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* 5^{7}* 7^{5} (viii)6/15 (ix)35/50 (x)77/210

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* 5^{7}* 7^{5} (viii)6/15 (ix)35/50 (x)77/210

Answer:

(i) 13/3125 Factorize the denominator we get 3125 =5 x 5 x 5 x 5 x 5 = 5^{5} 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 2^{n} 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 2^{n}*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 = 2^{6} x 5² so denominator is in form of 2^{n} 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 2^{n} x 5^{m} Hence it is none - terminating. (vi) 23/(2³ x 5²) Denominator is in form of 2^{n} x 5^{m} Hence it is terminating. (vii) 129/(2² x 5^{7} x 7^{5} ) Denominator has 7 in denominator so denominator is not in form of 2^{n} x 5^{n} 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 2^{n} 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 2^{n} x 5^{n} Hence it is none terminating.

Open your video in VLC player or add '.mp4' extension at end of the video

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

Please Click on G-plus or Facebook

Please send your queries at contact ncerthelp@gmail.com

Every effort has been made to ensure accuracy of data on this web site. We are not responsible for any type of mistake in data.
All pdf files or link of pdf files are collected from various Resources Or sent by Students. If any pdf file have any copyright voilation please inform us we shell remove that file from our website.Thanks