Question

find each product and record your solutions in scientific notation. 1. $(1.5\times10^{-5})(5\times10^{-3})$ 2. $(3\times10^{4})(7.2\times10^{7})$ 3. $(2.2\times10^{-4})(8.5\times10^{4})$

Explanation:

Step1: Multiply the coefficients

For $(1.5\times 10^{-5})(5\times 10^{-3})$, multiply $1.5$ and $5$: $1.5\times5 = 7.5$.

Step2: Add the exponents of 10

Add the exponents $- 5$ and $-3$: $-5+( - 3)=-8$.
So, $(1.5\times 10^{-5})(5\times 10^{-3})=7.5\times 10^{-8}$.

For $(3\times 10^{4})(7.2\times 10^{1})$:

Step1: Multiply the coefficients

Multiply $3$ and $7.2$: $3\times7.2 = 21.6$.

Step2: Add the exponents of 10

Add the exponents $4$ and $1$: $4 + 1=5$.
Since $21.6=2.16\times10^{1}$, then $(3\times 10^{4})(7.2\times 10^{1})=2.16\times10^{1}\times10^{5}=2.16\times 10^{6}$.

For $(2.2\times 10^{-1})(8.5\times 10^{4})$:

Step1: Multiply the coefficients

Multiply $2.2$ and $8.5$: $2.2\times8.5 = 18.7$.

Step2: Add the exponents of 10

Add the exponents $-1$ and $4$: $-1 + 4=3$.
Since $18.7 = 1.87\times10^{1}$, then $(2.2\times 10^{-1})(8.5\times 10^{4})=1.87\times10^{1}\times10^{3}=1.87\times 10^{4}$.

Answer:

1. $7.5\times 10^{-8}$
2. $2.16\times 10^{6}$
3. $1.87\times 10^{4}$