Powers: Scientific Notation
Given that $$0.001001 \times 10^q \gt 10^3$$, and $$q$$ is an integer, which of the following is the smallest possible value of $$q$$?
Incorrect.
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__Plug In__ $$q = 3$$:
>$$ 0.001001 \times 10^q \gt 10^3$$
>$$0.001001 \times 10^3 \gt 10^3$$
Shift the decimal point three spaces to the right.
>$$1.001 \ngtr 1{,}000$$
Since 1.001 is NOT greater than 1,000, this is NOT the correct answer.
Incorrect.
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__Plug In__ $$q = 4$$:
>$$ 0.001001 \times 10^q \gt 10^3$$
>$$0.001001 \times 10^4 \gt 10^3$$
Shift the decimal point four spaces to the right
>$$10.01 \ngtr 1{,}000$$
Since 10.01 is NOT greater than 1,000, this is NOT the correct answer.
Incorrect.
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__Plug In__ $$q = 5$$:
>$$0.001001 \times 10^q > 10^3$$
>$$0.001001 \times 10^5 \gt 10^3$$
Shift the decimal point five spaces to the right
>$$100.1 \ngtr 1{,}000$$
Since 100.1 is NOT greater than 1,000, this is NOT the correct answer.
Incorrect.
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Seven is not the least possible value for which $$0.001001 \times 10^q > 10^3$$.
Hence, this is not the correct answer.
Correct.
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__Plug In__ $$q = 6$$:
>$$ 0.001001 \times 10^q \gt 10^3$$
>$$0.001001 \times 10^6 \gt 10^3$$
Shift the decimal point six spaces to the right:
>$$1{,}001 > 1{,}000$$
Since 1,001 is greater than 1,000, this is the correct answer.
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