Determine the integer value of n if $10^{(n - 1)} < 0.0005 < 10^n$ .

Correct answer marked below

-4

-3

Correct

-2

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Explanation

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Official Explanation

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To find the integer n, we need to solve the inequalities

10^{(n - 1)} < 0.0005 < 10^n

. First, we rewrite 0.0005 in scientific notation:

0.0005 = 5 imes 10^{-4}

. This means we need to find n such that

10^{(n - 1)} < 5 imes 10^{-4} < 10^n

. The first part, [m]10^{(n…

Comments

PriyanshiMar 1, 2025

Thank you very much!

AndrewJan 2, 2024

Good question

RheaApr 1, 2025

thank you taking time to upload it!

What this question tests

Your ability to solve and combine linear inequalities and reason about ranges of values.

Failing to flip the inequality sign when multiplying or dividing by a negative, or missing an inclusive/exclusive endpoint.