An astronomer's infrared telescope is able to detect radiation with a wavelength of 0.00000957 meters. Write this number in scientific notation.

Break Down the Problem

1. Identify the value to be converted to scientific notation.
2. Determine the appropriate power of ten that the value corresponds to.

Relevant Concepts

Scientific notation represents a number in the form of $a \times 10^n$ where $1 \leq a < 10$ and $n$ is an integer.

Analysis and Detail

1. Given the number $0.00000957$ meters:
   • We can express $0.00000957$ in scientific notation by moving the decimal point to the right until it is just to the right of the first non-zero digit.
   • The decimal is moved 6 places to the right: $0.00000957 = 9.57 \times 10^{-6}$
   • Here, $9.57$ is between 1 and 10, and we moved the decimal 6 places, which gives us the exponent $-6$.

Verify and Summarize

• The conversion is accurate as we followed the rules for scientific notation.

Final Answer

The value $0.00000957$ meters in scientific notation is: $9.57 \times 10^{-6}$