Astronomical units AU

The given numerical data are the mean distances of planets from the Sun expressed in astronomical units. One astronomical unit is the mean distance of the Earth from the Sun, and approximately equals 150 000 000 km.
Express the given mean distances in metres, round to three significant figures, and write in the form a. 10n, where 1 ≤ a < 10, n € N.

a. Mercury 0.387
b. Venus 0.723
c. Earth 1
d. Mars 1.52
e. Jupiter 5.2
f. Saturn 9.54
g. Uranus 19.2
h. Neptune 30.1

Final Answer:

a₁ =  58050000000 m
a₂ =  108450000000 m
a₃ =  150000000000 m
a₄ =  228000000000 m
a₅ =  780000000000 m
a₆ =  1431000000000 m
a₇ =  2880000000000 m
a₈ =  4515000000000 m

Step-by-step explanation:

$$\begin{gathered} u=150000000\text{km}\to \text{m}=150000000\cdot 1000\text{m}=150000000000\text{m} \\ {a}_1=0.387\cdot u=0.387\cdot 150000000000=58050000000\text{m}\doteq 5.80\cdot 10^{10}\text{m} \end{gathered}$$

$a_2=0.723\cdot u=0.723\cdot 150000000000=108450000000\text{m}\doteq 1.08\cdot 10^{11}\text{m}$

$a_3=1\cdot u=1\cdot 150000000000=150000000000\text{m}\doteq 1.50\cdot 10^{11}\text{m}$

$a_4=1.52\cdot u=1.52\cdot 150000000000=228000000000\text{m}\doteq 2.28\cdot 10^{11}\text{m}$

$a_5=5.2\cdot u=5.2\cdot 150000000000=780000000000\text{m}\doteq 7.80\cdot 10^{11}\text{m}$

$a_6=9.54\cdot u=9.54\cdot 150000000000=1431000000000\text{m}\doteq 1.43\cdot 10^{12}\text{m}$

$a_7=19.2\cdot u=19.2\cdot 150000000000=2880000000000\text{m}\doteq 2.88\cdot 10^{12}\text{m}$

$a_8=30.1\cdot u=30.1\cdot 150000000000=4515000000000\text{m}\doteq 4.52\cdot 10^{12}\text{m}$

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