» Is 14/99 terminating or repeating?
Here are the steps to determine if 14/99 is a terminating decimal number:
1) Find the denominator of 14/99 in its lowest form.
The greatest common factor (GCF) of 14 and 99 is 1. Convert 14/99 to its simplest form by dividing the numerator and denominator by its GCF:
[tex] \frac{14 \div 1}{99 \div 1} = \red{ \frac{14}{99} } \\ [/tex]
2) Find the prime factors of the answer in Step 1.
The prime factors of 99 are all the prime numbers that you multiply together to get 99. The prime factors of 99 are:
[tex]3 \times 3 \times 11 [/tex]
3) Determine if 14/99 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 not the case here, which means that our answer is as follows:
[tex] \frac{14}{99} \\ \mathfrak\green{it \: is \: not \: terminating}[/tex]
