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\tto\taverage (miles) (rounded to nearest hundred thousand miles)
venus\tearth\t2.6 x 10^7
mercury\tvenus\t30,700,000
earth\tjupiter\t3.904 x 10^8
earth\tmars\t48,300,000
earth\tsaturn\t7.938 x 10^8
saturn\tjupiter\t403,400,000
jupiter\tmars\t3.42 x 10^8
question\twork\tsolution

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: Identify relevant distances

Distance from Earth to Jupiter: $3.904\times 10^{8}$ miles, from Earth to Saturn: $7.938\times 10^{8}$ miles, from Saturn to Jupiter: $403400000 = 4.034\times 10^{8}$ miles, from Jupiter to Mars: $3.42\times 10^{8}$ miles, from Mercury to Venus: $30700000=3.07\times 10^{7}$ miles, from Venus to Earth: $2.6\times 10^{7}$ miles, from Earth to Mars: $48300000 = 4.83\times 10^{7}$ miles.

Step2: Solve question 1

To find how much farther Earth is from Saturn than from Jupiter, subtract the distance from Earth to Jupiter from the distance from Earth to Saturn.
$7.938\times 10^{8}-3.904\times 10^{8}=(7.938 - 3.904)\times 10^{8}=4.034\times 10^{8}$ miles.

Step3: Solve question 2

To find the total distance traveling from Saturn to Jupiter and then from Jupiter to Mars, add the two distances.
$(4.034\times 10^{8})+(3.42\times 10^{8})=(4.034 + 3.42)\times 10^{8}=7.454\times 10^{8}$ miles.

Step4: Solve question 3

Distance from Saturn to Earth is $7.938\times 10^{8}$ miles and from Saturn to Jupiter is $4.034\times 10^{8}$ miles. Subtract the distance from Saturn to Jupiter from the distance from Saturn to Earth.
$7.938\times 10^{8}-4.034\times 10^{8}=(7.938 - 4.034)\times 10^{8}=3.904\times 10^{8}$ miles.

Step5: Solve question 4

To find the total distance from Mercury to Earth, add the distance from Mercury to Venus and from Venus to Earth.
$3.07\times 10^{7}+2.6\times 10^{7}=(3.07 + 2.6)\times 10^{7}=5.67\times 10^{7}$ miles.

Step6: Solve question 5

Distance from Earth to Venus is $2.6\times 10^{7}$ miles and from Earth to Mars is $4.83\times 10^{7}$ miles. Since $2.6\times 10^{7}<4.83\times 10^{7}$, Venus is closer. The difference is $4.83\times 10^{7}-2.6\times 10^{7}=(4.83 - 2.6)\times 10^{7}=2.23\times 10^{7}$ miles.

Answer:

1. $4.034\times 10^{8}$ miles
2. $7.454\times 10^{8}$ miles
3. $3.904\times 10^{8}$ miles
4. $5.67\times 10^{7}$ miles
5. Venus is closer by $2.23\times 10^{7}$ miles