Question:Unit digit in the given product=unit digit in `7^153 xx 1^72`. 

Now `7^4`gives unit digit 1.
:.`7^152` gives unit digit 1.
:.`7^152` gives unit digit `(1 xx 7)=7`
Also `1^72`gives digit 1.
:.Unit digit in the product =`(7 xx 1)=7`.

Question:Unit digit in `7^4` is 1` 

So,unit digit in `7^92` is 1.
:.Unit digit in `7^95` is 3.   [:. Unit digit in `1 xx 7 xx 7 xx `is 3 ]
Unit digit in `3^4`is 1
:. Unit digit in `3^56` is 1.
:. Unit digit in `3^58` is 9. [:.Unit digit in `1 xx 3 xx 3 xx` is 9]
:. Unit digit in `(7^95 - 3^58)` is 4.[Subtracting  unit digit 9 from unit digit]

Question:`4^11 xx 7^5 xx 11^2` 

=`(2 xx 2)^11 xx 7^5 xx 11^2`
=`2^11 xx 2^11 xx 7^5 xx 11^2`
=`2^22 xx 7^5 xx 11^2`.
:.The number of prime factors is (22 + 5 + 2)=29

Question:Convert the following into vulgar fractions :
(i)0.75  (ii) 3.004     (iii) .0056 

(i) `.075=75/100=3/4`.

 (ii) `3.004=3004/100=751/250`.

 (iii) `.0056/1000=7/1250`.

Question:Simplily :  (i) `1.84/2.99`   (ii) `.365/.584` 

(i) `1.84/2.99=184/299=8/13`.
(ii) `.365/.584=365/584=5/8`.

Question:Evaluate :  
           (i)` 617 + 6.017 + .617 +6.0017=?`
           (ii)`5.064 + 3.98 + .7036 + 7.6 + .3 + 2=?`
           (iii)`31.004 - 17.2386=?`
            (iv)`13 - 5.1967=?` 

(i) `617.0`
      `6.017`
     ` 0.617`
     `(+6.0017)/((629.6357)/(0))`

 (ii)`5.064`
     ` 3.98`
      `0.7036`
       `7.6`
       `0.3`
   `(+2.0)/((19.6476)/(913.0000))`

 (iii) `31.004`
         `(-17.2386)/(13.7654)`
   
 (iv) `(-5.1967)/(7.8033)`

Question:(i)`67.32 +? =431.146`  (ii) `107.07 -?=63.932`. 

(i) Let`67.32 + x =431.146`,
 Then, `x = (431.146 -67.32)=363.826`.
  (ii) Let `107.07 - x =63.932`.
Then,` x =(107.07 - 63.932) = 43.138`.

Question:Find the products :
          (i) `6.3204 xx 100`
          (ii) `0.5791 xx 1000`
          (iii) `.o69 xx 10000` 

(i)`6.3204 xx 100 =632.04 `.
(ii) `0.5791 xx 1000 = 579.1`.
 (iii) `0.069 xx 10000 = .0690 xx 10000 =690`.

Question:Find the products :
         (i)` 2.61 xx 1.3 `
                
         (ii) `2.1693 xx 1.4 `
                
         (iii) `.4 xx .04 xx .004 xx 40` 

(i)` 261 xx 13 =3393`.

 The sum of decimal places of given numbers =`(2 +1)=3`

  :.`2.61 xx 1.3 =3.393`.

 (ii) `21693 xx 14 = 303702`.
 
   Sum of decimal places =`(4 + 1)=6`

  :. `2.1693 xx 1.4 =3.03702`.

 (iii) `4 xx 4 xx 4 xx 40 =2560`.

 Sum of decimal places =`(1 + 2 + 3 )=6`.

 :.`4 xx .04 xx .004 xx 40 =.002560`.

Question:Given that `268 xx 74 = 19832`, find `2.68 xx .74`. 

Sum of decimal places =`(2 + 2)=4`.
:.`268 xx 74 = 1.9832`.