Question

When multiplying numbers in scientific notation you blank the coefficients and substract the exponents?

Answer 1

For the sake of example, let's multiply the two numbers
`2.3 * 10^5` and
`3.5 * 10^7` together. Altogether, we have:


`2.3*10^5*3.5*10^7`

Rearranging the expression, we can group the exponents and coefficients together:


`2.3*3.5*10^5*10^7`

Multiplying each out, we notice that since
`10^5` and
`10^7` have the same base (10), multiplying them has the effect of adding their exponents, which leaves us with:


`2.3*3.5*10^(5+7)=8.05*10^(12)`

The takeaway here is that multiplying two numbers in scientific notation together has the effect of multiplying its coefficients and adding its exponents.