Question

multiply. write your answer in scientific notat
7 (4.1×10^6)(2.4×10^2)
8 (3.95×10^8)(5.8×10^3)
9 (9.7×10^8)(6×10^11)

Explanation:

Step1: Multiply the coefficients

For $(4.1\times 10^{6})(2.4\times 10^{2})$, multiply $4.1$ and $2.4$: $4.1\times2.4 = 9.84$.

Step2: Add the exponents of 10

Add the exponents $6$ and $2$: $10^{6 + 2}=10^{8}$.

Step3: Combine the results

The result is $9.84\times 10^{8}$.

For $(3.95\times 10^{8})(5.8\times 10^{3})$:

Step1: Multiply the coefficients

$3.95\times5.8=22.91$.

Step2: Add the exponents of 10

$10^{8 + 3}=10^{11}$.

Step3: Adjust to scientific - notation

Since $22.91 = 2.291\times 10^{1}$, then the result is $2.291\times 10^{1}\times10^{11}=2.291\times 10^{12}$.

For $(9.7\times 10^{8})(6\times 10^{11})$:

Step1: Multiply the coefficients

$9.7\times6 = 58.2$.

Step2: Add the exponents of 10

$10^{8+11}=10^{19}$.

Step3: Adjust to scientific - notation

Since $58.2=5.82\times 10^{1}$, then the result is $5.82\times 10^{1}\times10^{19}=5.82\times 10^{20}$.

Answer:

1. $9.84\times 10^{8}$
2. $2.291\times 10^{12}$
3. $5.82\times 10^{20}$