`.

 Dividend contain` 2` places of decimal.
  
 :.`0.63 ÷ 9 = .07`.

 (ii) `204 ÷ 17 =12`.

 Dividend contains `4` places of decimal.
   
 :. `0.0204 ÷ 17 = .0012`.

 (iii) `31603 ÷ 13 = 2431 `.

 Dividend contains `4`places of decimal.
   
 :.`3.1606 ÷ 13 = .2431`.

Question:(i)` 0.006  ÷ ? =0.6`     (ii) `? ÷ .025 = 80` 

(i) `(0.006)/x = 0.6 or x`

` = (0.006)/(0.6) = (0.006 xx 10)/(0.6 xx 10) `

 `= (0.06)/6 = .01`

 (ii) ` x ÷ .0025 = 40` 0r `x/(.025) =80`.
     
   :. `x =  80 xx .025 = 2`.

Question:Evaluate :
  (i)` 35 ÷ .07`     

 (ii)` .00066 ÷ 0.11`   

 (iii)` 5.6÷ 0.008` 

(i) ` 35/.07 = (35 xx 100)/(.07 xx 100) = (3500)/7 = 500`.

 (ii) ` (0.00066)/(0.11) = (0.00066 xx 100)/(0.11 xx 100) = (.066)/11 = .006`.

 (iii) ` (5.6)/(0.008) = (5.6 xx 1000)/(0.008 xx 1000) = (5600)/8 = 700`.

Question:Find the H.C.F and L.C.M of` .63, 1.05`and `2.1`. 

Making the same number of decimal places ,the given numbers are `0.63, 1.05` and `2.10`.
Without decimal places ,these numbers are `63, 105` and `210`.
Now, H.C.F. of `.63, 1.05`and `210` is `21`.
:.H.C.F of `.63, 1.05` and `2.1` is `0.21`.
L.C.M. of `63, `05` & `210` is `630`.
:.L.C.M of `63, 1.05` and `2.1` is `6.30`.

Question:Arrange the fractions `5/8, 7/12, 13/16, 16/29,`and `3/4` in acsending order of magnitude. 

Converting  each of the given fraction into decimal form, we get :

`5/8 = 0.625, 7/12 = 0.5833, 13/16`

` = 0.8125, 16/29 = 0.5517 & 3/4 = 0.75`.
 
 Now `0.5517 < 0.5833 < 0.625 <0.75 < 0.8125`
 
 :. `16/29 < 7/12 <5/8 <3/4 < 13/16`.

Question:Express the following as vulgar fractions :
  (i) ` 0.6`     (ii) ` 0.37 `   (iii)  `0.053`   (iv) ` 3.142857` 

(i) `0.6 = 6/9 = 2/3. `      

(ii) ` 0.37 = 37/99`.   

(iii) ` 0.053 = 53/999`.

(iv) `3.142857 = 3+ 0.142857 `

   `= 3 + (142857)/(999999) `

   `= 3 (142857)/(999999)`.

Question:Express the following as vulgar fraction :
 (i) `0.17` (ii) `0.1254` (iii) `2.536` 

(i) ` 0.17 = (17-1)/90 = 16/90 = 8/45`.

 (ii) ` 0.1254 = (1254-12)/(9900)`

   ` = (1242)/(9900) = 69/(550)`.

 (iii) ` 2.536 = 2 + 0.536 = 2+ (536 - 53)/900`

   ` = 2 + 483/900 = 2 + 161/300 = 2 (161)/300`.

Question:`108 ÷ 36` of `1/4 + 2/5 xx 3 1/4`. 

Given Expression, 

`= 108 ÷ 9 + 2/5 xx 13/4`

`= 108/9 + 13/10`

`= (12 + 13/10)`

`= 133/10`

`= 13 3/10`.

Question:`1/3 ÷ 5/3 + 1/4 xx 3/5 - 2/5` of `5/7`. 

Given Expression,

`1/2 ÷ 5/3 + 1/4 xx 3/5 - 2/5` of `5/7`

`= 1/3 ÷ 5/3 + 1/4 xx 3/5 - 2/7`

`= 1/3 xx 3/5 + 3/20 - 2/7`

`= 1/5 + 3/20 - 2/7`

`= (4 + 3)/20 - 2/7`

`= 7/20 - 2/7`

`= ((49 - 40)/(140))`

`= 9/140`.

Question:`3.5 ÷ 0.7` of `7 + 0.5 xx 0.3 - 0.1` 

Given Expression ,

`= 3.5 ÷ 4.9 + 0.5 xx 0.3 - 0.1`

`= 3.5/4.9 + 0.15 - 0.1`

`= 5/7 + 15/100 - 1/10`

` 5/7 + (15 - 10)/100`

`= 5/7 + 5/100`

`= 5/7 + 1/20`

`= ((100 + 7)/(140))`

`= 107/140`

`= 0.764`