1. The problem is to understand the value of the probability expressed as $2.23 \times 10^{-7}$, which represents a very small number. 2. The expression $2.23 \times 10^{-7}$ is in scientific notation, where $2.23$ is the coefficient and $10^{-7}$ means we multiply by $0.0000001$. 3. To convert this to decimal form, move the decimal point in $2.23$ seven places to the left: $$2.23 \times 10^{-7} = 0.000000223$$ 4. This means the probability is $0.000000223$, which is a very small chance. 5. In the context of the problem, this small probability could represent the chance that everyone in a room of 101 people has different birthdays, which is extremely unlikely. 6. Understanding scientific notation helps us work with very large or very small numbers easily. Final answer: The value of $2.23 \times 10^{-7}$ in decimal form is $0.000000223$.