Question

Without actual division, determine which of the following are terminating decimals and which are non-terminating decimals: (show working)

56

25

305

108

391

256

41

49

131

36

Answer 1

Answer:

I thought 25 is terminating while some other are also..

and here many number are non terminating too.

example of steps here to check which one is teminating

Step-by-step explanation:

1) Find the denominator of 25/25 in its lowest form.

The greatest common factor (GCF) of 25 and 25 is 25. Convert 25/25 to its simplest form by dividing the numerator and denominator by its GCF:

25 ÷ 25

25 ÷ 25

=

1

1

Thus, the denominator of 25/25 in its lowest form is 1.

2) Find the prime factors of the answer in Step 1.

The prime factors of 1 are all the prime numbers that you multiply together to get 1. The prime factors of 1 are:

none

3) Determine if 25/25 is terminating

A fraction is a terminating decimal if the prime factors of the denominator of the fraction in its lowest form only contain 2s and/or 5s or no prime factors at all. This is the case here, which means that our answer is as follows:

25/25

= terminating

Answer 2

For terminating decimal the prime factorization of denominator should only contain factor 2 or factor 5 or both factors 2 and 5. Prime factorization of denominator containing factors 2 & any other number of factors 5 & any other number of factors 2,5 & any other number is non-terminating decimals