For the sake of example, let's multiply the two numbers [tex]2.3 \times 10^5 [/tex] and [tex]3.5 \times 10^7[/tex] together. Altogether, we have:
[tex]2.3\times10^5\times3.5\times10^7[/tex]
Rearranging the expression, we can group the exponents and coefficients together:
[tex]2.3\times3.5\times10^5\times10^7[/tex]
Multiplying each out, we notice that since [tex]10^5[/tex] and [tex]10^7[/tex] have the same base (10), multiplying them has the effect of adding their exponents, which leaves us with:
[tex]2.3\times3.5\times10^{5+7}=8.05\times10^{12}[/tex]
The takeaway here is that multiplying two numbers in scientific notation together has the effect of multiplying its coefficients and adding its exponents.
