To multiply the numbers in scientific notation, we can use the property of exponents and the rules of multiplication. Specifically, we multiply the coefficients together and add the exponents of the powers of 10.
Given: \[ (1.87 \times 10^9) \times (6.7 \times 10^6) \]
Step 1: Multiply the coefficients
First, multiply the coefficients (1.87 and 6.7): \[ 1.87 \times 6.7 = 12.529 \]
Step 2: Add the exponents
Next, add the exponents of the powers of 10: \[ 10^9 \times 10^6 = 10^{9+6} = 10^{15} \]
Step 3: Combine the results
Now combine the results from Steps 1 and 2: \[ 12.529 \times 10^{15} \]
Step 4: Convert to proper scientific notation
Since the coefficient \(12.529\) is greater than \(10\), we need to adjust it to be within the range of \(1\) to \(10\). We can express \(12.529\) as \(1.2529 \times 10^1\): \[ 12.529 = 1.2529 \times 10^1 \]
Now, we can combine this with the \(10^{15}\): \[ 1.2529 \times 10^1 \times 10^{15} = 1.2529 \times 10^{1+15} = 1.2529 \times 10^{16} \]
Final Answer
Thus, the final result in scientific notation is: \[ \boxed{1.2529 \times 10^{16}} \]
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