Question

find each product and record your solutions in scientific notation.

1. (1.5 x 10^-9)(5 x 10^-3)
2. (3 x 10^4)(7.2 x 10^5)
3. (2.2 x 10^-2)(8.5 x 10^6)

Explanation:

Step1: Multiply the coefficients

For $(1.5\times10^{-9})(5\times10^{-3})$, multiply $1.5$ and $5$: $1.5\times5 = 7.5$.
For $(3\times10^{4})(7.2\times10^{5})$, multiply $3$ and $7.2$: $3\times7.2=21.6$.
For $(2.2\times10^{-2})(8.5\times10^{6})$, multiply $2.2$ and $8.5$: $2.2\times8.5 = 18.7$.

Step2: Add the exponents of 10

For $(1.5\times10^{-9})(5\times10^{-3})$, add the exponents: $-9+( - 3)=-12$. So the result is $7.5\times10^{-12}$.
For $(3\times10^{4})(7.2\times10^{5})$, add the exponents: $4 + 5=9$. Since $21.6=2.16\times10^{1}$, the result is $2.16\times10^{1}\times10^{9}=2.16\times10^{10}$.
For $(2.2\times10^{-2})(8.5\times10^{6})$, add the exponents: $-2 + 6=4$. Since $18.7=1.87\times10^{1}$, the result is $1.87\times10^{1}\times10^{4}=1.87\times10^{5}$.

Answer:

1. $7.5\times10^{-12}$
2. $2.16\times10^{10}$
3. $1.87\times10^{5}$