Adding Decimals

Adding decimals

Welcome to the presentation on adding decimals.

Let's do some problems.

So let's say I had point zero zero eight-- that's an eight-- five plus--

and I'm writing it side by side on purpose-- one point seven nine nine.

So at first you're like,

these decimals, they confuse me, I give up.

But I'm going to show you that it's actually very staightforward

and it's actually no more difficult than doing normal addition.

And there's only one thing you have to think about

when you do decimals.

You have to line up the decimal points.

So let's start with the first number

and let's rewrite it so that we can actually do the math.

Point zero zero eight five.

Now for the second number

let's put the decimal point right below where that first decimal is on the top number,

and then rewrite the number.

So it's one point seven nine nine.

So all we did is we just rewrote both numbers with their decimal points lined up.

And we could've flipped them around.

We could've written the one point seven nine nine first and the point zero zero eight five below it.

What's key--

and if you get this point and you already know how to do addition,

you've already figured out how to do adding decimals--

is that you line up the decimal points.

So once you line up the decimal points

we're ready to start adding.

But hey Sal,

there's something very strange here you might say.

How can I add this five to a nothing?

Well there's a very easy solution to that.

Let's just put a zero right here.

And how can I do that?

How can I just randomly augment a number with a zero?

Well, I don't know if I've already shown you in another module,

but when you add trailing zeros to decimals,

it doesn't really change the value of the decimal.

And I think that make sense to you.

If I said one point one zero, that that's the same thing as one point one.

Which is the same thing as one point one zero zero.

It's all one and one tenth.

And these zeros just kind of add extra digits of precision,

which actually, don't change the actual value.

And maybe later when I'm teaching computer programming and computation,

the precision might matter.

But for now, it doesn't.

It's just the value.

So I added this zero here and you can always do that.

You can add trailing zeros

without actually changing the value of the number.

And now we're really ready to add.

Five plus zero is five.

Eight plus nine is seventeen.

One plus zero plus nine is ten.

Carry the one.

One plus zero plus seven is eight.

And then bring down this one

because there's nothing to add it to.

And we could have even added a leading zero here if you wanted to.

My wife's a doctor

and she says it's key that you always add that leading zero

so that no one gives someone the wrong amount of medicine.

But anyway, so now we are almost done.

We've done the addition,

and now we just have to figure out where to put the decimal point.

Well, the decimal point just drops straight down.

And we're able to do that

because we already lined up the decimal points.

So the answer to this problem is one point eight zero seven five.

It seems complicated, but all you have to do,

is line up the decimal points, add zeros where appropriate, and add.

And if you know how to add you already know how to do this.

Let's do another problem.

Fifty-eight point seven five plus point zero two eight.

Now if you saw a problem like this, written in this format,

your temptation might be to immediately start adding.

Add the five to the eight, the seven to the two, the eight to the zero.

And then just bring down the five or something of that nature.

And you would be wrong.

And I think you realize why you'd be wrong.

Because you forgot the first step.

The first step is line up the decimal points.

When you're doing addition with decimals,

the number one step is line up the decimal points.

So let's line up the decimal points.

So we can just rewrite that top number again.

Fifty-eight point seven five.

And now let's rewrite the bottom number

so that the decimal points line up.

So we'll put the decimal points right below it.

And it's point zero two eight.

And now we can add.

And just like before you might say,

how can I add nothing to this eight?

We can add a trailing zero to this top number

because it really doesn't change the value of the number

and now it kind of gives us a sense of security.

We have something to add to the eight.

So let's do that.

Zero plus eight is eight.

Five plus two is seven.

Seven plus zero is seven.

Eight plus blank space is eight.

And we could have added a zero there,

and it would've been the same thing.

Having the leading zero,

we wouldn't have given someone the wrong amount of medicine.

Five plus blank space is five.

And we just drop down that decimal point, and we're done.

It's that straightforward.

You line up the decimal points,

add any zeros that might make you feel more comfortable,

because it's often more comfortable to add to a zero than to add to a blank space.

And then you do your addition

and then you drop down the decimal point.

The answer is fifty-eight point seven seven eight.

And it's always good to kind of do a reality check.

To say, well, does my answer make sense?

I have fifty-eight point seven five, so roughly fifty-eight, almost fifty-nine.

Fifty-eight and three fourths.

And I'm adding a very small number to it.

I'm adding point zero two eight.

So my answer shouldn't change much

I guess is the way that you could view it.

It should still be around fifty-eight something,

because I'm only adding a very small amount.

If you had done it this way,

and you had just started adding immediately,

you would have gotten fifty-nine point something.

And you're like, boy, but I only added point zero two eight not point two eight.

And you would've been a little bit suspicious of your answer.

I hope I didn't confuse you,

but it's really healthy to always think about the magnitude of your numbers

and get a feel for just what you are adding

and not always do it purely mechanical.

Although sometimes it is fun just to chug through things.

Now let's do one more problem just for good measure.

I have some time left on the video.

One hundred two point one plus two point five six.

So once again, think about magnitude.

One hundred two point one plus two point five six,

that should be like one hundred four point something.

I won't do it in my head.

We'll do it on paper.

So first thing, we line up the decimal points.

One hundred two point one plus-- line up the decimal points-- two point five six.

Now we could add a trailing zero here and we're ready to add.

Zero plus six is six.

One plus five is six.

Two plus two is four.

Zero plus nothing is zero.

One plus nothing is one.

Bring down that decimal point.

One hundred four point sixty-six.

It was that easy.

Hopefully it's easy.

I don't want to make you think that it's easy if you're finding it hard

because it actually is hard the first time you do it.

But anyway,

I think you're ready now to try the module on adding decimals.

I hope you have fun!