Question

without performing division state whether the following rational numbers are terminating or non terminating recurring decimals 16/125 ,77/70, 161/230​

Answer 1

Step-by-step explanation:

p/q is terminating if

a) p and q are co-primes

and

b) q is of the form 2power m^5power n

where m and n are non negative integers

i)

11/12

11 and 12 have no common factors ,

so 11 and 12 are co-primes

12= 2power 2^3power 1

and the denominator 12 is not of the form 2power m^5power n

hence

11/12 is a non-terminating repeating decimal

ii)

15/1600=3/320

here, 3 and 320 have no common factors

so 3 and 320 are co-primes

320= 2power 6^5power 1

where, m=6 and n=1

and the denominator 320 is of the form 2power m^5power n

where, m and n are non negative integers

hence

15/1600 is a terminating decimal