How Do You Convert Seconds to Nanoseconds in Scientific Notation?

[member 731016]

Homework Statement

Please see below

Relevant Equations

Please see below

How do you convert $1.66 \times 10^{-7} s$ to $ns$? I know the answer is $166 ns = 160 \times 10^{-9} s$ however what is the thought process?

Many thanks!

 

[phinds]

Homework Statement:: Please see below
Relevant Equations:: Please see below

How do you convert $1.66 \times 10^-7 s$ to $ns$? I know the answer is $166 ns$ however what is the thought process?

Many thanks!

Do you know what "ns" MEANS ?

 

[member 731016]

Do you know what "ns" MEANS ?

Thanks for you reply @phinds! It means nanoseconds.

 

[phinds]

Thanks for you reply @phinds! It means nanoseconds.

And how do you express that in seconds?

 

[member 731016]

And how do you express that in seconds?

THanks for you reply @phinds! $1s = 1 \times 10^{-9} ns$. Oh I think I know where you going with this.

 

[member 731016]

THanks for you reply @phinds! $1s = 1 \times 10^-9 ns$. Oh I think I know where you going with this.

Sorry yeah it is just basic unit conversion.

$1.66 \times 10^{-7}s \times \frac {1ns} {1 \times10^{-9}s} = 166 ns$

 

[phinds]

Right, except you have 1.6 where the original says 1.66

 

[member 731016]

Right, except you have 1.6 where the original says 1.66

Oh whoops sorry @phinds! I'll fix that up.

 

[berkeman]

Sorry yeah it is just basic unit conversion.

$1.66 \times 10^{-7} \times \frac {1ns} {1 \times10^{-9}s} = 166 ns$

Yes, the thought process is to multiply the quantity you want to convert by "1", where the "1" is a fraction that is set up to cancel the old units with the denominator and result in the new units of the numerator. (the only thing you are missing in your equation that I quoted is to include the units of "s" in the first quantity, so that can be canceled by the denominator's "s" units in the multiplication)

I still remember my first semester "Introduction to Engineering" class, where a TA explained this trick to the class, and we all looked at each other like "Wow, I never thought of it like that before!". It's a simple trick, but very useful.

 

[member 731016]

Yes, the thought process is to multiply the quantity you want to convert by "1", where the "1" is a fraction that is set up to cancel the old units with the denominator and result in the new units of the numerator. (the only thing you are missing in your equation that I quoted is to include the units of "s" in the first quantity, so that can be canceled by the denominator's "s" units in the multiplication)

I still remember my first semester "Introduction to Engineering" class, where a TA explained this trick to the class, and we all looked at each other like "Wow, I never thought of it like that before!". It's a simple trick, but very useful.

Thank you @berkeman - nice to see the thought process explained!

 

[Tom.G]

THanks for you reply @phinds! $1s = 1 \times 10^{-9} ns$. Oh I think I know where you going with this.

Looks like a sign error! (or a VERY strange second)

 

[member 731016]

Looks like a sign error! (or a VERY strange second)

Haha, yes @Tom.G , I'm still working on my LaTex :)