[MrLuxC]

Hi, I am new here and self-educating myself with a General Chemistry E-book. I have a rather simplistic question concerning cubic conversions. I believe I am over-analyzing simplistic processes here. I am stumped and confused on how the starting value remains the same while only the unit of measure and exponents are being adjusted. I understand the conversion values (1km = 1000m, 1m=10dm), though I'm confused as to how the numerator and denominator in the conversion factors are being cubed and how it leads to the problem's solution.  I am hoping someone can explain / illustrate this to me differently then my book as I don't feel comfortable proceeding without registering this understanding. I'd appreciate it, and I do allow members to email me. Thank you.

Here is a linked image of the problem.

https://i.ibb.co/GRSkLCg/cubicconversion1.png

[sjb]

Are you more comfortable with Imperial measures, for instance? If there are 3 feet in a yard, how many cubic feet are there in a cubic yard?

[AWK]

The author of this text is suitable for politics - he can complicate the simplest things!
And it would be enough to convert meters to decimeters in an equivalent way (10¹ dm/1 m)³ and everything would be easy.

https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/Book%3A_The_Basics_of_GOB_Chemistry_(Ball_et_al.)/01%3A_Chemistry%2C_Matter%2C_and_Measurement/1.7%3A_Converting_Units

[Borek]

confused on how the starting value remains the same while only the unit of measure and exponents are being adjusted

Not sure what you mean by that, can you elaborate? Starting value is just what is is - a starting value, it doesn't change.

Or do you mean 1.35 keeps the same all the time? That's the beauty of the metric system, you convert by adding or removing zeros (multiplying or dividing by powers of ten). That's why it is so simple to use. When squaring or cubing conversion factors are still just powers of ten, this is just a simple math.