Given $P(A)=0.51, P(B)=0.7$ and $P(A \cap B)=0.477$, find the value of $P(A \cup B)$, rounding to the nearest thousandth, if necessary.

Step 1 ：Given \(P(A)=0.51\), \(P(B)=0.7\) and \(P(A \cap B)=0.477\), find the value of \(P(A \cup B)\), rounding to the nearest thousandth, if necessary.

Step 2 ：We need to find the probability of \(P(A \cup B)\). We can use the formula for the probability of the union of two events: \(P(A \cup B) = P(A) + P(B) - P(A \cap B)\).

Step 3 ：\(P(A \cup B) = 0.51 + 0.7 - 0.477\)

Step 4 ：\(P(A \cup B) = 0.733\)

Step 5 ：\(\boxed{0.733}\)