Astronomers often detect radio waves with wavelengths of 3,000,000,000nm3,000,000,000\operatorname{\mathrm{n}\mathrm{m}}. What is this wavelength expressed in decameters (dam)?

0.3dam⁡0.3\operatorname{\mathrm{da}\mathrm{m}}

Astronomers often detect radio waves with wavelengths of 3 , 000 , 000 , 000 nm 3,000,000,000\operatorname{\mathrm{n}\mathrm{m}} . What is this wavelength expressed in decameters (dam)?

Hey, guys. Let's check out this practice problem. So we've got astronomers who commonly detect radio waves with this wavelength here, this big number over here in nanometers. And we're gonna express this number in decameters. So here's what we gotta do. We've gotta basically just identify our starting and our target prefixes. So our starting prefix is n. So we're gonna look at our table of metric prefixes and n corresponds to nano. Our target prefix, we wanna basically express this wavelength in terms of decimeters in which this DA is the prefix. So we've gotta look for DA and that happens to be over here. Now we're just gonna move from one to the other from our starting to our target. So we're gonna move in this table from here all the way to here. So this is basically how many places we're gonna move our decimal to the left. We just have to figure out how many exponents or how many decimal places to move. And we're just gonna look at the exponents. So one way to do this is we've got an exponent of negative 9 and then positive one. So if you think about this, if you're moving all the way back to the base unit which is 0, you've moved 9 decimals or 9 exponents. And then you've got to just move this one last one to get to 10 to the first or decameters. So that means it in total you've actually jumped 10 exponents. So we're gonna take this number here 3 with 9 zeros after it, which is in nanometers. And if we want to get to decameters, we're gonna have to take the decimal and shift it to the left 10 places because that's the direction that we moved in the table. So when if this is a whole number, this is basically if there's a big number without a decimal, the decimal is assumed to be at the end. So now, we're just gonna jump to the left 10 times. So we're gonna go 1, 2, 3, 4, 5, 6, 7, 8, 9. Then we gotta go one more which the the decimal lands over here. So the decimal here is gonna be 0.3 decameters and that's answer choice b. Alright, guys. That's it for this one. Let me know if you have any questions.

Astronomers often detect radio waves with wavelengths of 3,000,000,000nm⁡3,000,000,000\operatorname{\mathrm{n}\mathrm{m}}. What is this wavelength expressed in decameters (dam)?

0.3dam⁡0.3\operatorname{\mathrm{da}\mathrm{m}}

3dam⁡3\operatorname{\mathrm{da}\mathrm{m}}

30dam⁡30\operatorname{\mathrm{da}\mathrm{m}}

0.03dam⁡0.03\operatorname{\mathrm{da}\mathrm{m}}

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Multiple Choice

Astronomers often detect radio waves with wavelengths of $3 comma 000 comma 000 comma 000 nm$ . What is this wavelength expressed in decameters (dam)?

$3 dam$

$0.3 dam$

$30 dam$

$0.03 dam$

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Astronomers often detect radio waves with wavelengths of 3,000,000,000nm3,000,000,000\(\operatorname{\mathrm{n}\)\(\mathrm{m}\)}. What is this wavelength expressed in decameters (dam)?

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Astronomers often detect radio waves with wavelengths of $3 comma 000 comma 000 comma 000 nm$ . What is this wavelength expressed in decameters (dam)?