in this lesson i want to focus on adding and subtracting two numbers using scientific notation so consider this example 9 times 10 to the 3 minus 5 times 10 to the 3. what's the answer now what is 9x minus 5x 9x minus 5x is 4x because both terms contain x the same variable you can simply subtract the coefficient in this case the nine and the five they're attached to the same thing ten to the three so all you need to do is subtract the coefficient so nine minus five is four so this is simply going to be four times ten to the three you can do that if these two are the same so go ahead and try these examples what's seven plus what's seven times ten to the four plus two times ten to the four and five times ten to the sixth minus three times ten to the sixth so seven plus two is nine and then the 10 to 4 will be carried over so that's the first answer 5 minus 3 is 2 and so we're going to carry over the 10 to the 6. and so that's a simple way to add or subtract two numbers in scientific notation now what will you do if the exponents are different so what is 12 times 10 to the 4 minus 4 times 10 to the 5. right now we cannot subtract 12 and 4 because these values are different so what we need to do is to convert one into the other so what i'm going to do is convert the smaller one into the larger one so let's convert the four into a five now if you move the decimal to the left what's going to happen to the exponent will it increase in value or decrease in value anytime you move the decimal to the left the exponent will increase in value as you move the decimal to the left the number will decrease from 12 to 1.2 and so to undo that to maintain balance you need to increase the exponent likewise if you increase the number by moving the decimal to the right you need to decrease the exponent such that the value remains the same so i'm going to move the decimal one unit to the left and so 12 is going to decrease to 1.2 and so the exponent is going to increase by one so now that these two are the same i both have the 10 to the 5 multiplier i can now subtract these two numbers so what is 1.2 minus 4 4 minus 1.2 is 2.8 so 1.2 minus 4 is going to be negative 2.8 and then this is going to be times 10 to the 5. so that's the answer let's try another example 3.6 times 10 to the 5 plus 2.7 times 10 to the 4. go ahead and work on that example so i'm going to convert the smaller exponent into the larger one so i'm going to move this decimal one unit to the left so i'm going to decrease 2.7 to 0.27 so i need to increase the exponent to maintain the same value so this is going to be 0.27 times 10 to the 5. so since i have the same multiplier i can now add 3.6 with 0.27 so this is going to be 7 6 and 2 is 8 3 and 0 is 3. so this is going to be 3.87 times 10 to the 5. and that's the solution now what about this one four point two times ten to the seven plus eight times ten to the five go ahead and pause the video so i'm gonna move this decimal two units to the right one two so the exponent can increase by two so i'm gonna have a zero here this is going to become point zero eight times ten to the seven and so now i can add it with four point two so four point two plus point zero eight that's going to be 4.28 so it's 4.28 times 10 to the 7. and that concludes that problem let's try one more so point five times ten to the seven minus nine point three times ten to the five so i'm going to move this one two units to the left so i can get a seven this is going to increase by two so there's going to be a zero here and so this is going to be .093 as opposed to 0.93 times 10 to the 7. and so now let's subtract what's 4.5 minus 0.093 so we need to add some zeros now we can't subtract 0 by 3 because that's going to be negative so we need to borrow a 1 to make this 10. so we can't borrow 1 from 0 because it's nothing but we can borrow a 1 from 50. so that's going to become 49. so this will be a 4 and this changes to a 9. so now 10 minus 3 is 7. 9 minus 9 is 0 4 minus 0 is 4 and this is also 4. so it's going to be 4.407 times 10 to the 7. so now you know how to add and subtract numbers using scientific notation you