Question

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:
a) 77/210
b) 15/1600
c) 19/34

Answer 1

Answer:

Step-by-step explanation:

All the three are non terminating decimals

Answer 2

Answer:

Rational numbers

Step-by-step explanation:

$\frac{77}{210} = \frac{7*11}{7*3*10}= \frac{11}{3*10}$

this is show that in denominator there is a 3 excluding 2*5 = 10

So, 77/210 is non terminating decimal.

Similarly

$\frac{15}{1600} = \frac{15}{16*100} = \frac{15}{2^{2} 10^{2}}$

so, the denominator of 15/1600 is in the form of $2^{m} and 5^{n}$

hence it is a terminating decimal..

Similarly

19/34 = 19/2*17

2*17 is not in the form of $2^{m} and 5^{n}$

hence it is non terminating decimal.