- Identify that both terms in the expression \((1.9 \times 10^{-4}) + (4.5 \times 10^{-4})\) share a common power of 10.
- Use the distributive property to factor out \(10^{-4}\), yielding \((1.9 + 4.5) \times 10^{-4}\).
- Perform the addition of the coefficients: \(1.9 + 4.5 = 6.4\).
- Finalize the result as \(\boxed{6.4 \times 10^{-4}}\).
Explanation
- Analyzing the Expression
We are given the sum of two numbers expressed in scientific notation: \((1.9 \times 10^{-4}) + (4.5 \times 10^{-4})\). Both terms share the same power of 10, specifically \(10^{-4}\). This structure allows us to simplify the addition by focusing on the coefficients.
- Factoring and Addition
To add these two terms, we can factor out the common power of 10. According to the distributive property of multiplication, \(a \times 10^n + b \times 10^n = (a + b) \times 10^n\). In our case, \(a = 1.9\), \(b = 4.5\), and \(n = -4\). Therefore, we have:
\[(1.9 \times 10^{-4}) + (4.5 \times 10^{-4}) = (1.9 + 4.5) \times 10^{-4}\]
- Calculating the Result
Now we add the coefficients: \(1.9 + 4.5 = 6.4\). Substituting this back into our expression, we obtain:
\[6.4 \times 10^{-4}\]
- Conclusion and Identification of the Answer
Comparing our result \(6.4 \times 10^{-4}\) with the given options, we identify it as one of the choices. Thus, the correct answer is \(6.4 \times 10^{-4}\).
Examples
Scientific notation is commonly used in fields like physics and chemistry to handle extremely small or large numbers efficiently. For instance, when measuring the microscopic distance between two molecules or the mass of an electron, researchers frequently use scientific notation to simplify calculations and maintain clarity. By adding numbers with the same exponents, as shown here, scientists can quickly combine data points and communicate results precisely.