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Scientific Notation and Unit Conversions

  • #1
125
1
"The average wavelength of white light is 5.0 x 10-7m. What would this be in nanometers?

The textbook answer key stated the answer as 500n but I have no idea how that is the answer.
I know that the value of nanometers is 10-9 so I figured you add -7 and -9 to get -16...

Thanks,
 

Answers and Replies

  • #2
157
0
[itex] 1 nm = 1 * 10^{-9} m[/itex]

[itex] \frac{1 nm}{1 * 10^{-9} m} = 1 [/itex]

[itex] 5.0 * 10^{-7} m = (5.0 * 10^{-7} m) * 1 = (5.0 * 10^{-7} m) * \frac{1 nm}{1 * 10^{-9} m} = ??? [/itex]

Make sure you keep track of units and it will help you avoid these types of mistakes.
 
  • #3
gneill
Mentor
20,692
2,699
Unit conversion is safely accomplished by multiplying your value by terms that are a ratio of 'equal things'. For example, there are 100 cm in one meter, so the ratio "1m/100cm" is effectively equal to 1. If you want to convert 47 cm to meters you would write:

$$47 cm \times \frac{1 m}{100 cm} = \frac{47}{100}m = 0.47 m$$

Note how the "cm" units cancel in the expression, leaving just m (meters).
Can you apply this method to your problem?
 
  • #4
125
1
Unit conversion is safely accomplished by multiplying your value by terms that are a ratio of 'equal things'. For example, there are 100 cm in one meter, so the ratio "1m/100cm" is effectively equal to 1. If you want to convert 47 cm to meters you would write:

$$47 cm \times \frac{1 m}{100 cm} = \frac{47}{100}m = 0.47 m$$

Note how the "cm" units cancel in the expression, leaving just m (meters).
Can you apply this method to your problem?
Thank you!
I understand it now
 
  • #5
HallsofIvy
Science Advisor
Homework Helper
41,770
911
"The average wavelength of white light is 5.0 x 10-7m. What would this be in nanometers?

The textbook answer key stated the answer as 500n but I have no idea how that is the answer.
I know that the value of nanometers is 10-9
This is your basic mistake- this doesn't even make sense! I understand that what you meant was "one nanometer is 10-9 meter" but not writing that leads you astray. From "1 n= 10-9 m" you can get the "unit fraction
"[tex]\frac{1 n}{10^{-9} m}= 1[/tex].
So we can write
[tex] (5.0 \times 10^{-7}m)(1)= \left(5.0 x 10^{-7} m\right)\frac{1 n}{10^{-9} m}[/tex]
The "m" units cancel but we are dividing fractions so "invert and multiply":
[tex](5.0 \times 10^{-7})(10^9) n= 5.0 \times 10^2 m[/tex]

so I figured you add -7 and -9 to get -16...

Thanks,
 

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