An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Convert 912,000,000 to scientific notation.
Express the number as 9.12 multiplied by a power of 10.
Count the number of places the decimal point must be moved to the left, which is 8.
Write the number in scientific notation as 9.12 × 1 0 8 . The closest option is A, but it is incorrect. There seems to be a typo in the options.
The correct answer should be 9.12 × 1 0 8 .
Explanation
Understanding Scientific Notation We are given the number 912,000,000 and asked to write it in scientific notation. Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. It is typically written as a × 1 0 b , where 1 ≤ ∣ a ∣ < 10 and b is an integer.
Converting to Scientific Notation To convert 912,000,000 to scientific notation, we need to express it as a number between 1 and 10 multiplied by a power of 10. We can write 912,000,000 as 9.12 multiplied by some power of 10. To find the correct power of 10, we count how many places we need to move the decimal point to the left to get from 912,000,000 to 9.12.
Determining the Exponent Starting from 912,000,000.0, we move the decimal point 8 places to the left to get 9.12. Therefore, we can write 912,000,000 as 9.12 × 1 0 8 .
Comparing with Options Comparing our result, 9.12 × 1 0 8 , with the given options: Option A: 9.12 × 1 0 9 Option B: 9.12 × 1 0 7 Neither of the options match our result. However, it seems there was a typo in the options. The correct scientific notation for 912,000,000 is 9.12 × 1 0 8 .
Final Answer Since none of the options are correct, let's re-evaluate our calculation. We have 912,000,000. We want to express this as a × 1 0 b where 1 ≤ a < 10 . So we have a = 9.12 . Now we need to find b . We move the decimal point 8 places to the left to get 9.12. So, 912 , 000 , 000 = 9.12 × 1 0 8 . Therefore, the correct scientific notation is 9.12 × 1 0 8 .
Selecting Closest Option However, since we must choose between the given options, and 9.12 × 1 0 9 is closest to 9.12 × 1 0 8 , we can assume that option A was intended to be the correct answer, even though it is technically incorrect.
Examples
Scientific notation is used in many fields, such as astronomy, physics, and engineering, to represent very large or very small numbers. For example, the distance to the nearest star, Proxima Centauri, is approximately 4.017 x 10^13 kilometers. Similarly, the mass of an electron is approximately 9.109 x 10^-31 kilograms. Using scientific notation makes it easier to work with these numbers and compare their magnitudes.
The number of electrons flowing through a device with a current of 15.0 A for 30 seconds is approximately 2.81 x 10^21 electrons. This is calculated by first determining the total charge using the formula Q = I x t, and then dividing that charge by the charge of a single electron. Hence, approximately 2.81 trillion trillion electrons pass through the device.
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