Question

adding and subtracting with scientific notation
the table shows distances between different planets in our solar system. use the table to help you answer the questions that follow. write all solutions in scientific notation.

from	to	average (miles)
mercury	venus	30,700,000
earth	jupiter	3.904 x 10^8
earth	mars	48,300,000
earth	saturn	7.438 x 10^8
saturn	jupiter	403,400,000
jupiter	mars	3.42 x 10^8

question | work | solution

1. how much farther is the earth from saturn than it is from jupiter?
2. suppose you traveled from saturn to jupiter, and then from jupiter to mars. what would be the total distance?
3. how much closer is saturn to jupiter than it is to earth?
4. find the total distance from mercury to earth.
5. which is closer to earth, venus or mars? how much closer is it?

Explanation:

Step1: Convert non - scientific notation to scientific

30700000 = 3.07×10^7, 48300000 = 4.83×10^7, 403400000 = 4.034×10^8, 3.42×10^8

Step2: Solve question 1

Distance from Earth to Saturn is 7.438×10^8 miles, from Earth to Jupiter is 3.904×10^8 miles.
Subtract: (7.438×10^8)-(3.904×10^8)=(7.438 - 3.904)×10^8 = 3.534×10^8 miles

Step3: Solve question 2

Distance from Saturn to Jupiter is 4.034×10^8 miles, from Jupiter to Mars is 3.42×10^8 miles.
Add: (4.034×10^8)+(3.42×10^8)=(4.034 + 3.42)×10^8 = 7.454×10^8 miles

Step4: Solve question 3

Distance from Saturn to Earth is 7.438×10^8 miles, from Saturn to Jupiter is 4.034×10^8 miles.
Subtract: (7.438×10^8)-(4.034×10^8)=(7.438 - 4.034)×10^8 = 3.404×10^8 miles

Step5: Solve question 4

Distance from Mercury to Venus is 3.07×10^7 miles, from Venus to Earth is 2.6×10^7 miles.
Add: (3.07×10^7)+(2.6×10^7)=(3.07 + 2.6)×10^7 = 5.67×10^7 miles

Step6: Solve question 5

Distance from Earth to Venus is 2.6×10^7 miles, from Earth to Mars is 4.83×10^7 miles.
Since 2.6×10^7<4.83×10^7, Venus is closer.
Subtract: (4.83×10^7)-(2.6×10^7)=(4.83 - 2.6)×10^7 = 2.23×10^7 miles

Answer:

1. 3.534×10^8 miles
2. 7.454×10^8 miles
3. 3.404×10^8 miles
4. 5.67×10^7 miles
5. Venus is closer by 2.23×10^7 miles