When I see a m/n equation, I thought it as the value of each part of m if m gets divided n number of times. For, 10/2, 10 to be divided into 2 parts so each part holds value equal to 5. 10/1 implies 10 to be divided into only 1 part so that single part holds all the value that is 10.
But, for 10/0.01, I cannot decipher the logic of dividing into 0.01 parts. Can someone help me to explain these in words along the same lines of dividing the number into those many parts.
X / Y = Z and X / Z = Y ought to be equivalent. Y and Z play a symmetric role in these equations, because these equations are also equivalent to X = Y × Z and X = Z × Y.
Depending on how you look at it, maybe Y is the number of parts and Z is the size of each part, or maybe Y is the size of each part and Z is the number of parts.
So, instead of reading "10/0.01 is 10 divided into 0.01 parts", you can say: "10/0.01 is the number of parts of size 0.01 that can fit into 10".
And indeed, it is true that if you have an empty bottle of volume 10L, and a small cup of volume 0.01L, then you can pour 10/0.01 = 1000 cups of water into the bottle.
Alternatively, if you insist on 10 being a number of cakes and 0.01 being a number of shares:
The population of Luxembourg is 0.01 of the population of France. If I give one cake to France and 10 cakes to Luxembourg, how much cake will a Luxembourger eat relatively to a French?
The answer is 10/0.01 = 1000. The share of cake eaten by a Luxembourger is 1000 bigger than the share of cake eaten by a French.