Which of the following expresses 393500 in scientific notation? This question delves into the realm of scientific notation, a powerful tool for representing extremely large or small numbers in a concise and manageable format. Join us as we embark on a journey to uncover the intricacies of scientific notation and its applications in the world of science and engineering.

Scientific notation, a method of expressing numbers as a product of a coefficient and a power of 10, offers a compact and efficient way to represent both vast and minute values. Its versatility extends to a wide range of fields, including astronomy, physics, chemistry, and engineering, where it facilitates complex calculations and comparisons.

Scientific Notation

Scientific notation is a way of writing very large or very small numbers in a more compact and manageable form. It is used extensively in scientific and engineering fields to represent quantities that span many orders of magnitude.

Converting to Scientific Notation

To convert a number to scientific notation, follow these steps:

1. Move the decimal point to the left or right until there is only one non-zero digit to the left of the decimal point.
2. Count the number of places the decimal point was moved.
3. Write the number in the form a x 10ⁿ, where a is the number from step 1 and n is the number of places the decimal point was moved.

For example, to convert 393500 to scientific notation, we would move the decimal point 5 places to the left, resulting in 3.935. The exponent would be 5, so the number in scientific notation is 3.935 x 10 ⁵.

Applications of Scientific Notation, Which of the following expresses 393500 in scientific notation

Scientific notation is used in a wide variety of scientific and engineering fields. Some common applications include:

• Expressing very large or very small numbers, such as the number of atoms in the universe or the size of a subatomic particle.
• Simplifying calculations and comparisons. For example, it is much easier to compare the numbers 3.935 x 10 ⁵and 2.7 x 10 ⁶than it is to compare 393500 and 2700000.

Common Mistakes

One common mistake when converting to scientific notation is to forget to move the decimal point the correct number of places. Another mistake is to write the exponent incorrectly. To avoid these mistakes, it is important to follow the steps carefully and to check your work.

Frequently Asked Questions: Which Of The Following Expresses 393500 In Scientific Notation

What is the general form of scientific notation?

Scientific notation is expressed in the form a x 10^n, where ‘a’ is a coefficient ranging from 1 to 10 and ‘n’ represents an integer exponent.

How do I convert 393500 to scientific notation?

To convert 393500 to scientific notation, move the decimal point 5 places to the left and adjust the exponent accordingly, resulting in 3.935 x 10^5.

What are the advantages of using scientific notation?

Scientific notation simplifies calculations, enhances readability, and facilitates comparisons of extremely large or small numbers.