What is the product of 41 and \( 8.4 \times 10^{4} \) expressed in scientific notation? Answer Attempt 1 out of 2 Answer: \( \square \times 10 \square \) Submit Answer

To find the product of 41 and \( 8.4 \times 10^{4} \), you first multiply the coefficients: \( 41 \times 8.4 = 344.4 \). Next, you keep the \( 10^{4} \) as is. So now you have \( 344.4 \times 10^{4} \). To express \( 344.4 \) in scientific notation, convert it to \( 3.444 \times 10^{2} \). Now, combine this with \( 10^{4} \): \( 3.444 \times 10^{2} \times 10^{4} = 3.444 \times 10^{6} \). So, the answer is \( 3.444 \times 10^{6} \). For those curious about scientific notation, it was developed in the 17th century and has made calculations easier for scientists and mathematicians alike. This notation allows for the compact representation of very large numbers (like the distance to stars) or very small numbers (like the size of atoms). It’s like giving your numbers a stylish new outfit! If you’re embarking on calculations involving scientific notation, remember to keep your base numbers between 1 and 10. A common mistake is accidentally moving the decimal point too far or not adjusting the power of ten correctly. Double-checking your steps can prevent these arithmetic mishaps!