Question

5. Is the fraction equivalent to a terminating decimal or a decimal that does not terminate? Explain how you know.

Answer 1

A fraction is said to be equivalent to a terminating decimal if when converted to a decimal has a countable number of digits after the decimal point.

Examples of fractions that are terminating decimals are:

`\begin{gathered} (2)/(5)=0.4 \\ (3)/(8)=0.375 \end{gathered}`

On the other hand, when the digits after the decimal point keep repeating indefinitely, we say such a fraction is equivalent to a repeating decimal.

Examples are:

`\begin{gathered} (7)/(9)=0.777777777\cdots=0.\bar{7} \\ (11)/(999)=0.011011011\cdots=0.\bar{011} \end{gathered}`