Enter the number in scientific notation. 86,792 =
The correct answer and explanation is:
The number 86,792 in scientific notation is written as 8.6792 × 10^4.
Explanation:
Scientific notation is a way of expressing very large or very small numbers more compactly and clearly. It expresses a number as the product of two factors:
- A decimal number between 1 and 10 (including 1 but less than 10).
- A power of 10 (expressed as 10 raised to an exponent).
For the number 86,792, follow these steps to convert it into scientific notation:
- Identify the decimal part:
Move the decimal point in 86,792 to the left until only one non-zero digit remains to the left of the decimal.- The decimal point in 86,792 is initially at the end (86,792.0).
- Moving the decimal point 4 places to the left gives 8.6792.
- Count the number of places moved:
The decimal was moved 4 places to the left. - Write the number as a product:
Since the decimal point moved 4 places left, multiply by 10 raised to the power of 4:
86,792 = 8.6792 × 10^4
The exponent 4 indicates the decimal point’s original position relative to its current position in 8.6792. The positive exponent shows the decimal point was moved left to convert to a number between 1 and 10.
This method is useful because it makes large numbers easier to read, write, and work with in calculations, especially in science and engineering. For example, 86,792 written as 8.6792 × 10^4 is much simpler to use in equations or when multiplying/dividing by other numbers in scientific notation.
In summary, the number 86,792 expressed in scientific notation is 8.6792 × 10^4 because the decimal moves four places to the left to form a number between 1 and 10, then multiplied by 10 raised to the fourth power to keep the original value.