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Convert [tex]\( 749 \, \text{nm} \)[/tex] to meters. [tex]\( (1 \, \text{m} = 1 \times 10^9 \, \text{nm}) \)[/tex]

Show your work and report your answer with correct significant figures. Use scientific notation if needed and include units.


Sagot :

To convert 749 nanometers (nm) to meters (m), we need to use the fact that 1 meter (m) is equal to 1 x 10^9 nanometers (nm). Here’s a detailed, step-by-step solution:

1. Identify the given value and the conversion factor:
- We are given a length of 749 nanometers (nm).
- We know the conversion factor is that 1 meter (m) is equal to 1 x 10^9 nanometers (nm).

2. Set up the conversion:
[tex]\[ 749 \, \text{nm} \times \left( \frac{1 \, \text{m}}{1 \times 10^9 \, \text{nm}} \right) \][/tex]

3. Perform the conversion:
- Divide the given value in nanometers by the conversion factor:
[tex]\[ 749 \, \text{nm} \div 1 \times 10^9 = 7.49 \times 10^{-7} \, \text{m} \][/tex]

4. Ensure significant figures are correct:
- The original number (749) has 3 significant figures.
- Our answer should also have 3 significant figures accordingly.

5. Write the final answer:
[tex]\[ 749 \, \text{nm} = 7.49 \times 10^{-7} \, \text{m} \][/tex]

Therefore, 749 nanometers is equal to [tex]\( 7.49 \times 10^{-7} \)[/tex] meters.