Question

1. 0.00001203
2. 6.5
3. 8
4. distance from the sun to the earth: 147,000,000 km
5. mass of an oxygen molecule: 0.000000000000000000000053 g

multiply and write the answers in scientific notation.

1. (0.00000008)(6000)
2. (750,000)(23,000,000)
3. (2.45×10⁻²)(5.1×10⁻⁸)
4. (4.05×10⁻⁶)(8.001×10⁸)
5. (3.5×10⁰)(1.25×10⁻¹⁰)
6. (1.415×10⁻²)(6.1×10⁰)
7. (5.15×10¹²)(9.1×10⁸)
8. (6.25×10²)(3.215×10⁹)
9. approximately how many atoms are in one gram of pure gold? (see example 4 for help with this problem.)
10. approximately how much would 8.0×10²⁴ atoms of silver weigh, in grams? (see example 4 for help with this problem.)

Explanation:

Step1: Recall scientific - notation rules

Scientific notation is of the form $a\times10^{n}$, where $1\leqslant|a|\lt10$ and $n$ is an integer.

Step2: Solve problem 23

First, rewrite the numbers in scientific - notation. $0.00000008 = 8\times10^{-8}$ and $6000 = 6\times10^{3}$. Then, multiply: $(8\times10^{-8})(6\times10^{3})=(8\times6)\times(10^{-8}\times10^{3}) = 48\times10^{-5}$. Adjust to proper scientific - notation: $4.8\times10^{-4}$.

Step3: Solve problem 24

Rewrite the numbers: $750000 = 7.5\times10^{5}$ and $23000000 = 2.3\times10^{7}$. Multiply: $(7.5\times10^{5})(2.3\times10^{7})=(7.5\times2.3)\times(10^{5}\times10^{7})=17.25\times10^{12}$. Adjust: $1.725\times10^{13}$.

Step4: Solve problem 25

Multiply the coefficients and add the exponents: $(2.45\times10^{-2})(5.1\times10^{-8})=(2.45\times5.1)\times(10^{-2}\times10^{-8}) = 12.495\times10^{-10}$. Adjust: $1.2495\times10^{-9}$.

Step5: Solve problem 26

$(4.05\times10^{-6})(8.001\times10^{8})=(4.05\times8.001)\times(10^{-6}\times10^{8})=32.40405\times10^{2}$. Adjust: $3.240405\times10^{3}$.

Step6: Solve problem 27

$(3.5\times10^{0})(1.25\times10^{-10})=(3.5\times1.25)\times(10^{0}\times10^{-10}) = 4.375\times10^{-10}$.

Step7: Solve problem 28

$(1.415\times10^{-2})(6.1\times10^{0})=(1.415\times6.1)\times(10^{-2}\times10^{0})=8.6315\times10^{-2}$.

Step8: Solve problem 29

$(5.15\times10^{12})(9.1\times10^{8})=(5.15\times9.1)\times(10^{12}\times10^{8}) = 46.865\times10^{20}$. Adjust: $4.6865\times10^{21}$.

Step9: Solve problem 30

$(6.25\times10^{2})(3.215\times10^{9})=(6.25\times3.215)\times(10^{2}\times10^{9})=20.09375\times10^{11}$. Adjust: $2.009375\times10^{12}$.

Answer:

1. $4.8\times10^{-4}$
2. $1.725\times10^{13}$
3. $1.2495\times10^{-9}$
4. $3.240405\times10^{3}$
5. $4.375\times10^{-10}$
6. $8.6315\times10^{-2}$
7. $4.6865\times10^{21}$
8. $2.009375\times10^{12}$