What is 0.000801 written in scientific notation?
A. $8.01 \times 10^{-6}$
B. $8.01 \times 10^{-4}$
C. $8.01 \times 10^{-5}$
D. $80.1 \times 10^{-5}$
Answer (2)
Convert the number to the form a × 1 0 b , where 1 ≤ ∣ a ∣ < 10 .
Move the decimal point in 0.000801 four places to the right to get 8.01.
Since the decimal was moved four places to the right, the exponent is -4.
Therefore, the scientific notation is 8.01 × 1 0 − 4 .
Explanation
Understanding Scientific Notation We need to express the number 0.000801 in scientific notation. Scientific notation requires the number to be written in the form a × 1 0 b , where 1 ≤ ∣ a ∣ < 10 and b is an integer.
Moving the Decimal Point To convert 0.000801 to scientific notation, we need to move the decimal point to the right until we have a number between 1 and 10. Moving the decimal point four places to the right gives us 8.01.
Determining the Exponent Since we moved the decimal point four places to the right, the exponent of 10 will be -4. Therefore, 0.000801 in scientific notation is 8.01 × 1 0 − 4 .
Final Answer Comparing our result with the given options, we see that 8.01 × 1 0 − 4 is one of the choices.
Examples
Scientific notation is extremely useful in fields like astronomy and chemistry, where you often deal with very large or very small numbers. For example, the distance to the nearest star, Proxima Centauri, is approximately 40,208,000,000,000 kilometers. Writing this in scientific notation, we get 4.0208 × 1 0 13 km, which is much easier to handle. Similarly, the mass of an electron is about 0.00000000000000000000000000000091093837 kg, which can be written as 9.1093837 × 1 0 − 31 kg. This notation simplifies calculations and makes these numbers more manageable.
The number 0.000801 can be expressed in scientific notation as 8.01 × 1 0 − 4 . This is achieved by moving the decimal point four places to the right and setting the exponent to -4. The correct option is B.
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