determine whether the number has a terminating decimal expansion, If it does give expansion 4/60

Question

 Is 4/60 a terminating decimal expansion if so give expansion.

Answer 1

you can determine if the decimal expansion of a fraction terminates or repeats

 

express the fraction in lowest terms

write the prime factorization of the denominator

if the prime factorization contains all 2's, all 5's, or a combination of 2's and 5's only, then the decimal expansion is terminating

if the prime factorization contains any other prime numbers other than 2's or 5's, then the decimal expansion will be repeating

examples...

1/2=0.5 (2)

3/4=0.75 (2*2)

2/5=0.4 (5)

7/8=0.875 (2*2*2)

9/10=0.9 (2*5)

11/16=0.6875 (2*2*2*2)

17/20=0.85 (2*2*5)

24/25=0.96 (5*5)

29/32=0.90625 (2*2*2*2*2)

19/40=0.475 (2*2*2*5)

37/50=0.74 (2*2*5*5)

111/125=0.888 (5*5*5)

and so on...

 

2/3=0.666...(3)

5/6=0.8333... (2*3)

5/7=0.714285714285714285... (7)

8/9=0.888... (3*3)

9/11=0.818181... (11)

11/12=0.91666... (2*2*3)

12/13=0.923076923076923076... (13)

17/21=0.809523809523809523... (3*7)

25/27=0.925925925... (3*3*3)

19/30=0.6333... (2*3*5)

9/19=0.473684210526315789473684210526315789...

Answer 2

Hi Wnada, a terminating decimal has digits that do not go on forever. An example is 1/25, or .04. No digits exists after the 4.

 

With, 4/60, or 1/15 (reduced fraction), the fraction as a decimal is: 0.06666....

 

Therefore, 4/60 is not a terminating decimal.

 

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