Question

proxima centauri is the closest star to earth and is approximately $4.0208 \times 10^{14}$ kilometers away. if ionic propulsion were used for a mission to proxima centauri at maximum velocity, the spacecraft would be able to travel about $4.9056 \times 10^{8}$ kilometers per year. approximately how many years would it take to reach proxima centauri?\
\bigcirc $8.2 \times 10^{5}$ years\
\bigcirc $8.2 \times 10^{6}$ years\
\bigcirc $1.97 \times 10^{5}$ years\
\bigcirc $1.97 \times 10^{6}$ years\
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question 9\
the population of rhode island in 2021 was about $1.096 \times 10^{6}$ people. that same year, the population of new york city was approximately 7.7 times the population of rhode island.\
what was the population of new york city expressed in scientific notation?\
$\square \times \square$ round the coefficient to the nearest thousandth

Explanation:

Question 8

Step1: Set up time formula

Time = $\frac{\text{Distance}}{\text{Velocity}}$

Step2: Substitute given values

$\frac{4.0208 \times 10^{13}}{4.9056 \times 10^8}$

Step3: Split into coefficient/exponent

$\frac{4.0208}{4.9056} \times 10^{13-8}$

Step4: Calculate coefficient & exponent

$0.82 \times 10^5 = 8.2 \times 10^4$

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Question 9

Step1: Set up population formula

NYC Population = $1.096 \times 10^6 \times 7.7$

Step2: Multiply coefficients first

$1.096 \times 7.7 = 8.3992$

Step3: Round coefficient to thousandth

$8.3992 \approx 8.399$

Step4: Combine with exponent

$8.399 \times 10^6$

Answer:

$8.2 \times 10^4$ years