Symbolism, Imagery, Allegory
Tom runs through money very quickly. Not only does he lose Squire Allworthy's five hundred pounds almost as soon as he leaves home (partly with Black George's help), but he also spends the rest of his cash quickly on rounds of drinks for his soldier buddies or on charity for his local highwayman. The point is: Tom is definitely careless with money.
The one exception to Tom's spendthrift ways is the hundred-pound note that Tom discovers in a small book that Sophia has dropped on the road to London. Tom hangs onto this hundred-pound note even when he is desperate for cash, and even when Partridge pressures him to just spend the money already.
Tom refuses, because he wants to use this money as a reason to see Sophia again. She is so deeply angry with him over his relationship with Mrs. Waters that she might refuse to see him unless he has a definite excuse, like returning a large sum of money that she has lost.
Tom's careful treatment of this hundred-pound note goes to show that Tom is willing to learn some self-discipline for Sophia's sake, even if his natural tendency is to spend everything in sight. Tom's issues with women are a little harder for him to overcome than his carelessness with money, but at least this hundred-pound note—which Tom carries safely for ages without ever seeming tempted to spend it—gives us our first real proof that Tom can learn to change for Sophia's sake.