An orange light has a wavelength of 630 nm. What is the wavelength in meters? Give your answer in proper scientific notation. [?] \times 10^{[?]} m Enter the coefficient in the green box and the exponent in the yellow box.
Answer (2)
Convert nanometers to meters using the conversion factor 1 m = 1 0 − 9 e wl in e m .
Multiply 630 nm by 1 0 − 9 to get 630 e wl in e × 1 0 − 9 e wl in e m .
Express 630 e wl in e × 1 0 − 9 in scientific notation as 6.30 e wl in e × 1 0 − 7 e wl in e m .
The wavelength of the orange light is 6.30 × 1 0 − 7 e wl in e m .
Explanation
Understanding the Problem We are given that the wavelength of an orange light is 630 nm (nanometers). We need to convert this wavelength into meters and express the result in scientific notation. Scientific notation is a way of writing numbers as a product of a number between 1 and 10 (the coefficient) and a power of 10 (the exponent).
Conversion Factor First, we need to know the conversion factor between nanometers and meters. We know that 1 nm = 1 0 − 9 m. This means that one nanometer is one billionth of a meter.
Converting to Meters To convert 630 nm to meters, we multiply 630 by the conversion factor 1 0 − 9 : 630 m = 630 m × 1 m 1 0 − 9 e wl in e m = 630 e wl in e × 1 0 − 9 e wl in e m
Expressing in Scientific Notation Now, we need to express 630 e wl in e × 1 0 − 9 in proper scientific notation. To do this, we want to write 630 as a number between 1 and 10 multiplied by a power of 10. We can write 630 as 6.30 e wl in e × 1 0 2 . So, we have: 630 e wl in e × 1 0 − 9 = ( 6.30 e wl in e × 1 0 2 ) e wl in e × 1 0 − 9 = 6.30 e wl in e × ( 1 0 2 e wl in e × 1 0 − 9 ) = 6.30 e wl in e × 1 0 2 − 9 = 6.30 e wl in e × 1 0 − 7
Final Answer Therefore, the wavelength of the orange light in meters, expressed in scientific notation, is 6.30 e wl in e × 1 0 − 7 m.
Examples
Scientific notation is extremely useful in fields like physics, astronomy, and chemistry where you often deal with very large or very small numbers. For example, the distance to the nearest star (other than the Sun) is about 4.0 e wl in e × 1 0 16 meters, and the size of an atom is around 1 0 − 10 meters. Using scientific notation makes these numbers easier to handle and understand.
The wavelength of orange light at 630 nm converts to meters as 6.30 x 10^{-7} m in scientific notation. This is achieved by using the conversion factor of 1 nm = 10^{-9} m and expressing the number in a form between 1 and 10. The final result is correctly expressed in scientific notation.
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