Question

homework:
ch. 8.7 add/sub sci. not. hw #2
name
date
pd
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)

*rounded to nearest hundred thousand miles |

venus	earth	$2.6 \times 10^7$
mercury	venus	30,700,000
earth	jupiter	$3.904 \times 10^8$
earth	mars	48,300,000
earth	saturn	$7.938 \times 10^8$
saturn	jupiter	403,400,000
jupiter	mars	$3.42 \times 10^8$

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? | | |
©maneuvering the middle llc, 2016

Explanation:

---

Question 1

Step1: Convert values to same exponent

Earth to Saturn: $7.938 \times 10^8$; Earth to Jupiter: $3.904 \times 10^8$

Step2: Subtract the two distances

$7.938 \times 10^8 - 3.904 \times 10^8 = (7.938 - 3.904) \times 10^8$

Step3: Calculate the coefficient

$4.034 \times 10^8$

---

Question 2

Step1: Convert Saturn-Jupiter to sci. notation

$403,400,000 = 4.034 \times 10^8$

Step2: Add to Jupiter-Mars distance

$4.034 \times 10^8 + 3.42 \times 10^8 = (4.034 + 3.42) \times 10^8$

Step3: Calculate the coefficient

$7.454 \times 10^8$

---

Question 3

Step1: Convert Saturn-Jupiter to sci. notation

$403,400,000 = 4.034 \times 10^8$

Step2: Subtract from Earth-Saturn distance

$7.938 \times 10^8 - 4.034 \times 10^8 = (7.938 - 4.034) \times 10^8$

Step3: Calculate the coefficient

$3.904 \times 10^8$

---

Question 4

Step1: Convert Mercury-Venus to sci. notation

$30,700,000 = 3.07 \times 10^7$

Step2: Convert Venus-Earth to match exponent

$2.6 \times 10^7$

Step3: Add the two distances

$3.07 \times 10^7 + 2.6 \times 10^7 = (3.07 + 2.6) \times 10^7$

Step4: Calculate the coefficient

$5.67 \times 10^7$

---

Question 5

Step1: Convert Earth-Mars to sci. notation

$48,300,000 = 4.83 \times 10^7$

Step2: Compare to Venus-Earth distance

$2.6 \times 10^7 < 4.83 \times 10^7$, so Venus is closer

Step3: Subtract to find difference

$4.83 \times 10^7 - 2.6 \times 10^7 = (4.83 - 2.6) \times 10^7$

Step4: Calculate the coefficient

$2.23 \times 10^7$

Answer:

QUESTION	SOLUTION
2. Suppose you traveled from Saturn to Jupiter, and then from Jupiter to Mars. What would be the total distance?	$7.454 \times 10^8$ miles
3. How much closer is Saturn to Jupiter than it is to Earth?	$3.904 \times 10^8$ miles
4. Find the total distance from Mercury to Earth.	$5.67 \times 10^7$ miles
5. Which is closer to Earth, Venus or Mars? How much closer is it?	Venus is closer, by $2.23 \times 10^7$ miles