Question

What is the product in scientific notation?
(2.3 x 10^-4)(5 x 10^-11)

Answer 1

when you multiply, you can re-order it. so
(2.3 * 10^-4) * (5 * 10^-11) is the same as
2.3 * 5 * 10^-4 * 10^-11

now multiply 2.3 * 5
also multiply 10^-4 * 10^-11 (add exponents)
can you do that ?

Answer 2

i'm not good at scientific notation at all >.<

Answer 3

2.3 * 5= 11.5
10^-4 * 10^-11 is 10^(-4 + -11) which is 10^-15
so the answer is
11.5 * 10^-15

However, we have to tweak this, because in scientific notation, the "number" (mantissa) is always between 1 and 10: \( 1 \le m < 10 \)
we have 11.5
to "fix" this, we write 11.5 as 1.15 * 10^1 (make the mantissa smaller, make the exponent bigger).
so
11.5 * 10^-15 becomes
1.15 * 10^1* 10^-15
or
1.15 * 10^-14 (we added the exponents 1+ -15 to get -14)