# Scientific Notation and Unit Conversions

"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,

$1 nm = 1 * 10^{-9} m$

$\frac{1 nm}{1 * 10^{-9} m} = 1$

$5.0 * 10^{-7} m = (5.0 * 10^{-7} m) * 1 = (5.0 * 10^{-7} m) * \frac{1 nm}{1 * 10^{-9} m} = ???$

Make sure you keep track of units and it will help you avoid these types of mistakes.

gneill
Mentor
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?

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

HallsofIvy
Homework Helper
"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
"$$\frac{1 n}{10^{-9} m}= 1$$.
So we can write
$$(5.0 \times 10^{-7}m)(1)= \left(5.0 x 10^{-7} m\right)\frac{1 n}{10^{-9} m}$$
The "m" units cancel but we are dividing fractions so "invert and multiply":
$$(5.0 \times 10^{-7})(10^9) n= 5.0 \times 10^2 m$$

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

Thanks,