For more information, please see full course syllabus of Basic Math

For more information, please see full course syllabus of Basic Math

## Discussion

## Study Guides

## Practice Questions

## Download Lecture Slides

## Table of Contents

## Transcription

## Related Books

### Percents, Fractions, and Decimals

#### Related Links

- Percent: A ratio that compares a number to 100
- To change from a percent to a fraction, put the number over 100
- To change from a percent to a decimal, move the decimal to the left two spaces and add a percent sign at the end
- To change a fraction to a decimal, divide the numerator to the denominator
- To change from a fraction to percent, first change to a decimal and move the decimal to the right two spaces
- To change a decimal to a fraction, count how many numbers are behind the decimal, and put the decimal number to the power of ten as the denominator
- To change a decimal to a percent, move the decimal point two spaces to the right

### Percents, Fractions, and Decimals

48%

- [48/100]
- [(48 ÷4)/(100 ÷4)]

320%

- [320/100]
- [(320 ÷10)/(100 ÷10)] = [32/10]
- [(32 ÷2)/(10 ÷2)] = [16/5] or 3[1/5]

47%

[3/4]

350%

- [350/100]
- [(350 ÷10)/(100 ÷10)] = [35/10]
- [(35 ÷5)/(10 ÷5)] = [7/2] or 3[1/2]

[15/100]

[9/4]

- 2.25

[12/15]

- 0.8

3%

- [26/100]
- [(26 ÷2)/(100 ÷2)]

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Percents, Fractions, and Decimals

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Percents 0:06
- Changing Percent to a Fraction
- Changing Percent to a Decimal
- Fractions 4:17
- Changing Fraction to Decimal
- Changing Fraction to Percent
- Decimals 10:10
- Changing Decimal to Fraction
- Changing Decimal to Percent
- Extra Example 1: Write Each Percent as a Fraction in Simplest Form 13:29
- Extra Example 2: Write Each as a Decimal 17:09
- Extra Example 3: Write Each Fraction as a Percent 22:45
- Extra Example 4: Complete the Table 29:17

### Basic Math Online Course

### Transcription: Percents, Fractions, and Decimals

*Welcome back to Educator.com.*0000

*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 it*0345

*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 decimal*1381

*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

1 answer

Last reply by: LeTaotao Xue

Wed Jul 4, 2018 12:55 AM

Post by ali digir on September 27, 2015

he video could not be loaded

0 answers

Post by ali digir on September 27, 2015

he video could not be loaded

2 answers

Last reply by: LeTaotao Xue

Wed Jul 4, 2018 12:55 AM

Post by Alexander Toledo on May 8, 2013

isn't it 220/1000?

0 answers

Post by judy lee on September 6, 2011

What about whole numbers????????????????????