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# Percents, Fractions, and Decimals - One Big Family

Given that $$0.0001402 \times 10^q < 5^{-2}$$, and $$q$$ is an integer, which of the following is the largest possible value of $$q$$?
Correct. [[Snippet]] Plug in $$q = 2$$: >$$0.0001402 \times 10^q$$ >$$= 0.0001402 \times 10^2$$. Shift the decimal point two places to the right: >$$= 0.01402$$. Since 0.01402 is less than 0.04, this is a possible answer choice. The next answer choice, $$q=3$$, will result in 0.1402 (after an additional shift of the decimal point to the right), which is greater than 0.04—too big, in fact. Therefore, $$q=2$$ is the greatest possible value for $$q$$, and this answer choice is indeed the correct one.
Incorrect. [[Snippet]] __Plug In__ $$q = 3$$: >$$0.0001402 \times 10^q < 5^{-2}$$ >$$0.0001402 \times 10^3 \stackrel{?}{<} \frac{1}{ 5^2}$$ >$$0.1402 \stackrel{?}{<} \frac{1}{25}$$ >$$0.1402 \nless 0.04$$. Since 0.1402 is *not* less than 0.04, eliminate this answer choice.
Incorrect. [[Snippet]] __Plug In__ $$q = 4$$: >$$0.0001402 \times 10^q < 5^{-2}$$ >$$0.0001402 \times 10^4 \stackrel{?}{<} \frac{1}{ 5^2}$$ >$$1.402 \stackrel{?}{<} \frac{1}{25}$$ >$$1.402 \nless 0.04$$. Since 1.402 is *not* less than 0.04, eliminate this answer choice.
Incorrect. [[Snippet]] __Plug In__ $$q= 5$$: >$$0.0001402 \times 10^q < 5^{-2}$$ >$$0.0001402 \times 10^5 \stackrel{?}{<} \frac{1}{5^2}$$ >$$14.02 \stackrel{?}{<} \frac{1}{25}$$ >$$14.02 \nless 0.04$$. Since 14.02 is *not* less than 0.04, eliminate this answer choice.
Incorrect. [[Snippet]] The number 1 is indeed a possible value of $$q$$, but it is not the *largest* possible value in which $$0.0001402 \times 10^q < 5^{-2}$$. Hence, this is not the correct answer. Look for a bigger number that is also possible.
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