Based on numismatic expertise, as the provided context does not contain specific valuation data, a 1946 Roosevelt dime's worth is determined by its silver content and its condition.
As the first year of issue for the Roosevelt dime series, this coin is composed of 90% silver and 10% copper. This gives it a base value tied directly to the fluctuating spot price of silver. This "melt value" is typically in the range of $1.50 to $2.50, though this can change daily. For any 1946 dime that is well-worn from circulation, its value will be limited to this silver content.
The collector, or numismatic, value depends heavily on the coin's condition and mint mark. These dimes were minted in Philadelphia (no mint mark), Denver (D), and San Francisco (S). In average circulated condition, all three are extremely common and worth their silver value. However, for coins in uncirculated condition, the value increases. A typical uncirculated 1946 dime might be worth a few dollars.
For higher-end collectors, the most important detail is the clarity of the horizontal bands on the torch on the coin's reverse. A coin that is professionally graded and designated as having "Full Bands" (FB) will carry a significant premium. A high-grade uncirculated 1946 dime with the Full Bands designation can be worth $20 to $30 or potentially more, depending on the specific grade assigned. To get a precise value for a specific coin, it is best to have it professionally appraised.
