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

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

### Rounding Decimals

#### Related Links

- Decimal
- Number
- Rational number
- 10
- Base
- Positional notation
- Decimal representation
- Rounding
- Round-off error
- Approximation

- Circle the number in the place value
- Look at the number after the circled number
- If 5 or greater, add 2 to the circled number
- If smaller than 5, do not make any changes to the circled number
- Rewrite the number, but replace all numbers behind the circled number with zeros

### Rounding Decimals

*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

### Rounding 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
- Decimal Place Value 0:06
- Example: 12,3454.6789
- How to Round Decimals 1:17
- Example: Rounding 1,234.567
- Extra Example 1: Rounding Decimals 3:47
- Extra Example 2: Rounding Decimals 6:10
- Extra Example 3: Rounding Decimals 7:45
- Extra Example 4: Rounding Decimals 9:56

### Basic Math Online Course

### Transcription: Rounding Decimals

*Welcome back to Educator.com; this lesson is on rounding decimals.*0000

*To begin, we need to go over the place values.*0007

*If I have a number right here, 12,345 and 6679 ten thousandths, each number has a place value.*0012

*The 1 right here is ten thousands.*0030

*The 2, the one right before the comma, thousands; this is hundreds, tens, ones.*0033

*The important part is looking at the numbers after the decimal point.*0041

*The decimal point is read as AND.*0048

*6, this first number is not one'ths; it is actually tenths.*0051

*It starts off as the tenths value with a -TH.*0056

*The next one would be hundredths, thousandths, ten thousandths; keep this in mind.*0061

*Make sure you look over this and remember these place values.*0070

*When we round decimals, the first thing you are going to do is circle...*0079

*You don't have to circle--but it just makes it easier--the number in the place value that you have to round to.*0085

*If you look at this example right here, it says this number to the nearest tenth.*0094

*I know that tenths is the first number after the decimal point.*0099

*I am going to take that; I am going to circle that number, 5.*0103

*Look at the number after the circled number; behind; the number behind is a 6.*0111

*That number behind the circled number, if it is greater than 5,*0123

*5 or greater, then you add one to the circled number,*0127

*meaning you are going to round that number up.*0132

*If it is smaller than 5--4, 3, 2, 1, or 0--then you don't make any changes to that circled number.*0135

*You keep it as a 5.*0143

*This circled number is either going to stay a 5.*0144

*Or it is going to become a 6 if you round up.*0147

*After you determine that, you are going to rewrite the number, the whole number, the whole thing,*0152

*but replace all the numbers behind the circled number with 0s.*0158

*That is the point of rounding; you are going to stop at this number.*0164

*That is going to be the last number you are going to write.*0168

*The rest are going to become zeros.*0169

*This number 6, the number behind the circled number, is greater than 5*0174

*which means I have to take this circled number and round it up.*0179

*I am going to add 1 to the circled number.*0184

*This number is going to become a 6; this number is now a 6.*0187

*I am going to rewrite all the numbers, the whole thing, but replace the last numbers with 0s.*0196

*My new number, after rounding, it is going to become 1 thousand 2 hundred and 34 and 6 tenths.*0203

*Then I can put 0s at the end of them.*0219

*This is my new number, my rounded number.*0223

*Let's do a few more example; round each.*0229

*Here is the number; this is read 4 hundred 26 and 93 hundredths.*0232

*This number right here, 93, you read it as a hundredths because that is the last number that you see there.*0241

*That is the last place value; this is tenths; this is hundredths.*0248

*You are going to read this as 93 hundredths.*0252

*It says to round this to the nearest tenths... sorry, tens.*0256

*The tens... number the tens value; this is ones; this is tens.*0263

*I am going to circle that; the number behind it is a 6.*0270

*It is greater than 5.*0275

*The 6 value is greater than 5 which means the circled number becomes a 3.*0278

*I have to round up by adding 1.*0285

*All the numbers before the 2 stay the same.*0291

*The numbers behind the 2 are replaced with 0s.*0294

*Don't forget the decimal though; you still have to have that decimal.*0298

*This number is before the 2; so 4.*0304

*The circled number... again remember we were going to round up.*0309

*That becomes a 3; the 6 becomes a 0; everything else becomes 0s.*0313

*If I round to the nearest tens, then this number is going to become 430 or 430.00.*0323

*The next one; round to the nearest tenths; the tenths.*0332

*Be careful, the tenths is the first number after the decimal point.*0339

*That is this 0; 0.*0343

*Then I look at the number right behind it which is a 9.*0348

*It is greater than 5; my zero rounds up.*0350

*I do 31 point ...0 becomes a 1; everything else becomes 0.*0357

*The next few examples; we have this number right here to the nearest hundredths.*0372

*Tenths, hundredths; circle this number; I look at the number behind it.*0377

*Is it 5 or greater?--yes it is.*0383

*That means this 2 rounds up to become a 3.*0386

*All the numbers before it stay the same, 22.8.*0391

*Instead of writing the 2, I have to write the 3.*0399

*The numbers behind it become 0s; that is my answer.*0402

*The next one, round this to the nearest hundredths again.*0408

*Hundredths... tenths, hundredths; circle it.*0413

*The number after it, the number behind it is a 3.*0420

*That is not 5 or greater; it is smaller than 5 which means my 6 stays the same.*0424

*If it is smaller than 5, the number behind it, this number right here,*0432

*if it is smaller than 5, then I don't make any changes to that 6.*0435

*I don't subtract 1; I just leave it the same.*0441

*It is either going to be the same; or you are going to add 1 to it.*0446

*It is 44 and 96 hundredths; and then 00.*0452

*This number to the nearest tenths.*0467

*The tenths is again this number right here, the first number after the decimal point.*0469

*Look at the number behind it; is the number behind it 5 or greater?*0474

*Yes, it is 5 or greater; it is 5.*0478

*I have to add 1 to that circled number; this becomes a 1 now.*0481

*693 and 1 tenths; I can put these as 0s.*0487

*The next, nearest tens.*0498

*The difference between this one and this one--tenths, tens; this one has the -TH.*0503

*That means it is this place value right here after the decimal point.*0510

*Tens would be this number right here because it is ones and tens.*0514

*I look at the number right behind it.*0521

*It is smaller than 5 which means my circled number stays the same.*0523

*This would be 60 or 69; my 3 changes to a 0, decimal point, 000.*0533

*Keep in mind, when you have 0s at the end of a number*0547

*after the decimal point, then I don't have to write them out.*0552

*Again only the 0s that are at the end of a number and behind the decimal point.*0557

*In that case, I don't have to write them; you could; you don't have to.*0563

*If there is a 0 before the decimal point, in front of it,*0571

*then you have to because 69 we know is different than 690.*0575

*You have to make sure to have that 0 there.*0581

*But these 0s, as long as they are at the end of a number,*0584

*and it is behind the decimal point, then you don't have to write them out.*0587

*But you could; you could just leave it like this; this is fine.*0592

*This number to the nearest thousands; no -TH.*0600

*That means that the thousands is the number right before the first comma.*0604

*Right in front of the first comma is the thousands.*0613

*I am going to circle that.*0616

*The number before it is a 5; it is 5 or greater.*0618

*That means I have to change this 0 to a 1.*0622

*I am going to write all the numbers before it--1, 8, 9.*0630

*Instead of writing the 0, I am going to write the 1; write my commas.*0636

*Remember all the numbers after the circled number are going to turn into 0s.*0643

*This was my circled number; that changed to a 1; 0 to 1.*0651

*It is going to become 000.00.*0654

*Again because these 0s are at the end of a number,*0659

*and they are behind the decimal point, I don't have to write them out.*0663

*But I could if I want; I could just leave it like that.*0666

*This is the number when you round this to the nearest thousands.*0671

*Now this one is to the nearest thousandths with a -TH.*0678

*We know it is behind the decimal point; here is tenths, hundredths, thousandths.*0683

*I am going to round to that number and circle it.*0691

*Look at the number behind it; it is a 7.*0695

*It is 5 or greater; 7 is bigger than 5.*0697

*That means I change the circled number to a 5; I round up.*0701

*Again the circled number, it is either going to stay the same if this number behind it is smaller than 5.*0707

*Or it is going to become 1 bigger if the number behind it is 5 or greater.*0715

*When I rewrite my number, I am going to write all the numbers in front of it up to my circled number.*0721

*All the numbers behind it becomes 0s; 5.055; this becomes 0 right there.*0727

*That is it for this lesson on rounding decimals; thank you for watching Educator.com.*0746

0 answers

Post by Jaden Wu on May 26 at 06:39:49 PM

cool

0 answers

Post by Don Ky on May 26, 2015

Hello, I came up with a edge case that wasn't covered and I don't know if this is correct.

What if we had a number like:

2,961.050 to the nearest "hundred"?

Would this round out to 3,000.000? Since I assume since the 9 in the hundreds position becomes zero and you would add 1 to the thousands? The rest of the number rounds out to zero?

Thanks

0 answers

Post by Carolina ordo on March 3, 2015

If you were rounding 5.0549 can you just put 5.055 or do you need to put the extra 0?

4 answers

Last reply by: Daryle Stewart

Tue Jun 13, 2017 12:28 PM

Post by sherman boey on July 23, 2014

44.9633 to nearest hundredths can the answer be 44.96? without adding two zeros behind?

0 answers

Post by Saakshi Dhingra on August 17, 2013

in the first example, could the decimal be pronounced as: six thousand seven hundred eighty nine ten thousanths?

0 answers

Post by binti farah on January 13, 2013

Its really nice the way she tought me

1 answer

Last reply by: David Martinuk

Fri Feb 8, 2013 10:33 PM

Post by Younas Khan on January 1, 2013

Hi, Quick question re Example 3. Rounding 693.051 to the nearest Tens.

I thought the answer would remain 693.051. The number to the right of 9 is less than 5 which means the 9 stays the same but why has the 3 changed to a zero? I thought this stays as a 3

0 answers

Post by michelle morris on May 28, 2012

You do a very good job on explainig i'm just having problems with place values

0 answers

Post by Maria Lugo on April 13, 2011

Well I think that was a good explanation on how to round decimals. Its looks very hard but if we all give it our all it would be easy to understand.....