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

(i) `63 /9 =7`
Dividend contains 4 places of decimal. 
`:. 63 / 9 =.07`

(ii) `204 /17 = 12`
Divided contains 4 places of decimal
`0.0204 / 17 =.0012`

(iii)  `31603 / 13 =2431`
Divided contains 4 places of decimal.
 `:. 3.1603 / 13 = .2431`

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

(ii) `.00066/.11`

(iii) `5.6/0.008` 

(i) `35/.07`

 `=(35 xx 100)/(.07 xx 100)` 

 `=3500/7` 

 `=500`


 (ii) `.00066/.11`

 =`(.00066 xx 100)/(.11 xx 100)` 

 =`.066/11` 

 = `006`


 (iii) `5.6/0.008`

 `=(5.6 xx 100)/(.008 xx 100)`

 `=5600/8` 

 `=700`

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)` 

 = `0.06/10` 

 `=.01`


(ii) `x/.025 = 80`

 or `x/.025=80` 

`:. x = 80 xx .025 =2`

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, 105 and 210 is 21.

 `:.` H.C.F of. 63, 1.05 and 2.10 is 0.21.

  L.C.M of 63, 105 and 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 ascending order of magnitude. 

Converting each of the given fractions 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`

Question:Find the square root of 1471369 

`:.  sqrt(1471369)` = 1213

Question:Evaluate: `sqrt(175.2976)` 

`:. sqrt(175.2976)` = 13.24

Question:Evaluate `sqrt(0.9)` upto places of decimal. 

`:. sqrt(0.9)` = 0.948

Question:Evaluate:
(i) `sqrt 48 xx sqrt 12` 
(ii) `sqrt 128/sqrt 162` 

(i) `sqrt 48 xx sqrt 12`

= `sqrt(48 xx 12)`

= `sqrt (2 xx 2 xx 12 xx 12)`

= `(2 xx 12)`

=24

(ii) `sqrt 128/sqrt 162`

= `sqrt(128/162)`

= `sqrt (64/81)`

=`8/9`