Question

Unsure how to set this problem up, help would be appreciated.

Answer 1

10 billion in scientific notation is \(1 \cdot 10^{9} \) or just \(10^9\)
you want to divide the earth's size by this number.

Answer 2

Divide 12,760km?

Answer 3

Divide 12,760km by 10^9

Answer 4

0.01276?

Answer 5

depends on what units .

I would first change 12760 km into scientific notation
then change from kilometers to meters or even cm
because the answer will be tiny after dividing by 10^9

Answer 6

faq im confused

Answer 7

when you have time , see
http://www.khanacademy.org/math/arithmetic/exponents-radicals/scientific-notation/v/scientific-notation

Answer 8

to change from km to meters, multiply by 1000

for example, 1 km becomes 1*1000= 1000 meters
5 km becomes 5*1000 or 5000 meters

in your case multiply 12,760km by 1000 to get
12760000 meters

I would change that to scientific notation.
move the decimal to the left, until it is between the 1 and the 2.
count the number of moves and make that the exponent on the 10
(see video if that does not make sense)

Answer 9

Ik 10^9 = 1,000,000,000

Answer 10

yes, but life is easier if you use exponents.
the rule for dividing becomes adding or subtracting exponents (much easier than trying to keep track of all those zeros)

for example

1000000/10000 using exponents is
\[ \frac{10^6}{10^4} = 10^{6-4} = 10^2 \]
or 100

Answer 11

So for this problem...

Answer 12

To find how big the Earth's diameter is on the scale first.

Answer 13

change 12760 km to meters by multiplying by 1000
change 12760000 meters to scientific notation

change that to scientific notation.
move the decimal to the left, until it is between the 1 and the 2.
count the number of moves and make that the exponent on the 10
(see video if that does not make sense)

Answer 14

7 moves

Answer 15

1.2760000 10^7?

Answer 16

yes. so 1.276 * 10^7 meters (keep track of the units)

now divide by 10^9
\[ \frac{1.276 \cdot 10^7}{10^9} \]
this is the same as
\[ 1.276 \cdot \frac{10^7}{10^9} \text{ meters}\]
can you do the division using the "exponent rule" ? (it will by 7-9 for the new exponent)

Answer 17

1276

Answer 18

no, keep things in scientific notation

try again

Answer 19

1.276 * 10^3

Answer 20

wait 10^-2

Answer 21

how do you get 10^3 ?

10^-2 is *much better*

Answer 22

0.01276

Answer 23

yes, though I tend to keep things in scientific notation until the very end.

remember, you have
1.276 * 10^-2 meters

looking at the answers, it looks like they rounded. Can you round this to 2 digits ?
you get
1.3 * 10^-2 meters

can you change this to centimeters ? (because some of the answers are in cm)
1 meter is 100 cm
to change from meters to cm multiply by 100 or 10^2

1.3 * 10^-2 * 10^2 cm

can you simplify that ?

Answer 24

when multiplying, add exponents

remember that 10^0 is the same as 1

Answer 25

1.3?

Answer 26

1.3mm?

Answer 27

yes 1.3 because 10^-2 * 10^2 is 10^(-2+2) = 10^0 =1

so 1.3 * 10^-2 * 10^2 = 1.3 * 1

as for the units, you have to keep track. re-read this:

1.3 * 10^-2 meters

can you change this to centimeters ? (because some of the answers are in cm)
1 meter is 100 cm
to change from meters to cm multiply by 100 or 10^2

1.3 * 10^-2 * 10^2 cm

Answer 28

still came out to 1.3 cm

Answer 29

but the only answer with 1.3 has mm after it

Answer 30

oh, I see the problem. I was dividing by 1 billion = 10^9

but the problems says divide by 10 billion which is 10^10

so we have to divide by 10
1.3 cm / 10 = 0.13 cm

there are 10 mm in one cm, so this is the same as 1.3 mm

Answer 31

Then approximately how far away would the two objects be on this scale?

Answer 32

or , re-doing it
\[ 1.276 \cdot \frac{10^7}{10^{10}} \text{ meters} \\ 1.3 \cdot 10^{-3} \text { meters}\]

there are 1000 or 10^3 millimeters in 1 meter. multiply by 10^3 to change to mm:
\[ 1.3 \cdot 10^{-3} \cdot 10^3\text { mm} \\1.3 \ mm\]

Answer 33

Then approximately how far away would the two objects be on this scale?

Answer 34

do the same thing. divide earth's distance from the sun by 10^10