Question

there is still controversy about whether or not pluto should be considered a planet. planets are mainly defined by their orbital path the issue of size is something to consider. the table below lists the planets, including pluto, and their approximate diameter in meters.

number the planets (smallest to biggest) 1 - 9 based on diameter	planet	approximate diameter (m)
	venus	$1.21\times10^{7}$
	earth	$1.28\times10^{7}$
	mars	$6.79\times10^{6}$
	jupiter	$1.43\times10^{8}$
	saturn	$1.2\times10^{8}$
	uranus	$5.12\times10^{7}$
	neptune	$4.96\times10^{7}$
	pluto	$2.3\times10^{6}$

complete these statements based on the table.
the diameter of the largest planet is ______ orders of magnitude greater than the diameter of the smallest planet.
this means the diameter of the largest planet is approximately ______ times the diameter of the smallest planet. write the number in standard form.

for 5 - 10, find the product or quotient. make sure your answer is in scientific notation. show all work!
example: $(2.8\times10^{7})\times(1.9\times10^{4})$
$(2.8\times1.9)\times(10^{7}\times10^{4})$
$5.32\times10^{11}$

1. $(1.3\times10^{9})\times(4.7\times10^{5})$
2. $(3.4\times10^{-2})\times(8.5\times10^{6})$

Explanation:

Step1: Identify largest and smallest planet diameters

The largest planet diameter is Jupiter's, $1.43\times 10^{8}$ m, and the smallest is Pluto's, $2.3\times 10^{6}$ m.

Step2: Calculate orders of magnitude difference

Use the formula $\text{Orders of magnitude}=\lfloor\log_{10}\frac{d_{1}}{d_{2}}
floor$, where $d_{1}$ is the larger diameter and $d_{2}$ is the smaller diameter. $\log_{10}\frac{1.43\times 10^{8}}{2.3\times 10^{6}}=\log_{10}( \frac{1.43}{2.3}\times10^{2})$. $\frac{1.43}{2.3}\approx0.62$, and $\log_{10}(0.62\times 10^{2})=\log_{10}(0.62) + 2\approx - 0.21+2 = 1.79$. So the orders of magnitude is 2.

Step3: Calculate how many times larger

$\frac{1.43\times 10^{8}}{2.3\times 10^{6}}=\frac{1.43}{2.3}\times10^{8 - 6}\approx0.62\times10^{2}=62$.

Answer:

2
62