Question

Which of the following rational numbers have the terminating decimal
reprsentation?
1)3/5
2)7/20
3)2/13
4)27/40​

Answer 1

Answer:

3/5, 7/20 & 27/40

Step-by-step explanation:

for a decimal representation to terminate,

the denominator should be of the form,

2^m x 5^n

a. 3/5

therefore,

5= 5¹ x 2^0

therefore,

5 can be written in the form, 2^m x 5^n

therefore, 3/5= 0.6

similarly,

b. 7/20

20= 2² x 5¹

hence, 7/20 has a terminating decimal expansion.

therefore, 7/20= 0.35

similarly,

c. 2/13

13=13x1

since 13 can not be written in the form, 2^m x 5^n,

thus it will not have a terminating decimal expansion...

similarly,

d. 27/40

40=2³x5¹

hence, 27/40 also has a terminating decimal expansion...

therefore, 27/40= 0.675

Therefore, only 3/5, 7/20 & 27/40 will have terminating decimal expansions...

I hope it helps!!

Answer 2

Answer:

here is your answer

Step-by-step explanation:

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