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For more information, please see full course syllabus of Basic Math
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Lecture Comments (7)

0 answers

Post by Anders Jensen on September 8, 2017

so... 1/20 = .05 bc, if 1/10=.1 then half of .1 is... .05?

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.....

Connecting Decimals and Fractions

Related Links

  • Some fractions can be written as decimals
  • ½ = 0.5
  • ¼ = 0.25
  • 1/10 = 0.1
  • 1/100 = 0.01

Connecting Decimals and Fractions

Convert decimal to fraction: 0.50
  • [50/100]
  • [(50 ÷50)/(100 ÷50)] = [1/2]
Convert decimal to fraction: 0.05
  • [5/100]
  • [(5 ÷5)/(100 ÷5)]
Convert from fraction to decimal: [4/10]
Converting from fraction to decimal [6/100]
Converting from fraction to decimal: [2/100]
Convert from decimal to fraction: 0.65
Convert from decimal to fraction: 0.32
Convert from decimal to fraction: 0.09
Convert from fraction to decimal: [7/100]
Convert from fraction to decimal: [16/100]

*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.


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

Transcription: Connecting Decimals and Fractions

Welcome back to; 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 dollar0377

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