Basic Math Comparing and Ordering Decimals

Welcome back to Educator.com.0000

This lesson, we are going to be looking at decimals.0002

We are going to compare and order them from least to greatest.0005

Before we go into that, let's look at some place values.0014

When we have a decimal... let's look at this decimal right here.0020

This is read 1 million 2 hundred and 34 thousand 5 hundred and 67 and 89 hundredths.0024

Right here, after the second comma, since our first comma is right here, our second comma is million.0036

A million 2 hundred and 34 thousand 5 hundred and 67 and 89 hundredths.0046

The 1 will be the million; 2 will be hundred thousands; 3 is ten thousands.0055

The 4 is thousands; 5 is hundreds; the 6 is tens; ones.0061

The decimal right here is read AND.0069

We are going to say 5 hundred 67 and 89 hundredths.0073

This right here, the first number after the decimal, is going to be tenths place with a -TH.0079

The next number is the hundredths place.0088

To figure out which decimal has a larger value, we need to look at the whole number first.0095

The whole number is going to be the number before the decimal place.0102

Here the whole number is 10; 10 is a number before the decimal place.0107

Whole number is 10 here; here it is 100.0114

We know that 100 is bigger than 10.0118

The larger value between these two is going to be 100.5.0124

We don't care what the number is after the decimal place0128

because the whole numbers are going to determine the larger value.0131

The next one, 1.01 or 1.10.0138

Here our whole number is 1; here the whole number is 1.0144

In this case, since we have the same whole number, we have to look at the values after the decimal place.0149

Here I have 1.01; and this would be 1.10.0158

We are going to go the next number which is 0; here is 1.0164

Whenever the whole numbers are the same, we are going to go to the next value which is the tens place.0172

In this case, it is 0; in this case, it is 1.0180

Even though this sounds like this is 1 and this is 10, this can be the same thing as 1.1.0184

If I have a 0 at the end of my decimal, at the very end,0196

and it is behind my decimal place, then I can just drop it.0203

This can be the same thing as 1.1.0206

Or it could be the same thing as 1.100.0209

Or I can even add ten 0s behind it.0214

It would still be the same value.0218

As long as it goes after my decimal point at the very end of the number,0221

then all those 0s mean the same thing, doesn't mean anything.0228

In this case, since I know that, I am just going to look at this 1, this first place right here, the tenths place.0233

1 is bigger than the 0 so I know that this number is actually going to be bigger than this number.0247

1.1 or 1.10 is greater than 1.01.0254

The next one, again look at the whole number; they are both the same, 44.0260

I am going to take a look at the next place value.0268

Again they are the same; they are both 4s.0273

Then I look at the next one; this is the 0.0275

Remember I can add 0s here if I want to because it is after the decimal place at the very end.0279

This can also be 0; they are also the same.0286

In this case, even though before I had the 0... 40 sounds like it would be bigger than 4.0292

Since I can add the 0s right here, they have the same value.0301

In this case, they are the same; they are equal.0306

44.40 is the same thing as, equal to 44.4.0311

The next one is 18.6; and this is 16.8.0320

Again first look at the whole number before the decimal place.0328

18 is larger than 16.0333

Automatically without even looking at the numbers after the decimal place...0337

even though 8 is bigger than 6, the whole number itself 18 is larger than 16.0341

This automatically becomes the bigger number.0349

These examples have a few numbers.0358

We are going to order them from the smallest to the biggest of values.0363

Again since I am comparing five different numbers, I want to first just look at their whole numbers.0370

This one has a 4, 10, 5, 5, and 6.0378

Just the numbers before the decimal point; those are the whole numbers.0384

Since I am going from least to greatest, which one has the smallest whole number?0389

I know that this one does, 4.0395

This decimal right here would be the least; it would be the smallest.0398

It is going to be 4.1; that is the smallest.0402

Then I have 5s; I have two decimal numbers with whole numbers of 5.0407

I have to compare these two now because I know that these two numbers are going to go next.0415

Since they have the same whole number, I am going to look at the next value.0419

This one is 1; this one is 0.0425

I know that 5.1 is bigger than 5.01 so this number is going to go next.0429

And the next smallest, 5.01; and then this one, 5.1.0437

I have two numbers left; I have 10.01 and I have 6.0.0446

6 is a smaller number than 10 if you look at the whole numbers.0451

6.0 is going to go next; 10.01, the biggest number, is going to go last.0457

I have 1, 2, 3, 4, 5 numbers; and then 1, 2, 3, 4, 5 numbers in order from least to greatest.0467

Another example, again I am going to look at the whole numbers.0477

This has a 0 as a whole number.0481

1, there is a 2, 0, and an 8; going from least to greatest again.0484

My least numbers, my smallest numbers are going to be the numbers with no whole number, 0 as a whole number.0492

It is going to be this one, 0.6 or 0.99.0498

From those two, I am going to look at the next number, in the tenths place.0504

6 is smaller than 9 so I know that this one is going to be the smallest.0509

0.6 is first; and then it is going to be that one, 0.99.0517

From the remaining numbers, my whole number here is 1, this is 2, and this is 8.0526

I know that this one is going to go next, 1.32.0532

Then it is going to be 2.02; and then 8.3.0540

There are my numbers, my decimal numbers in order from least to greatest.0551

The next example, again just look at the whole numbers--100, 101, 111, 110, and another 100.0557

Just looking at their whole numbers, 100 is my smallest.0571

I have two of them.0578

I have to look at the next place value of the tenths.0580

0 is smaller than 9, just looking at that number alone.0591

This is going to be my smallest value, 100.07.0598

Then it is going to be 100.9.0607

Then from the three numbers, 101 is the next smallest... 0.4.0612

Then from these two, 110 is smaller than 111 so it is going to be 110.8.0623

This one right here is going to be the largest value, 111.1.0633

Let's do one more example; again we are ordering from least to greatest.0641

You are going to look at all of your decimal numbers.0649

We have five numbers we are going to be comparing.0652

Before you look at all the numbers, let's just look at the whole numbers.0656

That one has no whole number, 0.0662

Whole numbers are all the numbers before the decimal place.0665

This is 0; this is 1, 0, and 1.0668

I know that the decimal numbers with no whole number,0675

with 0 as a whole number, are going to be the smaller numbers.0679

Between this one, this one, and that one.0684

Between those three numbers, I am going to have my least, my smallest value.0689

From those, you are going to look at the next place value which is the tenths place value.0696

That is 1; this one is 0.0704

Not for this one because that has a whole number.0708

I am just comparing the ones with the same whole number of 0.0711

Within this place value, this is 1, this is 0, and this is 0.0717

I know that this one right here, this one, and one of those two is going to be the smallest number.0723

I look at the next place value since they are the same.0733

Again they are the same; they are both 0s.0737

Look at the next one; 1 is smaller than 9.0741

This is smaller than that number.0749

That is going to make it the smallest number, 0.001.0754

Then this is my next smallest, 0.009.0761

Then this one right here because that had no whole number, 0.1.0770

I have two numbers left between 1.0001 and 1.1.0777

Since they have the same whole number, you are going to look at the tenths place.0786

This is 0; this is 1; this is bigger than that number.0793

So this is going to go next, 0001.0800

Then your largest number, the greatest value is going to be 1.1.0805

That is it for this lesson; thank you for watching Educator.com.0814