8 EE A 4 Scientific Notation Part 2 Addition Lightboard

okay hello this video is on adding in scientific notation okay quick review of what we learned in our introduction to scientific notation we said that times 10 to the is how we write in scientific notation so scientific notation is way to write very large number into shorthand way it has two factors and they produce the larger number product okay so the first factor called coefficient and this coefficient this factor has to have at least value of one but cannot be more than 10 okay and then it's multiplied by base of 10 to an exponent exponential power okay so this is scientific notation right here we'll talk about our rule in just little bit when we get to more difficult problems okay so let's look at this problem right here we have four point two times ten to the third plus three point one times ten to the third okay we want to get our problem where we have the same power of 10 so in this case we have both power of 10 of 10 to the third that's what we want we have that we can simply add four point two plus three point one and all that's going to be multiplied by 10 to the third power and four point one plus three point four point two plus three point one is seven point three times ten to the third power okay the second problem again we have 10 to the fourth 10 to the fourth that's what we want same same exponential power so we have three point three plus one point six times ten to the fourth power we add those together we get four point nine four point nine times ten to the fourth power and that's our answer okay take the third one again we have ten to the sixteenth ten to the sixteenth so we our answer will have ten to the sixteenth in it but we have two point eight plus six point three and again times ten to the 16th power and we add those together we're going to have eight nine point one times ten to the 16th power eight nine point one all right now let's look at some that are little bit more difficult okay let's look at this example we have four point six times ten to the seventeenth plus three point eight times ten to the sixteenth okay now in this case we have powers of ten that are two different exponents so we need to get the exponents to the same power all right we can either decrease this one or increase this and we're going to do it both ways the first time we're going to decrease this to ten to the 16th all right that's still going to be plus this will stay the same three point eight times ten to the 16th okay so we have rule if we decrease power power decreases we're going to move the decimal to the right all right so we decrease by one we're going to move the decimal to the right by one so move that to the right once it becomes forty six times ten to the 16th plus three point eight times two is sixteen okay so now we will add forty six plus three point eight and that is times 10 to the 16th all right that becomes 49 point eight times ten to the sixteenth okay now is scientific notation we look over here it's at least one yes is it less than ten note so we've got to move it around we need to move it one place here that becomes four point nine eight okay so if we decrease this side we've got to increase this side it becomes 10 to the 17th all right now let's do it this time by increasing this side so the four point six times 10 to the 17th will stay the same plus now we want 10 to the 17th now if our power increases our decimal moves to the left so our three point eight will move to the left and become point three eight okay all right so now we have both 10 to the 17th on both sides both factors will add four point six plus 0.38 and that's times 10 to the 17th okay so that becomes four point nine eight times 10 to the 17th and if we confirm our answers we get the same answer doing it both ways let's do another one okay eight point seven times ten to the negative six plus three point two times ten to the negative five all right again we want our kids to have the same exponent same power so we'll do it both ways again first off we're going to change this one to negative five okay and still be plus three point two times ten to the negative five okay so let's look up here what did we do when we change it from negative six to negative five well we actually increased it so the power increases we're going to move the decimal to the left so our new decimal will become 0.87 okay so now we have 0.87 plus 3.2 and all that's going to be times 10 to the negative five okay so then we'll add this together and we should get four point zero seven times ten to the negative five and that's our answer okay so let's do it this time let's change this side to ten to the negative six so this side will stay the same eight point seven times ten to the negative six plus and we're going to change this to ten to the negative six okay now we are decreasing because our negative six is less than negative five so if we decrease our power power decreases we move the decimal to the right the other side will increase so 3.2 becomes 32 times 10 to the negative six all right now so we add eight point seven 22 hilar eight point seven plus 32 times 10 to the negative six all right that becomes forty point seven times ten to the negative six okay we're not finished because this is yes it's at least one what it's less than is not less than ten so we've got to change we've got to move this one place okay so now that becomes four point zero seven if we decrease this side we have to increase the power of ten so again to increase the power of ten we go to negative five and that's our answer now do these match yes okay so we did it two ways and we came up with the same answer you can do it either way as long as your answer is finished in scientific notation okay five point four one seven times ten to the fourteenth plus three point one times ten to the twelfth okay again we want our base our tens to have the same exponent so we've either got it decrease or increase let's increase all right so we're going to change this one to ten to the fourteenth this will stay the same now if we power increases we move the decimal to the left we make this side of the multiplication sign larger we have to make this side smaller so we're going to increase by two we've got decrease by two circularly one two so we added 0.03 one times ten to the 14th alright so now we're going to add five point four one seven and we're going to add point zero three one and all that's going to be times 10 to the 14th all right and that will be five point four four eight times ten to the 14th okay let's look at two more six times ten to the six plus three point two seven times ten to the seventh okay again we want our powers attended to be the same so we're going to have to increase ridiculous decrease this 10 we're going to change this to 10 to the sixth okay this then will stay the same six times 10 to the 6 plus now if we power decrease this we will move the decimal to the right okay play the decimal to the right becomes 32 point seven times ten to the sixth okay so now we'll add six plus 32 point seven and that's times 10 to the sixth power okay that becomes thirty eight point seven times ten to the sixth now we want it at least one less than ten it's not less than ten so it's going to move it to the left that becomes three point eight seven times now if we decrease this side we have to increase this side so 10 to the seventh power and that's our final answer all right let's look at this one seven point one nine times ten to the 14th plus five point zero two times ten to the 16th okay we have 14 into 16 all right what did we do up here we decreased up here so let's increase down here so we're going to change this to 10 to the 16 plus five point zero two times 10 to the 16 all right so we're increasing by two so if our power increases we're going to move the decimal to the left put the move the decimal to the left two places two times one two we'll add zero so it becomes point zero point zero seven one nine times 10 to the 16th we have 10 16th 10 to 16 so we can add so now we have five point zero two plus point zero seven one nine now that's going to be times ten to the sixteenth all right so this becomes five point zero nine one nine times ten to the sixteenth and that is our final answer or at least one less than ten more times the power of ten okay in quick review we said scientific notation is way to take very large number and write it short-handed we use two factors the coefficient times power of 10 and we said if we move the decimal to the right our power decreases if we move the decimal to the left or power increases all right well thanks for watching and please subscribe if you haven't already and we'll see on the next video