# Question 6e1cb

Jan 9, 2018

$2.22530000 \cdot {10}^{31} m$

#### Explanation:

You want to find the total distance that the spaceship travels from Earth to Saturn.

From Earth to Mars is $2.2253 \cdot {10}^{28}$ and from Mars to Saturn it’s $1.19666 \cdot {10}^{9}$. Given the info, you just have to add it together to find the total distance

So $2.2253 \cdot {10}^{28} + 1.19666 \cdot {10}^{9} = 2.22530000 \cdot {10}^{28} k m$

Since the question wants it in meters, you have to multiply that by 1000 (1km=1000m)

$2.22530000 \cdot {10}^{28} k m \cdot 1000 = 2.22530000 \cdot {10}^{31} m$

Jan 9, 2018

See a solution process below:

#### Explanation:

Assuming they flew in a straight line we can write the expression for the distance the spaceship as:

$\left(2.2253 \times {10}^{28} \text{km") + (1.19666 xx 10^9"km}\right)$

We can rewrite: $\left(2.2253 \times {10}^{28} \text{km}\right)$ as:

$\left(22253000000000000000 \times {10}^{9}\right)$

Substituting this gives:

$\left(22253000000000000000 \times {10}^{9}\right) + \left(1.19666 \times {10}^{9} \text{km}\right) \implies$

$\left(22253000000000000000 + 1.19666\right) \times {10}^{9} \text{km} \implies$

$22253000000000000001.19666 \times {10}^{9} \text{km}$

Because $1 \text{km" = 1000"m}$ we can write:

22253000000000000001.19666 xx 10^9"km" xx (1000"m")/(1"km") =>

22253000000000000001.19666 xx 10^9color(red)(cancel(color(black)("km"))) xx (1000"m")/(1color(red)(cancel(color(black)("km")))) =>#

$22253000000000000001.19666 \times {10}^{9} \times 1000 \text{m} \implies$

$22253000000000000001.19666 \times {10}^{9} \times {10}^{3} \text{m} \implies$

$22253000000000000001.19666 \times {10}^{12} \text{m}$

For all intents and purposes the distance from Earth to Mars is negligible and the distance from Earth to Saturn via Mars can be rounded to:

$22253000000000000000 \times {10}^{12} \text{m} \implies$

$2.2253000000000000000 \times {10}^{31} \text{m} \implies$

$2.2253 \times {10}^{31} \text{m}$