Question

in 1 - 6, find each product or quotient. record answers in both scientific and standard notation.

1. (4.3×10^(-3))(2×10^(-5))
2. (8×10^(-3))(0.0003)
3. (3.5×10^(4))(2×10^(3))
4. \frac{1.2×10^(8)}{4×10^(3)}
5. \frac{5000000}{2.5×10^(3)}
6. \frac{9×10^(11)}{1.5×10^(7)}

scientific: ________
standard: ________
scientific: ________
standard: ________
scientific: ________
standard: ________
scientific: ________
standard: ________
scientific: ________
standard: ________
scientific: ________
standard: ________

Explanation:

Step1: Multiply the coefficients and add the exponents for multiplication

For $(4.3\times 10^{-3})(2\times 10^{-5})$, multiply $4.3$ and $2$ to get $4.3\times2 = 8.6$, and add the exponents $-3+( - 5)=-8$. So in scientific - notation it is $8.6\times 10^{-8}$. In standard notation, $8.6\times 10^{-8}=0.000000086$.

Step2: Rewrite the non - scientific number in scientific notation for multiplication

For $(8\times 10^{-3})(0.0003)$, rewrite $0.0003 = 3\times 10^{-4}$. Then multiply the coefficients $8\times3 = 24$ and add the exponents $-3+( - 4)=-7$. So in scientific notation it is $24\times 10^{-7}=2.4\times 10^{-6}$. In standard notation, $2.4\times 10^{-6}=0.0000024$.

Step3: Multiply the coefficients and add the exponents for multiplication

For $(3.5\times 10^{4})(2\times 10^{3})$, multiply $3.5$ and $2$ to get $3.5\times2 = 7$, and add the exponents $4 + 3=7$. So in scientific notation it is $7\times 10^{7}$. In standard notation, $7\times 10^{7}=70000000$.

Step4: Divide the coefficients and subtract the exponents for division

For $\frac{1.2\times 10^{8}}{4\times 10^{3}}$, divide $1.2$ by $4$ to get $\frac{1.2}{4}=0.3$, and subtract the exponents $8 - 3 = 5$. So $0.3\times 10^{5}=3\times 10^{4}$. In standard notation, $3\times 10^{4}=30000$.

Step5: Rewrite the non - scientific number in scientific notation for division

For $\frac{5000000}{2.5\times 10^{3}}$, rewrite $5000000 = 5\times 10^{6}$. Then divide the coefficients $\frac{5}{2.5}=2$ and subtract the exponents $6 - 3 = 3$. So in scientific notation it is $2\times 10^{3}$. In standard notation, $2\times 10^{3}=2000$.

Step6: Divide the coefficients and subtract the exponents for division

For $\frac{9\times 10^{11}}{1.5\times 10^{7}}$, divide $9$ by $1.5$ to get $\frac{9}{1.5}=6$, and subtract the exponents $11 - 7 = 4$. So in scientific notation it is $6\times 10^{4}$. In standard notation, $6\times 10^{4}=60000$.

Answer:

1. Scientific: $8.6\times 10^{-8}$, Standard: $0.000000086$
2. Scientific: $2.4\times 10^{-6}$, Standard: $0.0000024$
3. Scientific: $7\times 10^{7}$, Standard: $70000000$
4. Scientific: $3\times 10^{4}$, Standard: $30000$
5. Scientific: $2\times 10^{3}$, Standard: $2000$
6. Scientific: $6\times 10^{4}$, Standard: $60000$