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## Question 1. 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)23/2³*5² (vii)129/2²* 57* 75 (viii)6/15 (ix)35/50 (x)77/210

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Question 1. 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)23/2³*5²
(vii)129/2²* 57* 75
(viii)6/15
(ix)35/50
(x)77/210

(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 5m 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*5m . 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 5m
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 5m
Hence it is none - terminating.
(vi) 23/(2³ x 5²)
Denominator is in form of 2n x 5m
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 5m 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 x5m 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.

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Without actually performing the long division, state whether rational numbers will have a terminating decimal expansion or non-terminating
how to check for terminating ration number with long division, Without long division Check rational numbers terminating