Without actual division, state whether the following rational number is terminating decimal or not. $$\dfrac{5}{12}$$.
$$\dfrac{5}{12}=\dfrac{5}{2\times 2\times 3}=\dfrac{5}{2^2\times 3}$$
$$\dfrac{5}{12}$$ Has the prime factors in the denominator as $$2$$ and $$3$$.
Thus $$\dfrac{5}{12}$$ is not a terminating decimal.
Look at several examples of rational numbers in the form $$\displaystyle\frac{p}{q}(q\neq 0)$$, where $$p$$ and $$q$$ are integers with no common factors other than $$1$$ and having terminating decimal representaions (expansions). Can you guess what property $$q$$ must satisfy?
Which of the following fractions will terminate when expressed as a decimal? (Choose all that apply.)
If $$\displaystyle d=\frac { 1 }{ { 2 }^{ 3 }\times { 5 }^{ 7 } } $$ is expressed as a terminating decimal, how many non zero digits will $$d$$ have?
Without actually performing the long division, state whether the following rational number have terminating or non-terminating repeating (recurring) decimal expansion: $$\frac{3}{8}$$
Without actually performing the long division, state whether the following rational number has terminating or non-terminating repeating (recurring) decimal expansion: $$\dfrac{29}{343}$$
Without actually performing the long division, state whether the following rational number have terminating or non-terminating repeating (recurring) decimal expansion: $$\dfrac{13}{125}$$
Without actually performing the long division, state whether the following rational number have terminating or non-terminating repeating (recurring) decimal expansion: $$\dfrac{7}{80}$$
Without actually performing the long division, state whether the following rational number have terminating or non-terminating repeating (recurring) decimal expansion: $$\frac{64}{455}$$
Without actually performing the long division, state whether the following rational number have terminating or non-terminating repeating (recurring) decimal expansion: $$\frac{6}{15}$$
Without actually performing the long division, state whether the following rational number have terminating or non-terminating repeating (recurring) decimal expansion: $$\frac{35}{50}$$