Question

use the information in the table to put the planets in order from shortest day to longest day.

planet	day length (hrs)
venus	$5.832 \times 10^3$
earth	$2.4 \times 10^1$
saturn	$1.1 \times 10^1$
neptune	$1.6 \times 10^1$

list planets from shortest to longest day.

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circle all of the problems that were solved correctly.

a. $9.2 \times 10^{16} - 9.5 \times 10^{14} = 9.105 \times 10^{16}$

b. $7.3 \times 10^{-1} - 6.9 \times 10^{-2} = 6.61 \times 10^{-1}$

c. $1.21 \times 10^{-8} - 4.6 \times 10^{-7} = 3.39 \times 10^{-7}$

Explanation:

Part 1: Ordering Planets by Day Length

Step1: Convert to Standard Form

Mercury: \(1.408 \times 10^3 = 1408\) hrs
Venus: \(5.832 \times 10^3 = 5832\) hrs
Earth: \(2.4 \times 10^1 = 24\) hrs
Saturn: \(1.1 \times 10^1 = 11\) hrs
Neptune: \(1.6 \times 10^1 = 16\) hrs

Step2: Order from Shortest to Longest

Compare the values: \(11 < 16 < 24 < 1408 < 5832\)
Corresponding planets: Saturn, Neptune, Earth, Mercury, Venus

Part 2: Checking Correctly Solved Problems

Problem a:

Step1: Rewrite with Same Exponent

\(9.5 \times 10^{14} = 0.095 \times 10^{16}\)

Step2: Subtract

\(9.2 \times 10^{16} - 0.095 \times 10^{16} = (9.2 - 0.095) \times 10^{16} = 9.105 \times 10^{16}\)
So, a is correct.

Problem b:

Step1: Rewrite with Same Exponent

\(6.9 \times 10^{-2} = 0.69 \times 10^{-1}\)

Step2: Subtract

\(7.3 \times 10^{-1} - 0.69 \times 10^{-1} = (7.3 - 0.69) \times 10^{-1} = 6.61 \times 10^{-1}\)
So, b is correct.

Problem c:

Answer:

s:

Part 1 (Planet Order):

Saturn, Neptune, Earth, Mercury, Venus

Part 2 (Correct Problems):

a. \(9.2 \times 10^{16} - 9.5 \times 10^{14} = 9.105 \times 10^{16}\)
b. \(7.3 \times 10^{-1} - 6.9 \times 10^{-2} = 6.61 \times 10^{-1}\)