Question
scientific notation of 7.5 x 4.1 x 10^6
Answers
GPT-4o mini
To express the product of \(7.5\), \(4.1\), and \(10^6\) in scientific notation, we first multiply the numerical coefficients:
\[
7.5 \times 4.1 = 30.75
\]
Now, we can express \(30.75\) in scientific notation. To do this, we write \(30.75\) as \(3.075 \times 10^1\).
We then combine this with \(10^6\):
\[
30.75 \times 10^6 = 3.075 \times 10^1 \times 10^6
\]
Using the property of exponents that states \(a^m \times a^n = a^{m+n}\), we combine the powers of ten:
\[
3.075 \times 10^{1 + 6} = 3.075 \times 10^7
\]
Thus, the final result in scientific notation is:
\[
3.075 \times 10^7
\]
\[
7.5 \times 4.1 = 30.75
\]
Now, we can express \(30.75\) in scientific notation. To do this, we write \(30.75\) as \(3.075 \times 10^1\).
We then combine this with \(10^6\):
\[
30.75 \times 10^6 = 3.075 \times 10^1 \times 10^6
\]
Using the property of exponents that states \(a^m \times a^n = a^{m+n}\), we combine the powers of ten:
\[
3.075 \times 10^{1 + 6} = 3.075 \times 10^7
\]
Thus, the final result in scientific notation is:
\[
3.075 \times 10^7
\]