QQuestionAstronomy
QuestionAstronomy
Write the number indicated in each statement in scientific notation.
(a) A light-year, the distance that light travels in one year, is about 5,900,000,000,000 mi.
(b) The diameter of an electron is about 0.0000000000004 cm.
(c) A drop of water contains more than 33 billion billion molecules.
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Answer
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Step 1:I'll solve this problem step by step, carefully following the LaTeX formatting guidelines:
Step 2:: Convert 5,900,000,000,000 mi to scientific notation
• Scientific notation format is $$5.9 \times 10^{12}$$ mi
• Count the number of digits to the right of the first non-zero digit • First non-zero digit is 5 • Total digits after 5 are 12
Step 3:: Convert 0.0000000000004 cm to scientific notation
• Scientific notation format is $$4 \times 10^{-12}$$ cm
• Count the number of zeros after the decimal point before the first non-zero digit • There are 11 zeros • First non-zero digit is 4
Step 4:: Convert 33 billion billion molecules to scientific notation
• This simplifies to $$3.3 \times 10^{19}$$ molecules
• 33 billion billion = 33 \times 10^{9} \times 10^{9}
Final Answer
(a) 5.9 \times 10^{12} mi (b) 4 \times 10^{- 12} cm (c) 3.3 \times 10^{19} molecules
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