Why do I get giant values when I plug in very small decimal values in symbolic algebra?

syms v
eqn = ((40-20)/(25-20)) == ((0.0010057-0.0009996)/(v-0.0009996))

eqn = 

Answer 1

[DGM]

When doing symbolic operations, it's going to always try to give exact representations of numbers. Ratios of integers are exact, whereas floating point representations are not necessarily exact. You can convert to a more familiar numeric form if you want.

Consider:

syms v
eqn = ((40-20)/(25-20)) == ((0.0010057-0.0009996)/(v-0.0009996))

eqn = 

S = solve(eqn,v) % expressed as integer ratios

S = 

format long % just so we can see all the digits
double(S) % decimal representation

ans = 
   0.001001125000000

The result should satisfy the equation

((40-20)/(25-20)) % LHS

ans = 
     4

((0.0010057-0.0009996)/(S-0.0009996)) % RHS is exactly equal

ans = 

4

Though note that the floating point representation isn't exactly the same.

((0.0010057-0.0009996)/(double(S)-0.0009996))

ans = 
   3.999999999999858

[Carlos Puente]

Thank you! This solved my problem!