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# Scientific notation word problem: speed of light

Amazingly, we can figure out how far the sun is from the earth if we know how to multiply numbers in scientific notation. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• At how do the seconds cancel out?
• When you have the same units on the top and bottom of a fraction, you can divide the top and the bottom by that unit to simplify the fraction, so it cancels out. This is just like if you have 6/8 and you divide the top and the bottom by 2 to get 3/4.
• So what about when you are dividing in scientific notation, how do you know which number goes on top? I have 9 x 10^-5 and 3 x 10^-6. Do i put the one with the highest exponent on top or the biggest number. 9 x 10^-5 would go on top right? thanks
• It depends on what the situation or problem is. It is completely legal within the laws of mathematics to do a/b or b/a, but they yield different quotients. If the problem asks you divide 9*10^-5 by 3*10^-6, then the 9*10^-5 would be on top (or, it would be the numerator). Consequently, if the problem asks you to divide 3*10^-6 by 9*10^-5, 3*10^-6 would be on top.
Correct me if I am wrong or if this answer is confusing.
• when he makes 10 to the 10th power, it looks like ten to the 16th.
• When are we actually ever going to need this in the real world
• If you want to be a scientist, you might want to learn this.
• Does anyone know how to calculate 4 to the -3 power?
• 4^-3, negative exponents cause it to reciprocate, so you would have 1/4^3 or 1/64.
• at what are they doing there??
• How do you solve this problem? Sirius, the brightest visible star in the sky, is about 8.6 light years away from Earth. One light year is 9.46 x 10^15 kilometers. Find the distance between Earth and Sirius in kilometers. Express your answer in scientific notation with 3 significant figures. I don' t understand how to figure this out. The 8.6 light years doesn't have the scientific notation part on the other side. so how would you solve this one?
• You could solve it using proportions. We are given that 1 lightyear = 9.46 x 10^15 km. We are looking for how many kilometres = 8.6 lightyears. One possible way to set up the proportion is:
9.46 x 10^15 km / 1 lightyear = # of kilometres from Earth to Sirius / 8.6 lightyears

We can solve the proportion for the # of kms:
9.46 x 10^15 km/lightyear = # of kms / 8.6 lightyears
(9.46 x 10^15) x (8.6) km = # of kms
(9.46 x 8.6) x (10^15 * 10^0) = # of kms --> 10^0 = 1 therefore 8.6 x 10^0 = 8.6
81.356 x 10^(15+0) --> using exponent rules
81.356 x 10^15
8.1356 x 10^16 --> scientific notation the first number must be between 1 and 10 :)