बिना लम्बी विभाजन प्रक्रिया किये बताइए कि निम्नलिखित परिमेय संख्याओं के दशमलव प्रसार सांत है या असांत आवर्ती है :
(i) `(13)/(3125)` (ii) `(17)/(8)` (iii) `(64)/(455)`
(iv) `(15)/(1600)` (v) `(29)/(343)` (vi) `(23)/(2^(3)5^(2))`
(vii) `(129)/(2^(2)5^(7)7^(5)` (viii) `(6)/(15)` (ix) `(35)/(50)` (x) `(77)/(210)`

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:(i) (13)/(3125) (ii) (17)/8 (iii) (64)/(455) (iv) (15)/1600 (v) (29)/(343) (vi) (23)/(2^35^2) (vii) (129)/(2^25^77^5) (viii) (6)/(15) (ix) (35)/(50) (x) (77)/(210)

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:(i) (13)/(3125) (ii) (17)/8 (iii) (64)/(455) (iv) (15)/1600 (v) (29)/(343) (vi) (23)/(2^35^2) (vii) (129)/(2^25^77^5) (viii) (6)/(15) (ix) (35)/(50) (x) (77)/(210)

Write down the fractional number for each of the following: (i) (2)/(3) (ii) (4)/(9) (iii) (2)/(5) (iv) (7)/(10) (v) (1)/(3) (vi) (3)/(4) (vii) (3)/(8) (viii) (9)/(14) (ix) (5)/(11) (x) (6)/(15)

Solve (i) 2-(3)/(5)(ii)4+(7)/(8)(iii)(3)/(5)+(2)/(7)(iv)(9)/(11)-(4)/(5)(v)(7)/(10)+(2)/(5)+(3)/(2)(vi)(2)(2)/(3)+(3)(1)/(2) (vii) (8)(1)/(2)-(3)(5)/(8)

Evaluate : (i) (3)/(4)-(4)/(5) (ii) -3-(4)/(7) (iii) (7)/(24)-(19)/(36) (iv) (14)/(15)-(13)/(20) (v) (4)/(9)-(2)/(-3) (vi) (7)/(11)- (-4)/(-11) (vii) (-5)/(14) -(-2)/(7) (viii) (-5)/(-8)-(-3)/(4)

Write five fractions equivalent to each of the following: (i) (2)/(3) (ii) (4)/(5) (iii) (5)/(8) (iv) (7)/(10) (v) (3)/(7) (vi) (6)/(11) (vii) (7)/(9) (viii) (5)/(12)

Convert each of the following Into an improper fraction: (i) 5(5)/(7) (ii) 9(3)/(8) (iii) 6(3)/(10) (iv) 3(5)/(11) (v) 10(9)/(14) (vi) 12(7)/(15) (vii) 8(8)/(13) (viii) 51(2)/(3)

Find the multiplicative inverse (i.e., reciprocal) of : {:((i) (13)/(25), (ii) (-17)/(12) , (iii) (-7)/(24), (iv) 18, (v) -16),((vi) (-3)/(-5) , (vii) -1, (viii) (0)/(2), (ix) (2)/(-5), (x) (-1)/(8)):}

Multiply : (i) (3)/(4) by (5)/(7) (ii) (9)/(8) by (32)/(2) (iii)(7)/(6) by 24 (iv) (-2)/(3) by (6)/(7) (v) (-12)/(5) by (10)/(-3) (vi) (25)/(-9) by (3)/(-10) (vii) (-7)/(10) by (-40)/(21) (viii) (-36)/(5) by (20)/(-3) (ix) (-13)/(15) by (-25)/(26)

Find the value of: (i) (-4) -: 2/3 (ii) (-3)/5 -: 2 (iii) (-4)/5 -: (-3) (iv) (-1)/8 -: 3/4 (v) (-2)/(13) -: 1/7 (vi) (-7)/(12) -: ((-2)/(13)) (vii) 3/(13) -: ((-4)/(65))