Without Long Division Check Rational Numbers Terminating Exercise 1.4 Chapter 1 Real Numbers Maths Class 10 NCERT

Answer:

(i) 13/3125
Factorize the denominator we get
3125 =5 x 5 x 5 x 5 x 5 = 5⁵
So denominator is in form of 5^m so 13/3125 is terminating .
(ii) 17/8
Factorize the denominator we get
8 =2 x 2 x 2 = 2³
So denominator is in form of 2ⁿ so 17/8 is terminating .
(iii) 64/455
Factorize the denominator we get
455 =5 x 7 x 13
There are 7 and 13 also in denominator so denominator is not in form of 2ⁿ*5^m . hence 64/455 is not terminating.
(iv) 15/1600
Factorize the denominator we get
1600 =2 x 2 x 2 x2 x 2 x 2 x 5 x 5 = 2⁶ x 5²
so denominator is in form of 2ⁿ x 5^m
Hence 15/1600 is terminating.
(v) 29/343
Factorize the denominator we get
343 = 7 x 7 x 7 = 7³
There are 7 also in denominator so denominator is not in form of 2ⁿ x 5^m
Hence it is none - terminating.
(vi) 23/(2³ x 5²)
Denominator is in form of 2ⁿ x 5^m
Hence it is terminating.
(vii) 129/(2² x 5⁷ x 7⁵ )
Denominator has 7 in denominator so denominator is not in form of 2ⁿ x 5ⁿ
Hence it is none terminating.
(viii) 6/15
divide nominator and denominator both by 3 we get 2/5
Denominator is in form of 5^m so it is terminating.

(ix) 35/50 divide denominator and nominator both by 5 we get 7/10
Factorize the denominator we get
10=2 x 5
So denominator is in form of 2ⁿ x5^m so it is terminating
(x) 77/210.
simplify it by dividing nominator and denominator both by 7 we get 11/30
Factorize the denominator we get
30=2 x 3 x 5
Denominator has 3 also in denominator so denominator is not in form of 2ⁿ x 5ⁿ
Hence it is none terminating.