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# Scientific notation word problem: speed of light

It is possible to simplify multiplication and division using scientific notation. This can be used to calculate the distance between the sun and the earth, which is 1.5 times 10 to the 11th power meters. This is an incredibly large distance and difficult to visualize. Scientific notation can be used to simplify calculations and understand large numbers. This involves using the commutative property to rearrange the numbers and multiplying the units, and then adding the exponents to simplify the equation. Created by Sal Khan and Monterey Institute for Technology and Education.

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• At how do the seconds cancel out?
• It cancels out because when it was m/s and s it cross cancel or cross reduce which is when u take the 2 numbers/variables diagonal from each other and reduce them but in this instance it is the same so they take each other out
(1 vote)
• 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 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.
• Hello, I'm not from the US and in my country we don't include units in the computation, only the the result's unit when giving the answer.
Do you always include them in computation? Thanks in advance to whoever answers.
• Yes, you do. I'm not from the US, either.
• when he makes 10 to the 10th power, it looks like ten to the 16th.
• 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 :)