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Number theory Difficulty 3.0 AMC 10/12 Find the answer Canada

If $k$ is the smallest positive integer such that $(2^k)(5^{300})$ has 303 digits when expanded, then the sum of the digits of the expanded number is

(A) $11$ (B) $10$ (C) $8$ (D) $7$ (E) $5$

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.