How the conversions work
American, decimal, and fractional are three conventions for the same underlying number: the price of a wager. They differ in how that price is displayed, which is why a U.S. sportsbook and a European exchange can show the same wager with very different-looking lines.
American odds
American odds are quoted relative to a $100 wager. Positive numbers (e.g., +150) tell you how much profit a $100 stake returns. Negative numbers (e.g., -110) tell you how much you must risk to win $100 in profit. -110 implies that the book is pricing the outcome at a 52.4% chance, before its margin.
Decimal odds
Decimal odds (used in Europe and Australia) show the total payout per $1 wagered, including the stake. A decimal price of 2.50 means a $1 bet returns $2.50 total ($1.50 profit + $1 returned). +150 American equals 2.50 decimal; -110 American equals approximately 1.91 decimal.
Fractional odds
Fractional odds (common in the UK on horse racing) show profit relative to stake. 5/2 means $5 profit for every $2 wagered. 10/11 (often called "odds-on") means $10 profit on every $11 wagered. Convert by computing the fraction plus 1 to get decimal, then convert decimal to American.
Why convert?
If you compare prices across U.S. and offshore books, or read European betting analysis, you will see all three formats. Converting on the fly removes the friction. Sharp bettors typically work in decimal because compound math (parlays, expected value) is cleanest in decimal form.
For more on what these numbers mean, see How to Read American Odds and Line Shopping.