If $$\displaystyle d=\frac { 1 }{ { 2 }^{ 3 }\times { 5 }^{ 7 } } $$ is expressed as a terminating decimal, how many non zero digits will $$d$$ have?
Given, $$d=\cfrac{1}{2^3\times5^7 } $$.
Multiply and divide by $${2^4}$$,
$$\Rightarrow d=\cfrac{2^4}{2^3 \times 5^7 \times 2^4}$$
= $$\cfrac{16}{2^7 \times 5^7 }$$
= $$\cfrac{16}{10^7 }$$
=$$0.0000016 $$
Hence, $$d$$ will have two non-zero digits, $$1$$ and $$6$$, when expressed as a decimal.
Therefore, option $$B$$ is the correct answer.
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.)
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: $$\frac{35}{50}$$
Without actually performing the long division, state whether the following rational number has terminating or non-terminating repeating (recurring) decimal expansion: $$\dfrac{129}{2^{2}*5^{7}*7^{5}}$$