QuestionConvert the distances $d_{1} = 349000000000000000 \mathrm{~km}$ , $d_{2} = 45000000000000 \mathrm{~km}$ , $d_{3} = 427000000000000000 \mathrm{~km}$ to scientific notation and find the total distance traveled.

Studdy Solution

STEP 1

Assumptions1. The distance from Earth to Arcturus is $349000000000000000 \mathrm{~km}\left(d_{1}\right)$ . The distance from Arcturus to the comet is $45000000000000 \mathrm{~km}\left(d_{}\right)$ 3. The distance from the comet to Earth is $427000000000000000 \mathrm{~km}\left(d_{3}\right)$ 4. We need to convert these distances to scientific notation5. We need to calculate the total distance traveled by the crew

STEP 2

Let's convert the distances to scientific notation. The general form of a number in scientific notation is $a \times10^{b}$ , where $1 \leq a <10$ and $b$ is an integer.
For $d_{1}$ , we can write it as $.49 \times10^{17}$ km.
$d_{1} =.49 \times10^{17} \mathrm{~km}$

STEP 3

For $d_{2}$ , we can write it as $.5 \times10^{13}$ km.
$d_{2} =.5 \times10^{13} \mathrm{~km}$

STEP 4

For $d_{3}$ , we can write it as $4.27 \times10^{17}$ km.
$d_{3} =4.27 \times10^{17} \mathrm{~km}$

STEP 5

Now, let's calculate the total distance traveled by the crew. This is the sum of $d_{1}$ , $d_{2}$ , and $d_{3}$ .
$Total\, distance = d_{1} + d_{2} + d_{3}$

STEP 6

Plug in the values for $d_{1}$ , $d_{2}$ , and $d_{3}$ to calculate the total distance.
$Total\, distance =3.49 \times10^{17} \mathrm{~km} +4.5 \times10^{13} \mathrm{~km} +4.27 \times10^{17} \mathrm{~km}$

STEP 7

To add these numbers, we need to express them with the same exponent. We can do this by expressing $d_{2}$ with an exponent of17, which gives us $0.045 \times10^{17}$ km.
$Total\, distance =3.49 \times10^{17} \mathrm{~km} +0.045 \times10^{17} \mathrm{~km} +4.27 \times10^{17} \mathrm{~km}$

STEP 8

Now, we can add these numbers.
$Total\, distance = (3.49 +0.045 +4.27) \times10^{17} \mathrm{~km}$

STEP 9

Calculate the total distance.
$Total\, distance =7.805 \times^{17} \mathrm{~km}$ The crew of the starship Intrepid traveled a total distance of $7.805 \times^{17}$ km.

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QuestionConvert the distances $d_{1} = 349000000000000000 \mathrm{~km}$ , $d_{2} = 45000000000000 \mathrm{~km}$ , $d_{3} = 427000000000000000 \mathrm{~km}$ to scientific notation and find the total distance traveled.

Studdy Solution

STEP 1

STEP 2

Let's convert the distances to scientific notation. The general form of a number in scientific notation is $a \times10^{b}$ , where $1 \leq a <10$ and $b$ is an integer.
For $d_{1}$ , we can write it as $.49 \times10^{17}$ km.
$d_{1} =.49 \times10^{17} \mathrm{~km}$

STEP 3

For $d_{2}$ , we can write it as $.5 \times10^{13}$ km.
$d_{2} =.5 \times10^{13} \mathrm{~km}$

STEP 4

For $d_{3}$ , we can write it as $4.27 \times10^{17}$ km.
$d_{3} =4.27 \times10^{17} \mathrm{~km}$

STEP 5

Now, let's calculate the total distance traveled by the crew. This is the sum of $d_{1}$ , $d_{2}$ , and $d_{3}$ .
$Total\, distance = d_{1} + d_{2} + d_{3}$

STEP 6

Plug in the values for $d_{1}$ , $d_{2}$ , and $d_{3}$ to calculate the total distance.
$Total\, distance =3.49 \times10^{17} \mathrm{~km} +4.5 \times10^{13} \mathrm{~km} +4.27 \times10^{17} \mathrm{~km}$

STEP 7

To add these numbers, we need to express them with the same exponent. We can do this by expressing $d_{2}$ with an exponent of17, which gives us $0.045 \times10^{17}$ km.
$Total\, distance =3.49 \times10^{17} \mathrm{~km} +0.045 \times10^{17} \mathrm{~km} +4.27 \times10^{17} \mathrm{~km}$

STEP 8

Now, we can add these numbers.
$Total\, distance = (3.49 +0.045 +4.27) \times10^{17} \mathrm{~km}$

STEP 9

Calculate the total distance.
$Total\, distance =7.805 \times^{17} \mathrm{~km}$ The crew of the starship Intrepid traveled a total distance of $7.805 \times^{17}$ km.

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Studdy Solution

STEP 1

STEP 2

STEP 3

For d2d_{2}d2​, we can write it as .5×1013.5 \times10^{13}.5×1013 km.d2=.5×1013 kmd_{2} =.5 \times10^{13} \mathrm{~km}d2​=.5×1013 km

STEP 4

For d3d_{3}d3​, we can write it as 4.27×10174.27 \times10^{17}4.27×1017 km.d3=4.27×1017 kmd_{3} =4.27 \times10^{17} \mathrm{~km}d3​=4.27×1017 km

STEP 5

Now, let's calculate the total distance traveled by the crew. This is the sum of d1d_{1}d1​, d2d_{2}d2​, and d3d_{3}d3​.Total distance=d1+d2+d3Total\, distance = d_{1} + d_{2} + d_{3}Totaldistance=d1​+d2​+d3​

STEP 6

STEP 7

STEP 8

Now, we can add these numbers.Total distance=(3.49+0.045+4.27)×1017 kmTotal\, distance = (3.49 +0.045 +4.27) \times10^{17} \mathrm{~km}Totaldistance=(3.49+0.045+4.27)×1017 km

STEP 9

Calculate the total distance.Total distance=7.805×17 kmTotal\, distance =7.805 \times^{17} \mathrm{~km}Totaldistance=7.805×17 kmThe crew of the starship Intrepid traveled a total distance of 7.805×177.805 \times^{17}7.805×17 km.

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For $d_{2}$ , we can write it as $.5 \times10^{13}$ km.
$d_{2} =.5 \times10^{13} \mathrm{~km}$

For $d_{3}$ , we can write it as $4.27 \times10^{17}$ km.
$d_{3} =4.27 \times10^{17} \mathrm{~km}$

Now, let's calculate the total distance traveled by the crew. This is the sum of $d_{1}$ , $d_{2}$ , and $d_{3}$ .
$Total\, distance = d_{1} + d_{2} + d_{3}$

Now, we can add these numbers.
$Total\, distance = (3.49 +0.045 +4.27) \times10^{17} \mathrm{~km}$

Calculate the total distance.
$Total\, distance =7.805 \times^{17} \mathrm{~km}$ The crew of the starship Intrepid traveled a total distance of $7.805 \times^{17}$ km.