A terminating decimal can be written in the form $\frac{a}{10^b}$, where $a$ and $b$ are integers. So we try to get a denominator of the form $10^b$: $$\frac{21}{2^2\cdot5^7}\cdot\frac{2^5}{2^5}=\frac{21\cdot32}{10^7}=\frac{672}{10^7}=\boxed{.0000672}.$$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Convert $\frac{21}{2^2 \cdot 5^7}$ to a terminating decimal.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
.0000672
Convert $\frac{21}{2^2 \cdot 5^7}$ to a terminating decimal.
test