Basic Math Percents, Fractions, and Decimals

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For the next lesson, we are going to go over percents, fractions, and decimals.0002

We are going to learn how to change percents into fractions and percents into decimals.0009

First, a percent is a ratio that compares a number to 100.0020

We know that this symbol right here represents percent.0026

To change from a percent to a fraction, all you are going to do,0031

since we know that a percent is a ratio of the number to 100,0036

to change a percent to a fraction, all you have to do is drop this little symbol and put the number over 100.0042

If I have 17 percent, all I have to do is take this number and put it over 100 and then simplify.0051

That becomes my fraction.0060

If I have let's say 50 percent, to change this to a fraction, I am just going to take the number.0064

I am going to drop this percent sign.0073

Since I am changing it to a fraction, I no longer need the percent.0075

Going to put it 50/100; 50/100, I know I can simplify that.0079

I know that 50 goes into both numbers.0087

I can divide the top and the bottom by 50.0090

50 divided by 50 is 1.0095

100 divided by 50 is 2 because 50 fits into 100 two times.0099

50 percent into a fraction becomes 1/2.0105

That is how you change from a percent to a fraction.0111

To change from a percent to a decimal, we are going to divide it by 100.0115

We are actually going to put it over 100, but we are actually going to divide it.0124

To divide it, whenever you divide a number by 100, you just move the decimal point to the left two spaces.0131

If you get confused which way to move it, just know that percent is always a bigger number than a decimal.0142

Decimals are small; percents are always bigger.0149

In order to make this number, because it is a percent...0155

If I change it to a decimal, then I have to make it smaller.0157

Think that you are going to make it smaller.0160

When you make it smaller, you have to move the decimal over to the left so that the number will get smaller.0162

Again the decimal point here, if you don't see one, it is always at the end.0170

There is always an invisible decimal there.0175

I am going to write in my decimal point.0179

Then I am going to move it two spaces to the left.0182

It is going to go one; that is one number; that is one space.0185

Two, that is another space; 17 percent becomes 0.17.0189

Again just two spaces to the left because percent is bigger than the decimal.0199

You have to make it smaller by moving it to the left.0204

Another number, if I have let's say 5 percent, remember drop the percent sign.0209

Then you are going to move the decimal point; let me write it out here.0216

5, the decimal point is at the end of it, end of the number.0221

You are going to go one and then two; then put that point there.0225

But since there is an empty space here, I have to fill it in with a 0.0230

5 percent becomes 0.05; that is the decimal.0235

Again percent to a fraction, all you have to do is put the number over 100.0243

To change it from a percent to a decimal, you just move it to the left two spaces.0250

For fractions, if I want to change a fraction to a decimal,0259

I am going to think of this little bar, that fraction line, as divide.0266

It is just going to be A divided by B.0271

You are actually going to divide it.0274

It is going to be A divided by B.0276

Again fraction to a decimal, you are going to just divide the top number into the bottom number.0280

Here is a fraction here; 3/4, I am going to divide 3 and 4.0286

It is going to be 3 divided by 4.0294

Make sure, make sure this top number, even though it is smaller, this top number has to always go inside.0296

When you divide, 3 inside; 4 on the outside.0303

The top number gets to go inside.0312

This number is bigger than the number inside; but that is OK.0318

Remember here the decimal point is always at the end of a number.0324

If you don't see it, it is always at the end.0327

When you have a decimal point, you can always put 0s behind it as many as you want.0330

I can put a hundred 0s if I want to.0338

I am not going to; but I could if I want to.0341

It is OK for you to put 0s at the end of it0345

as long as it is behind the decimal point and it is at the end.0349

Here remember if I want to divide the decimal, I have to bring this decimal point up.0353

I know 4 goes into 3 zero times; it doesn't fit into 3.0360

But 4 goes into 30 how many times?0365

4 times 6 is 24; 4 times 7 is 28; 4 times 8 is 32.0370

I know that this is 7; 4 times 7 is 28.0378

If I subtract it, I get 2; bring down this 0.0385

4 goes into 20 five times; that becomes 20; you subtract it; it becomes 0.0390

3/4 then becomes this number here; becomes 0.75; that becomes my decimal.0400

Again fraction to decimal, you are going to do the top number divided by the bottom number.0413

Solve it out; you are going to get your decimal.0419

Usually it keeps going; let's say it doesn't give you a remainder of 0.0423

Then you end up having to keep going.0430

Usually you are going to only write it maybe two or three numbers after the decimal place.0433

It depends on what your teacher wants.0439

If your teacher says two numbers behind the decimal point, then two numbers.0441

Three numbers, then three numbers; make sure you round it though.0447

The last number, you are going to have to round it based on the number behind it.0451

You are going to either keep it as a 5 or you are going to round it up.0455

This right here, I can only write 2 because it stopped.0460

The remainder became a 0; I don't have to keep going.0466

That would just be my answer; I am done.0469

If I want to change a fraction to a percent, I have to first change my fraction to a decimal.0473

I am going to do exactly what I did up here.0483

Then I am going to change my decimal to a percent by moving it to the right two spaces.0486

I am going to move the decimal point over to the right two spaces.0497

Remember to change from a percent to a decimal, I moved it to the left two spaces.0500

Decimal point, left two spaces.0514

But if I am doing the opposite, if I am going to from decimal to a percent,0523

it is the same thing, but then I have to get bigger.0532

Remember decimal is smaller than the percent.0534

I have to go to the right to make it bigger; right two spaces.0537

Decimal place is going to go to the right.0543

Again change your fraction to a decimal.0545

3/5, if you divide it, it becomes 0.6; 0.6.0551

Then I am going to move it to the right two spaces.0557

It is going to go one, two; there is my new decimal point.0560

Again I have empty space; I have to fill it with a 0.0565

This 0 in the front, I can just drop that because 060 is the same thing as 60.0568

If a 0 is in the front, then that doesn't really matter.0576

You can just let it go; just drop it; erase it; this becomes 60 percent.0579

If I have another decimal, let's say I have 0.50.0588

Again you are going to take this; you are going to go one, two.0598

Leave it there; it is going to become 50 percent.0601

Now decimals.0611

To change a decimal to a fraction, you are going to count how many numbers you have behind the decimal point.0614

If I have 0s at the end here, remember you can add 0s at the end of a number, behind the decimal point.0625

You don't have to count those; just count the numbers here.0631

I have one, two; I have two numbers behind the decimal point.0638

That means I am going to put this number 15 without the decimal point over two 0s.0642

I have to put 1 in front of it; it is going to be 100.0652

If I have 0.155 and I want to change this to a fraction, I have one, two, three numbers behind the decimal point.0656

Then I am going to take that number; put it on top.0670

On the bottom, I am going to put three 0s.0673

That is going to be 1000.0677

One, two, three 0s with the 1 in front of it, that is 1000.0679

This would be your fraction; this is 0.15; 15/100.0684

Again since it is a fraction, you have to simplify it.0691

You are going to see a common factor.0697

What number goes into both 15 and 100?0700

I know that 5 goes into 15 and 5 goes into 100.0703

I can divide both top and bottom by 5.0708

This becomes... 15 divided by 5 is 3; over... 100 divided by 5 is 20.0713

That becomes your fraction.0724

Then to change a decimal to a percent, again we already went over this.0730

Decimal to a percent, you are going to remember take the decimal point and move it to the right two spaces.0734

Again if you get confused which one do I move to the right and which one do I move to the left?0742

It is always going to be two spaces.0746

But it depends on what you are changing it to.0749

Always think that to percent is bigger than the decimal; decimals are small.0753

Think of change like 15 cents; that is small; decimal points are small.0758

You want to make the number bigger.0764

The way to make the number bigger is to move the decimal point over to the right to make it whole numbers.0767

You go one, two; then decimal point at the end of 15.0775

It becomes 15 percent.0780

If I have a decimal point 0.155, to change it to a percent, you are going to go one, two again.0783

That is going to become 15.5 percent.0791

Even though you still see a decimal, this is still percent because you moved it two spaces.0798

Anytime you move the decimal point two spaces to the right, it becomes a percent.0802

Let's do some examples; write each percent as a fraction in simplest form.0809

Remember percents, you always just put it over 100.0815

No matter what, you are always going to just put it over 100.0820

Take this number 42; we are going to get rid of that percent sign.0824

We are changing it to a fraction; it is going to be 42/100.0830

Always just put it over 100.0835

These are both even numbers; I know that I can simplify.0838

Since they are both even... this one ends in a 2; this one ends in a 0.0843

They are both even numbers; I can divide each of them by 2.0848

42 divided by 2; 2 goes into 4 two times; becomes 4.0853

I am going to bring down the 2; 2 goes into 2 one time.0864

42 divided by 2 is 21; over... 100 divided by 2.0868

You are cutting it in half; 100, cut it in half is 50.0875

My answer is 21/50; that is simplest form.0881

Same thing here; 10 percent, we are going to write it over 100.0892

Percent to a fraction, you always just put it over 100.0896

If I have a 0 on top and a 0 on the bottom, I can just cross out the 0s.0901

This is going to be 1/10; 10 percent to a fraction is 1/10.0907

Same thing here; I take this whole number, 220; put it over 100.0918

0 on the top; 0 on the bottom; I can't do it like this.0925

If I have 0 here, 0 here, I can't cross out those two.0932

One has to be on the top and one has to be on the bottom for you to be able to cross it out.0936

This is 22/10; but then look.0941

This is called an improper fraction because the top number is bigger than the bottom number.0946

I need to change it to a mixed number.0952

In order for me to change it, I want to see how many times does 10 fit into 22?0955

There is going to be leftovers; but how many times can it fit into 22?0963

10 times 2 is 20; that is going to be two whole numbers.0969

How many are remaining?--2; there is 2 leftovers.0975

Over... keep the same denominator, 10.0982

2/10, I can simplify this because they are both even.0989

2 goes into both the top and the bottom; this becomes 2.0992

2 divided by 2 is 1; over 5; this is my answer.0997

Again all I did was put this number over 100, just like I always do when I change percent to fraction.1002

I crossed out the 0 at the top and the bottom 0; it is 22/10.1009

Then I just changed it to a mixed number; it became 2 and 2/10.1016

Then simplified this fraction; 2/10 became 1/5.1023

Write each as a decimal; percent to a decimal.1031

Again percent to a decimal, that is when you...1037

Decimal to percent or percent to decimal, that is just when you move the decimal point two spaces.1040

But percents remember are bigger than the decimal.1046

I have to turn this number, to change it to a decimal, I have to make this number smaller.1049

Remember smaller means move the decimal point to the left; that makes it smaller.1054

Take the 68 percent; I am going to put my decimal point here because I don't see it.1061

It is always at the end; then I go one, two, point.1067

To write it again, it just becomes 0.68; that is my decimal number.1073

Now I have a fraction.1085

To change it to a decimal, I just need to divide these two numbers, 5 divided by 8.1086

Let's do it right here so I have some space to work with.1096

Here 5 inside; the top number always goes inside; 8 on the outside.1100

Again I need to make this longer.1108

Decimal point is at the end of the number.1110

I can put as many 0s as I want as long as it is at the end of a number and behind the decimal point.1114

Bring the decimal up; 8 goes into 50 how many times?1123

I know that 8 times 5 is 40; 8 times 6 is 48.1128

8 times 7 is 56; so I know it is 6.1137

This is 48; if I subtract, then I get 2; I bring down the 0.1141

How many times does 8 fit into 20?1150

8 times 2 is 16; 8 times 3 is 24; it has to be 2.1156

That becomes 16; subtract it; I get 4.1162

Remember I can add another 0 if I would like; put a 0 there.1167

8 goes into 40 five times; that goes in evenly; I have 0 left.1171

My answer here, 5/8, becomes 0.625.1180

I could put a 0 here if I want to.1188

I could put a 0 here if I want to in the front because that just means zero whole numbers; zero 1s.1191

Percent, again percent to decimal, you are just moving the decimal point over.1203

Make it smaller; so two spaces to the left.1207

340, the decimal point is right here at the end; go one, two.1212

To write it again, it becomes 3.40 or 3.4.1219

I don't have to write the 0.1224

Remember it is behind the decimal point and at the end of a number.1225

For this one, again 3 divided by 50; let's do it here.1233

Put the top number inside; 50 goes on the outside.1243

Point, decimal at the end; I can add a few 0s if I want.1253

50 goes into 30... 30 is too small; it is smaller than 50.1259

50 goes into 30 zero times.1266

I put a 0 on top of this to represent that I am talking about 30.1268

That is 0 times 50 is 0; subtract it; I get 30.1274

Bring down this 0; how many times does 50 go into 300?1282

I know that 5 times 6 is 30; let's try that.1292

50 times 6; 0; 30; yes, 50 times 6 is 30.1299

50 times 6 is... I'm sorry... 300; then that is going to become 0.1307

I don't need to bring anything else down because I have no remainders.1318

3 divided by 50 is 0.06; this 0, you cannot drop.1323

You have to have this 0 because that is between a decimal and another number.1331

If the 0 was right here, then you can drop this.1337

You don't have to put that there because it is at the end of a number and behind the decimal point.1341

This 0 is not at the end of a number because there is another number here.1346

But this one you can put because that just means zero whole numbers, zero 1s.1351

That you can write there if you would like.1357

That is a decimal for that fraction.1362

Write each fraction as a percent.1367

Here anytime you want to go to percent, you always need a decimal.1372

I have a fraction; I need to change it first to a decimal1381

so that I can just move the decimal point two spaces and make that into a percent.1385

Change this to a decimal.1393

99 divided by 100, this is going to be... decimal point at the end; put a 0 here.1396

100 goes into 99 zero times; 100 goes into 990 nine times.1415

Bring the decimal point up because 9 times 100 is 900.1426

Subtract it; 090; bring down another 0; 100 goes into 900 nine times.1433

Here this is 0.99 in decimal; but remember we are changing it to percent.1448

I need to move the decimal over which way?--left?1457

No, right, because again percent is bigger than decimal.1460

You have to make the number bigger by moving it to the right.1463

This becomes 99 percent.1466

That would be the same thing from a percent into a fraction.1475

Remember how we just always put it over 100.1478

See how that is 99 over 100.1480

The next one, 6 divided by 5 first.1484

6 inside; the top number goes inside; 5 on the outside.1490

Decimal point at the end; bring it up; 5 goes into 6 one time.1496

That becomes 5; subtract it; write the 1.1505

I can add a 0 here because it is behind the decimal point; bring it down.1510

5 goes into 10 two times; that becomes 10; subtract it; I get no remainders.1516

My decimal or this fraction is 1.2.1525

Again to change it to percent, I am going to move the decimal point right here.1532

Two spaces to the right to make it bigger; it goes one, two.1536

Again I have empty space here; I have to put a 0 there.1542

This is 120 percent.1548

This next one, this one is going to be a little bit harder.1558

14 divided by 15; remember that the top number has to go inside.1563

Decimal at the end; add 0s; 15 goes into 14 zero times.1571

Bring the decimal point up; how about to 140?-1580

Let's see; I know that if I multiply this by 10, I get 150.1587

Let me just try something a little bit smaller than 10 because this 140 is smaller than 150.1597

I am going to try 9; 15 times 9 is 45.1604

9 times 1 is 9; add 4 is 13; 135.1611

Isn't that only five away from 140?1619

I know that 9 has to be the correct number; that is the closest one.1622

That is 135; subtract it; I get 5; bring down the 0.1629

15 goes into 50 how many times?--15 times... let's see... 3 is 5.1638

How about 3?--it is 45; that is only 5 away from 50.1654

Then 3 has to be the correct answer; 3, you get 45.1662

Subtract it; I get another 5; you can add a 0; bring it down.1670

I know that again it is 3; 45; 5.1677

It is going to keep going; 0; bring down the 0; 3.1686

I can just stop here because I have enough numbers to give me my decimal.1696

Again if I just want to make it 0.93, two or three decimal places,1701

if I want to stop here, then I can just base this number on that, the one behind it.1711

It is smaller than 5; it will just stay a 3.1716

If this number where the arrow is pointing to, if that number was 5 or bigger, I can round it up to 0.94.1720

I can do 0.93 or I can do 0.933; decimal.1727

But again I am changing it to percent; this is going to go one, two.1734

There is the new decimal point right there; 93.3 percent.1740

I can drop the 0 because it is in the front; that doesn't mean anything.1747

There is my answer.1753

Here we have a table; the first problem, 50 percent.1760

I want to change it to a fraction and decimal.1769

Same thing here; this is a decimal.1772

I want to write this as a fraction and as a percent.1774

I have to fill in all these.1780

Percent to a fraction.1783

Remember anytime I want to change a percent to a fraction, I just put it over 100.1786

This will be 50/100; that is it; but I just have to simplify.1791

50/100, again 50 goes into both the top and the bottom; I can just divide.1799

This is just 1/2.1807

To change it to a decimal, you can do two things; you can move this.1812

Remember percent to decimal, you move it to the left two spaces.1819

Or from a fraction to a decimal, you just divide, top number divided by bottom number.1823

This is easier because all I have to do is move this decimal point.1828

It starts right here at the end; it goes one and two.1833

The decimal point is going to be right in front of the 5.1838

0.50; you can leave it like that.1841

Or you can drop this 0 because the 0 is at the end of a number.1847

It is behind the decimal point.1852

This will be 0.50 or 0.5; that is part two.1854

The next one, 0.07, that is the decimal.1864

I want to change it to a percent; again I am making it bigger.1868

That means I have to move the decimal point over to the right to make it bigger.1872

Two spaces; it is going to go one, two.1877

It is going to go right there, right behind the 7.1881

07 percent or 07 is the same thing as... let me just erase the 0.1885

7 percent is the same thing as 7 percent.1896

I can just leave it like that.1899

To change this to a fraction, remember percent to a fraction, you just put it over 100.1903

Or from a decimal to a fraction, remember you count the number of numbers behind the decimal point.1912

That is two; you are going to put two 0s in the denominator.1917

Either way it is the same thing; it is 7/100.1921

See if you can simplify; no, because there is no common factors.1926

No numbers that go into both 7 and 100; so that is it.1931

The third one, same thing here; percent to a fraction; put this number over 100.1938

8... let me write that over; 8/100.1945

Here we have both even numbers; divide this top and the bottom by 2.1955

8 divided by 2 is 4; over... 100 divided by 2 is 50.1962

Look, I can simplify this again because top and the bottom number are both even again.1971

Divide this by 2; I know that 4 divided by 2 is 2.1977

50 divided by 2 is 25 because that is half of 50.1983

This is my answer.1988

Then to decimal; here I make it smaller.1992

Move it to the left two spaces; it is going to go one and two.1996

See how from right here, it went one; then it went two with an empty space.2002

It has to be 0.08 because you have to fill in the empty space with a 0.2008

8 percent; at the end, one, two, decimal point; fill in this space with 0.2016

The last one, from a fraction to percent and decimal.2027

In order for me to go from a fraction to a percent, I have to give the decimal point first.2035

Divide; 4 inside; 5 outside; point; bring it up; put a 0.2041

5 goes into 4 zero times; 5 goes into 40... 5 times 8 is 40.2052

If we subtract it, you get a remainder of 0; that means I am done.2064

My decimal is going to be 0.8 or 0.8; it is the same thing.2069

Then from decimal to percent, make it bigger.2077

0.8; that means I have to move it to the right two spaces.2082

I go one, two; empty space; put a 0; becomes 80 percent.2086

That is it for this lesson; thank you for watching Educator.com.2101