Write the following in scientific notation in their respective SI units ( 3 dig fig)
a) 286.6 km
b) 0.864um
c) 760mg
d) 62.1 ps
You're welcome.
Perhaps you should explain what you don't understand about this. I'll do a couple for you to get you started. For scientific notation, you place the decimal to the right of the FIRST number and follow that with x 10^y where y is the number of places to the right or left that you moved the decimal from its initial resting place. Since you want 3 digits you round the third digit if there are more.
286.6 km rounds to 287 and that is 2.87 x 10^2 km
0.864 um stays 0.864 um and that is 8.64 x 10^-1 um
Since it isn't easy to type subscripts and superscripts on the keyboard, the new way of writing these is to let E replace the x 10 then follow that by the y value in 10^y. Those two examples above then become
2.87E2 and 8.64E-1.
You do the other two. I shall be happy to check your work if you wish.
It got me confuse the km ....in the end
Yes I wish to check my work
That km, um, mg, and ps are just the units and don't have anything to do with writing in scientific notation. km is kilometers, um is micrometers, mg is milligrams, ps is picoseconds.
So my numbers above would be
2.87E2 km and 8.64E-1 um.
I shall be happy to check your work on the last two if you post it.
2.87 x 10^5
8.64x10^ negative 7
7.60x10^negative 1
6.21x10^ negative 11
I eleminated
km
286.6/1km x 1000 m/ 1km = 286600. 2.87x10^ 5 m
Is it wrong or I live the way it is in km
0.864. 8.64x10^ -1 um
760mg. 7.60 x10^2
62.1ps. 6.21x 10^1
Thank you so much
Thank you
Excellent! You have done a great job. I would rewrite them this way AND I would add the units. This really is two exercises in one; i.e., first to write in scientific notation AND to change to SI units.
2.87 x 10^5 m
8.64x10^ negative 7 or 8.64 x 10^-7 m
7.60x10^negative 1 or 7.60 x 10^-1 g
6.21x10^ negative 11 or 6.21 x 10^-11 s
Technically the last three are not right because the scientific notation allows you to use the E language as I've shown above OR to use the 10^y where y is +number of -number. It does not allow you write "negative". Everyone would know exactly what you meant; however, picky instructors, like me, will count that wrong. I have shown above how to write those last three correctly. USUALLY, when I taught, I would ask the student to show his/her work and it would look like this. The short answer, for example, of 0.864 um = 8.64 x 10^-7 m would look like this to show all the work.
0.864 um = 8.64 x 10^-1 um and 8.64 um x (10^-6 m/1 um) = 8.64 x 10^-7 m. I'm lazy and I don't like to do any more typing than necessary so I would do all of this in the scientific E notation like this.
0.864 um x (1E-6 m/1 um) = 0.864E-6 m = 8.64E-7 m
286.6 km = 287 km to three digits = 287 km x (1000 m/1 km) = 287E3 m = 2.87E5 m.
The others are done the same way. Keep up the good work.