Standard Form: Addition and Subtraction of Numbers in Standard Form

Hi! Welcome back. So right now we want to learn about addition and subtraction for numbers in standard form.<br> For numbers having the same exponent, they can be added or subtracted in standard form. So how can this be done? It can be done simply by adding and subtracting the mantissas and then keep the exponent the same. Let?s look at some examples of how we can do this.<br> Two point six times ten raised to the power of four, plus four point three raised to the power of four. I?ve mentioned to you that if the standard form numbers have the same exponent then we can perform the addition. So first what we do is we check if they have the same exponent. So, the first number over here, ten power of four? ten power four. Since they have the same exponent, what we can do is we add up the mantissas, but we keep the exponent the same. So, two point six, plus four point three. Since we are keeping the exponent, so we have times ten raised to the power of four. Two point six plus four point three we get six point nine times ten power four. Alright.<br> Now, what if we have eight point three times ten raised to the power of negative three, minus two point eight times ten raised to power of negative three. Let?s check if they have the same exponent. Ten power negative three, ten power negative three. They have the same exponent. Therefore, but we must check if it is addition or subtraction. So in this case we have eight point three subtract two point eight time times ten raised to power of negative three. Eight point three minus two point eight we get five point five, and then times ten raised power negative three.<br> Now, what if we have numbers of which their exponents are not the same? So to solve this type of question, what we do is we have to express one of the numbers in nonstandard form so that the numbers will have the same exponent and then we will be able to solve for the addition or subtraction.<br> Now let?s look at some examples. Five point eight times ten raised power three plus eight point seven times ten raised power four. Alright. So, for this question, if you want to perform addition and subtraction, we have to check for the exponent to see if they are the same. In this case we have ten power three and ten power four. Clearly, they?re not the same. So how to solve this? We need to change one of numbers here to nonstandard form so that their exponent would become the same. So how do we do it? First let?s choose one to change. In this example I will show you by changing this number here to nonstandard form. So, ten power three if you want to change it to ten power four how do we make it to be the same? By adding one to three. But as we do something here, we need to do something here also. So, take note, if we plus any number here we have to move this decimal point to the left by how many times of number here shown. So, this is positive one, so we move it to the left one time. So we have our new decimal point over here. So, this question here will become zero point five eight times ten raised to power of four, plus eight point seven times ten raised to power of four. Now we check for the exponent. Are they the same yet? They are. So, we can add them up together. Zero point five eight plus eight point seven times ten raised to power four. Zero point five eight plus eight point seven, we get nine point two eight times ten raise power four. And the we check if they?re in standard form. This is A times ten power n. So, this is it in standard form.<br> Now another example. If we have three point two four times ten power negative three, minus one point one one times ten raised power negative four. In this case we check the exponent and also the exponent over here. They are not the same. So we change either of this. Let?s see. How about this time around why don?t we change this one. If we want to change this negative four to become negative three, what do we do? We plus one. Adding one, negative four plus one is negative three. If we plus one here we need to move this decimal point to the left one time. New decimal point over here. So we have three point two four times ten raised power negative three, minus zero point one one one times ten raised power negative three. Now do we have the same exponent already? Yeah. So three point two four minus zero point one one one written in bracket and then times ten raised to power of negative three. Three point two four minus zero point one one one, we get three point one two nine and then times ten raised to power of negative three. Okay?<br> So right now, try this example.<br>