# Significant Figures rule help

## Homework Statement

This is probably a ridiculous question for many of you, but I want to make sure I have understood the significant figures rule. I am putting this in the physics section because it's from my physics book.

## The Attempt at a Solution

a) Seconds in 1.00 year:
1 year x 365 x 24 x 60 x 60 = 31,536,000 seconds in a year = 3.15 x10^7 sec/y.

b) Nanoseconds in 1.00 year:
(Seconds in a year) x (nanoseconds in a second)= 31,536,000x1x10^-9 = 0.031536 = 3.15 x 10^-2 nanoseconds in a year.

c) Years in 1.00 seconds:
1.00seconds x (1 minute/60 seconds) x (1 hour / 60 minutes) x (1 day/ 24 hours) x (1 year/365 days) = 3.17x 10^-8 year in 1.00 seconds.

Would this be correct?

Thank you so much.

a) and c) looks good.
b) How many nano seconds is there in 1 second?
Is there really 3.15 x 10^(-2) nanosseconds i a year ?

Would it be 31536000 x 1second/(1x10^-9)=3.15 x 10^16 ?

Thanks for pointing this out and for your help!

Would it be 31536000 x 1second/(1x10^-9)=3.15 x 10^16 ?

Thanks for pointing this out and for your help!

Yea, that's correct.

If you want to be strict with sig figs, your answer should only have 2 because youre multiplying by 24 and 60 in your work. However, conversion factors like that can conveniently be extended to 24.0 hours/1.00 day and 60.0 minutes/1.00 hour. Its no big deal for conversions, but if a measurement has 2 sig figs, your answer is only accurate to 2 sig figs