Question

I NEED EXPLANATION THX
(3.2 x 10^2) x (1.05 x 10^3)

Answer 1

3.36 x
`10^(5)`

Explanation:

So we have (3.2 x 10²) x (1.05 x 10³). Note that these are both numbers in scientific notation.

Sort of like grouping like terms in algebra, the easiest way to multiply two numbers in scientific notation is deal with the decimal parts and tens separately: multiply the decimal numbers and then multiply the tens.

First let's multiply the decimals: 3.2 x 1.05 = 3.36

Now multiply the tens, remembering the index rule
`(a^(x))(a^(y) )=a^(x+y)`:

10² x 10³=
`10^(2+3)`=
`10^(5)`

So altogether, our answer is 3.36 x
`10^(5)`