2.05 The laws of exponents and scientific notation
Use scientific notation to complete the expression.
1 \times 10^{ - 2 } \times 2 \times 10^{ - 5 } = 2 \times ⬚
Evaluate the following. Express your answer in scientific notation.
3 \times 10^{5} \times 7 \times 10^{2}
\left( 4.3 \times 10^{13}\right) \times \left( 1.3 \times 10^{ - 6 }\right)
\left( 9.3 \times 10^{12}\right) \times \left( 8.4 \times 10^{8}\right)
\left( 5.2 \times 10^{20}\right) \times \left( 9.6 \times 10^{12}\right)
\left( 9 \times 10^{9}\right) \times \left( 5.5 \times 10^{ - 6 }\right)
\left( 41.83 \times 10^{28}\right) \div \left( 4.7 \times 10^{18}\right)
1.77 \times 10^{9} + 3.24 \times 10^{10}
2.35 \times 10^{ - 7 } - 4.72 \times 10^{ - 8 }
\dfrac{73.8 \times 10^{17}}{9 \times 10^{12}}
\dfrac{3 \times 10^{3}}{12 \times 10^{ - 1 }}
\dfrac{800\,000 \times 180\,000\,000}{6\,000\,000\,000}
11\,000\,000 \times 0.004 \times 0.0005 \times 20\,000
4.088 \times 10^{15} \div \left( 5.6 \times 10^{8} \right)
Evaluate \left( 3.7 \times 10^{ - 4 }\right)^{2}. Give your answer in scientific notation, correct to five significant figures
Evaluate \dfrac{6.45 \times 10^{9} \times 4.3 \times 10^{ - 3 }}{8.3 \times 10^{4}}. Give your answer in scientific notation, correct to four decimal places.
A country’s land size is approximately 84\,000 \text{ mi}^{2} and its population is approximately 21 million people.
Express the following in scientific notation:
The land size in square miles
The population
Determine the population density measured in \dfrac{\text{ mi}^{2}}{\text{person}} and write using scientific notation.
The speed of light is approximately 3 \times 10^{5}\, \dfrac{\text{km}}{\text{s}}. If a star that is 7.525 \times 10^{12} \text{ km} away from Earth is born, how long after it is born would we see it from Earth? Give your answer in scientific notation, rounding to 1 significant figure.
The volume of a sphere is given by V = \dfrac{4}{3} \pi r^{3}.
Planet A has a radius of 4 \times 10^{10} \text{ km}, while Planet B has a radius of 8 \times 10^{17} \text{ km}.
How many times greater than the volume of Planet A is the volume of Planet B? Give your answer in scientific notation.
The average mass of a grain of sand on a beach is about 1.5 \times 10^{ - 5 } \text{ g}. Over several years, a beach goes through a natural process of weathering and loses approximately 9.5 \times 10^{10} grains of sand.
What mass of sand is lost over this time period? Give your answer in scientific notation.
The mass of a planet is approximately 8.1 \times 10^{21} \text{ kg} and the mass of its single moon is \\7.9 \times 10^{19} \text{ kg}. Determine the combined mass of the planet and its moon in scientific notation.
Evaluate each of the following expressions. Write your answers using scientific notation:
Evaluate each of the following expressions, writing your answer in standard form:
Evaluate each of the following expressions. Write your answers using scientific notation: