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

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

### Connecting Decimals and Fractions

#### Related Links

- Decimal
- Number
- Rational number
- 10
- Base
- Fraction
- Integer
- Ratio
- Division
- Decimal fractions
- Decimal mark
- Fractional part
- Integer part

- Some fractions can be written as decimals
- Â½ = 0.5
- Â¼ = 0.25
- 1/10 = 0.1
- 1/100 = 0.01

### Connecting Decimals and Fractions

- [50/100]
- [(50 ÷50)/(100 ÷50)] = [1/2]

**1**)/(

**2**)]

- [5/100]
- [(5 ÷5)/(100 ÷5)]

**1**)/(

**20**)]

**0**

**.**

**40**

**0**

**.**

**06**

**0**

**.**

**02**

*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

### Connecting Decimals and Fractions

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
- Examples: Decimals and Fractions 0:06
- More Examples: Decimals and Fractions 2:48
- Extra Example 1: Converting Decimal to Fraction 6:55
- Extra Example 2: Converting Fraction to Decimal 8:45
- Extra Example 3: Converting Decimal to Fraction 10:28
- Extra Example 4: Converting Fraction to Decimal 11:42

### Basic Math Online Course

### Transcription: Connecting Decimals and Fractions

*Welcome back to Educator.com; this lesson is on connecting decimals and fractions.*0000

*When we connect fractions to decimals and decimals to fractions, let's think about money.*0007

*For fractions and decimals, I can represent each with a dollar.*0017

*If I have half a dollar, 1/2 is half.*0024

*If I have half a dollar, I have fifty cents.*0029

*Keep in mind that 0.5 is the same thing as 0.50 or 50 cents.*0035

*When the numbers are after the decimal place, I can put as many 0s as I want.*0045

*The number does not change.*0051

*I know that half a dollar is the same as 50 cents or 0.5.*0056

*1/2 would be the same as 0.5.*0065

*If I have 1/4 from a dollar, how can I divide the dollar up into 4 parts?*0070

*4 of what makes a dollar?--the answer is quarters.*0082

*We know that 4 quarters make 1 dollar.*0089

*If I have 1 out of 4 quarters, if I have 1 quarter, then I have 25 cents or 0.25.*0093

*How about this one?*0107

*What would I have if I divide the dollar up into 10 parts?*0110

*I would have 1 dime.*0115

*1/10 would be the same thing as having 1 dime which is 0.1 or 0.10.*0118

*Remember this is the same as this.*0131

*How about this one?*0136

*If I divide up the dollar into 100 parts, then I would have 100 pennies.*0139

*Having 1 of those parts, having 1 penny, is going to be 0.01 or 1 cent.*0149

*1/100 is having 1 cent, 0.01.*0160

*Let's look at this again; this fraction right here, 3/4.*0170

*I am going to again relate it to the fraction 1/4; remember 1/4.*0177

*If I have 1 part out of the 4 that I divided the dollar into, then I have 1 quarter which is 0.25.*0183

*This is the value of 1 quarter.*0200

*If you look at this fraction, this is 3/4.*0203

*The dollar is still divided into 4 parts which is still the quarter.*0207

*If I have 3 quarters, how much do I have?*0213

*I have 0.75 or 75 cents.*0218

*If I want to do this mathematically, I can take the 3 and divide it by 4.*0229

*3, this right here means divide; 3 divided by 4.*0237

*That means I can take 3 divided by 4.*0242

*This is a whole number; I have to put a decimal after it.*0249

*Then I can add as many 0s as I want; let's make this longer.*0254

*4 goes into 3 zero times; I am going to raise up this decimal.*0263

*4 goes into 30 how many times?--let's see.*0268

*4 times 7 is 28; subtract this; this is 2; bring down the 0.*0273

*4 goes into 20 five times.*0286

*If I want to convert 3/4, this fraction into a decimal, I can just do 3 divided by 4.*0297

*I am still going to get the same answer of 0.75.*0305

*But if I know that I can take this and think of the dollar,*0309

*and I know I can divide the dollar into 4 parts which is 4 quarters,*0315

*and I have 3 of those parts, then I have 75 cents.*0319

*Right here, 0.7; 0.7 is the same thing as 0.70.*0327

*0.7 is the same thing as having 70 cents; what gives me 70 cents?*0344

*If I have 7 dimes, then I will have 70 cents.*0351

*Then I can say that this is having 7 over... the value of a dime is 10 cents.*0359

*7/10 would be the same thing as 70 cents.*0370

*If I want to just take this without relating it to the dollar*0377

*and just convert it back to a fraction, I can take this number right here, 7.*0382

*I am going count how many numbers I have after the decimal place.*0388

*It has to be after the decimal place; 7, I only have one number.*0392

*Take that number; place it over a 10.*0398

*One 0 because I have only one number after the decimal place.*0405

*So I am only going to have one 0 here.*0409

*Let's go over more examples.*0414

*Convert from fraction to decimal or decimal to fraction.*0417

*Here we have a decimal; I am going to convert it to a fraction.*0421

*If I look at this, if I have 25 cents, I have 1 quarter.*0429

*1 quarter would be having 1 quarter out of... how many quarters equal a dollar?*0438

*4; so having 1 quarter, 25 cents or 0.25, is the same thing as 1/4.*0446

*Another way to do this, I take this number, 25.*0457

*I am going to make that into my numerator.*0465

*Then I am going to count how many numbers do I have after the decimal place?*0468

*I have two numbers; I have one, two.*0475

*I am going to put that many 0s after my 1 as my denominator.*0479

*This becomes 25/100.*0487

*I have to simplify this because this fraction... I know that 25 can go into 100.*0491

*I am going to take this 25; I am going to divide by 25.*0499

*Then I have to divide the bottom number by the same number.*0503

*25 divided by 25 is 1; 100 divided by 25 is 4.*0509

*0.25 is going to be the same thing as 1/4.*0518

*The next example is a fraction 3/10; I can convert this into a decimal.*0527

*Again let's relate it to money.*0536

*If I have 10 as my denominator, then what do I have?*0538

*10 parts to make a dollar would be 10 dimes.*0546

*I know that I am working with dimes here.*0553

*If I have 3 dimes, then how much do I have?*0556

*How can I write that into a decimal?--I would have 30 cents.*0561

*Having 3 dimes is the same thing as 30 cents.*0569

*Or 3/10 is the same thing as 0.30 or 0.3 because again this is the same thing.*0576

*I can put a 0 here because it is after the decimal place.*0585

*Another way you can do this, just divide; 3 divided by 10.*0592

*I have to add 0s at the end of it.*0601

*10 goes into 30 three times; but I have to write it over the 0.*0605

*Then I have to bring up my decimal; this becomes 30.*0612

*If I subtract, I get 0.*0617

*3/10 or 3 divided by 10 is going to be 0.3.*0621

*This next example, 0.77, I am going to convert this into a fraction.*0630

*If I have 0.77 or 77 cents, I have the same thing as 77 pennies.*0637

*Again I can write that number at the top.*0653

*How many pennies are equal to a dollar?*0659

*I know that 100 are equal to a dollar.*0662

*This is the same thing as saying I have 77 pennies.*0665

*0.77 is the same thing as 77/100.*0671

*Again without thinking of money, I can just take this number, 77, as my numerator.*0677

*Count how many numbers I have after my decimal place which is 2.*0685

*That means I am going to add two 0s which is 100 as my denominator.*0690

*It is the same thing.*0697

*This fourth example here, I have a fraction and I am going to convert this into a decimal.*0704

*This top number tells me how many I have.*0712

*This bottom number tells me how many out of 100 I have or how many out of a dollar I have.*0716

*If I have 100 parts to make a dollar, what do I have?*0722

*I have the penny because 100 pennies equals 1 dollar.*0727

*I know that I have 9 of them.*0732

*9 out of 100 would be the same thing as having 9 pennies.*0734

*In order to write this as a decimal, if I have 9 pennies, how much do I have?*0743

*I have 9 cents which is written like that.*0748

*9 out of 100 is the same thing as 0.09.*0753

*You can also think of this as 9 divided by 100.*0761

*You can take 9 divided by 100.*0768

*But since this is 100, I can do a shortcut here.*0771

*Whenever my denominator is 10 or 100 or 1000, any number that is a multiple of 10,*0779

*all I am going to do is take that top number... let's write that out; the top number is 9.*0787

*I am going to count how many 0s I have here.*0794

*I have one; I have two 0s.*0796

*Since I have two 0s, I am going to take that number 2.*0800

*I am going to place this decimal point right there.*0806

*The decimal point always goes after the number.*0812

*I am going to move the decimal point two places because again there are two 0s here.*0815

*If I had a 10, I only have one 0.*0822

*I would only move it one place value.*0826

*If I had 1000, I would have three 0s.*0828

*I would have to move it three place values.*0833

*Again I am going to take this decimal point.*0837

*I am going to move it two place values going to the left.*0839

*I am going to go one and two.*0844

*There is where my decimal point is going to go.*0848

*Then I have a space right here; I have to put a 0 right there.*0852

*For this shortcut, you can only do that if the denominator is a multiple of 10.*0856

*It has to be 10, 100, or 1000, and so on.*0861

*Otherwise you are going to have to do 9 divided by 100.*0866

*Again this sign right here means divide.*0870

*We can do 9 divided by 100 to change that into a decimal.*0872

*But I also knew that this bottom number right here, it takes 100 pennies to make a dollar.*0878

*Since it takes 100 pennies to make a dollar and I have 9 of them,*0888

*I would have 9 cents; I can just write that as 0.09.*0892

*That is it for this lesson; thank you for watching Educator.com.*0898

1 answer

Last reply by: Professor Pyo

Mon Oct 26, 2015 6:48 PM

Post by EN N on October 26, 2015

Hi Mary, there's a mistake in the practice questions section. The last question says, 'Convert from decimal to fraction: [16/100].' It's supposed to be convert FRACTION to DECIMAL.

0 answers

Post by Wasay Ahmad on February 4, 2013

yah i saw that too it got me confused a little bit until i looked back.

0 answers

Post by Victor Castillo on January 24, 2013

You said .07 when you meant .7.....