Sure, let's break down the process step by step to convert the wavelength of blue light from nanometers to meters and express it in scientific notation.
1. Understand the Given Data:
- We are given the wavelength of blue light as 483 nm (nanometers).
2. Convert Nanometers to Meters:
- To convert from nanometers to meters, we use the conversion factor where [tex]\( 1 \text{ nm} = 10^{-9} \text{ m} \)[/tex].
- Therefore, the wavelength in meters is calculated as:
[tex]\[
\text{Wavelength in meters} = 483 \text{ nm} \times 10^{-9} = 483 \times 10^{-9} \text{ m}
\][/tex]
3. Express in Scientific Notation:
- To express [tex]\( 483 \times 10^{-9} \)[/tex] in scientific notation, we write it in the form [tex]\( a \times 10^b \)[/tex], where [tex]\( a \)[/tex] is a number between 1 and 10.
- Here, [tex]\( a = 4.83 \)[/tex] and [tex]\( 10^b \)[/tex] takes care of placing the decimal point correctly.
- The result is:
[tex]\[
4.83 \times 10^{-7} \text{ m}
\][/tex]
4. Confirming the Conversion:
- The result [tex]\( 4.83 \times 10^{-7} \text{ m} \)[/tex] indicates that the original wavelength of 483 nm has been correctly converted to meters and expressed in scientific notation.
Thus, the wavelength of the blue light in meters can be expressed as:
[tex]\[
4.83 \times 10^{-7} \text{ m}
\][/tex]
So, the values for the mantissa and exponent in scientific notation are:
[tex]\[
\boxed{4.83 \times 10^{-7} \text{ m}}
\][/tex]
