Question #9defc

1 Answer
Daniel L. · Wessly Kennidy
May 6, 2016

see below

Explanation:

#13/2#= Finite decimal
#11/3#= Repeating decimal
#3/5#= Finite decimal
#15/6#= Finite decimal
#17/7#= Repeating decimal
#15/8#= Finite decimal

Every fraction is a rational number, so it cannot be an infinite decimal. Infinite decimal represent irrational numbers like #sqrt(2)#

To check if a fraction is a finite or periodic (repeating) decimal you have to:

  • simplify the fraction

  • check the prime factorization of its denominator.

If the factorization consists only of #2# and #5# the fraction can be written as a finite decimal, else the fraction can be only written as a repeating (periodic) decimal.

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