What is 673.5 in scientific notation
The Correct Answer and Explanation is :
To express the number 673.5 in scientific notation, we first need to understand the format of scientific notation, which is ( a \times 10^n ). In this format, ( a ) is a number greater than or equal to 1 but less than 10, and ( n ) is an integer that indicates how many places the decimal point has been moved.
To convert 673.5 into scientific notation, follow these steps:
- Identify the significant digits: The number 673.5 has three significant digits: 6, 7, and 3, with the decimal point after the 5.
- Move the decimal point: We want to move the decimal point to the left until we have a number between 1 and 10. In this case, moving the decimal point two places to the left gives us 6.735.
- Count the moves: We moved the decimal point 2 places to the left, which means our exponent ( n ) will be 2.
- Combine the parts: Now, we can write this in scientific notation:
[
673.5 = 6.735 \times 10^2
]
Thus, the scientific notation for 673.5 is ( 6.735 \times 10^2 ).
Why Use Scientific Notation?
Scientific notation is especially useful in fields like science and engineering where dealing with very large or very small numbers is common. It allows for easier readability and computation. For example, instead of writing 0.000000567, we can simply write ( 5.67 \times 10^{-7} ). This notation simplifies calculations involving multiplication and division, as you can work with the coefficients separately from the powers of ten.
In summary, converting numbers to scientific notation facilitates better understanding and manipulation of numbers, particularly in data analysis, research, and problem-solving in various scientific fields.