An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Approximately 2.81 × 1 0 21 electrons flow through an electric device delivering a current of 15.0 A for 30 seconds. This is calculated using the relationship between current, charge, and the number of electrons each carrying a charge of about 1.6 × 1 0 − 19 C .
;
7.5 × 1 0 − 5
Explanation
Understanding the Problem We are given the number 0.75 × 1 0 − 4 and asked to convert it into correct scientific notation. Scientific notation requires the number to be in the form a × 1 0 b where 1 ≤ ∣ a ∣ < 10 and b is an integer.
Adjusting the Decimal Place In the given number 0.75 × 1 0 − 4 , the value a = 0.75 which is less than 1. To convert this to scientific notation, we need to adjust the decimal place in 0.75 so that it is between 1 and 10. We can do this by moving the decimal point one place to the right, which gives us 7.5.
Adjusting the Exponent Moving the decimal point one place to the right is equivalent to multiplying by 10. To compensate for this, we must divide by 10, which means decreasing the exponent of 10 by 1. So, we have: 0.75 × 1 0 − 4 = 7.5 × 1 0 − 4 − 1 = 7.5 × 1 0 − 5
Final Answer Therefore, the number 0.75 × 1 0 − 4 in correct scientific notation is 7.5 × 1 0 − 5 .
Examples
Scientific notation is used in many fields, such as physics, astronomy, and chemistry, to represent very large or very small numbers. For example, the speed of light is approximately 3.0 × 1 0 8 meters per second, and the mass of an electron is approximately 9.11 × 1 0 − 31 kilograms. Using scientific notation makes it easier to work with these numbers and compare their magnitudes. Imagine calculating the distance light travels in a year or the total mass of electrons in a large atom; scientific notation simplifies these calculations significantly.
