An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Move the decimal point in 0.00000070 to the right until the number is between 1 and 10, resulting in 7.0.
Count the number of places the decimal point was moved (7 places) and since the original number is less than 1, the exponent is -7.
Express the number in scientific notation as 7.0 × 1 0 − 7 .
The coefficient is 7.0 and the exponent is -7, so the answer is 7.0 × 1 0 − 7 .
Explanation
Understanding Scientific Notation We are asked to express the number 0.00000070 in scientific notation. Scientific notation is a way of writing numbers as a product of a number between 1 and 10 (including 1 but excluding 10) and a power of 10. The number 0.00000070 is less than 1, so the exponent of 10 will be negative.
Moving the Decimal Point To convert 0.00000070 to scientific notation, we need to move the decimal point to the right until we have a number between 1 and 10. In this case, we move the decimal point 7 places to the right to get 7.0.
Determining the Exponent Since we moved the decimal point 7 places to the right, the exponent of 10 will be -7. Therefore, 0.00000070 in scientific notation is 7.0 × 1 0 − 7 .
Final Answer Thus, the coefficient is 7.0 and the exponent is -7.
Examples
Scientific notation is incredibly useful in fields like astronomy and chemistry, where you often deal with extremely large or small numbers. For instance, the distance to a faraway galaxy might be 3.086 × 1 0 19 kilometers, and the mass of a hydrogen atom is approximately 1.67 × 1 0 − 27 kg. Using scientific notation makes these numbers easier to handle and compare.
For a current of 15.0 A flowing for 30 seconds, approximately 2.81 × 1 0 21 electrons pass through the device. This is calculated by first determining the total charge and then dividing by the charge of a single electron. Understanding the relationship between current, charge, and electrons is key to this calculation.
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