Question

Dimensional Analysis question
A very large unit of measurement is the zettameter (zm). 1 zm = 1021 m, but astronomers measures distances in even bigger units called astronomical units (the au). One au is defined to be approximately 107 miles (the average distance between the center of the earth and the center of the sun). An even bigger unit is called the parsec, which is equal to about 2x105 au. When astronomers talk about intergalactic space however it’s even more convenient to use units of kiloparsecs. Given that 1.6 km = 1 mile, about how many kiloparsecs are there in a zettameter?

Answer 1

Do you understand some of it?

Answer 2

I got to go in 17min, so the more responsive you are, the faster we finish.

Answer 3

Yes, the work I've came up with so far is,

10^18 km x (1mi/1.6 km) x (1au/10^7 mi ) x )1 Kiloparsec/2x10^8 au)

Answer 4

I got 3 x 10^18 Kiloparsecs, but the answer key says the answer is 1/3 x 10^3 Kiloparsecs
I don't know what I'm doing wrong

Answer 5

the conversions should be 1 zm = 10^21 m
1 au = 10^7 mi
1 parsec = 2x10^5 au

Answer 6

and so 1 kiloparsec= 2x10^8 au

Answer 7

1000 parsec=1 parsec
1 parsec=2,00,000Au
1Au=107 miles
1zm=1021m

Answer 8

Yes you right.

Answer 9

But after calculating, my final answer is different from the answer in the answer key

Answer 10

one zm has 1021m, so lets start with that.

Answer 11

is my setup wrong?

Answer 12

its meant to be 10^21

Answer 13

I converted 10^21 m to km, which is 10^18 km

Answer 14

\[\frac{ 1021m }{ 1 } \times \frac{ 0.001km }{ 1m } \times \frac{ 1mile }{ 1.6km } \times \frac{ 1Au }{ 107miles } \times \frac{ 1 parsec }{ 2\times10^5 Au } \times \frac{ 0.001 kiloparsec }{ 1 parsec }\]

Answer 15

ahh i forgot to convert parsec to kiloparsec
thanks so much!!

Answer 16

Ah, nice job attempting though!

Answer 17

I have to go now. If you have any questions in 2 hours, I can help.

Answer 18

alright thanks so much