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Subtracting in scientific notation

Learn how to subtract numbers written in scientific notation. The problem solved in this video is (4.1 * 10^-2) - (2.6 * 10^-3).

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• In this video, I still don't understand the concept of this. Please answer, because I don't know what to do
• Hello:)
So I have replied to other students questions, and when Sal asked us to pause and solve on our own, I ended up solving differently than what he had us do. Now, this may be an exception, but Ii believe we can use this method as well. It may depend on the question, but maybe this will make it simpler to understand.
Step (1) Solve the problem 4.1 * 10^-2. Okay, so move the decimal to the left two times. 0.041.
Step (2) Solve the second problem 2.6 * 10^-3. Okay, so move the decimal to the left three spaces. 0.0026
Step (3) Subtract 0.0026 from 0.041
0.0410 <---(You have to add a zero in order to
0.0026 subtract. Or you could always do it in
0.0384
Step (4) Turn into Scientific Notation~ you have to move the decimal over to the right two times in order for it to become a scientific notation. So you would write 3.84 * 10^-2, and the exponent is negative because in order for you to go back to the original answer, you would have to move the decimal two times to the left. Whenever you move the decimal to the left, the exponent is going to be negative.
There ya go! Another way to solve for these kinds of problems :) I hope this helped you and anyone else who was confused. If I made any mistake or anyone has any comments or questions, just let me know. I love to hear your feedback:)
• late at night homework is fun if you watch the videos but why is it fun
• ...because the videos help make the homework easier! The human brain is designed to have fun working with easy stuff that once wasn't easy!
• at , why does he divide by 10?
• You Cannot have a scientific notation over 10 so he divides 38.4 by 10 to make it valid for a scientific notation, giving you the answer of 3.84 x 10^-2
• I have a question. Why Can't You Just Use a big number like 676 and multiply it by 10 to the power of 3 to express 676, 000? Why is it that we need to express it as 6.76 multiplied by 10 to the power of 5? Isn't it the same thing? If we had a random long number like 162537901468 then it would be a long and complicated decimal... Why can't we just express it as 162 times 10 to the power of 9 just approximately instead of writing a looooong and confusing decimal?
• I don't understand what Sal does to the 4.1 x 10^-2.
• What do you do when one exponent is negative and one positive
• when an exponent is negative it should have the subtraction sign/negative sign on it like in scientific notation which we learn in algebra.
(1 vote)
• I'm a little confused... I was doing the Practice and I don't think Sal explains which number we have to multiply and divide. For example, 4.2*10^-3 + 2.9*10^-4. I don't which one I should be multiplying snd dividing.
• This can be done with either part, as long as the exponents are made the same. Once the exponents are made the same, we can add (or subtract) the numbers that multiply the common power of 10, keep the common power of 10, then convert to scientific notation in the end.

For your example, 4.2*10^-3 + 2.9*10^-4, you could use 42*10^-4 + 2.9*10^-4 for the first step, or use 4.2*10^-3 + 0.29*10^-3 for the first step. Either will give the same result in the end, because 44.9*10^-4 is equivalent to 4.49*10^-3.
• I'm a little confused for my hw it says (8.41 x 10^5)-(7.9 x 10^6) equals -7.14 x 10^6 is it true or false . I said it was false and my friend said it was true I need help.
• 8.41*10^5=841000
7.9*10^6=7900000
841000-7900000=-7059000
7059000=7.059*10^-6
• So the first step (when you make the 4.1 into 41 and 10-2 to 10-3) which side do you know to convert? Like how do I know if I am suppose to convert the 10-3 to 10-2 or the 10-2 to 10-3? Because converting which side makes a big difference in the answer...
• It should not make any difference in the answer.
converting 41x10^-3 - 2.6x10^-3 gives 38.4x10-3 and moving the decimal back gives 3.84x10-2.
Doing it the other way moves the decimal of 2.6 to the left, so you have 4.1x10^-2 - .26x10_2 =3.84x10^-2.