Rounding Numbers

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Rounding off is important when we deal with money.
Money comes in 10, 20, 50, and 100 notes.
We can think about dollar amounts more clearly if we picture them as being made up of individual bank notes.

We can round whole numbers to the nearest 10, 100, 1000, etc by finding out if our number is closer to the current 10, 100, 1000, or closer to the next 10, 100, 1000.

We have found that it is easiest to do rounding off by thinking of the half way point between two numbers.

Rounding to the Nearest 10

The “tens” in our number system are 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, etc.

For the tens 20 and 30, the halfway point between them is 25.

If we have a value of 25, 26, 27, 28, or 29 then it is closer to 30, if we are looking to go to the nearest 10.

If we have a value of 21, 22, 23, or 24, then it is not even halfway to 30. These values are closer to 20. This means that they round off to 20 when rounding to the nearest 10.

The halfway value when rounding to tens is 5, 15, 25, 35, 45, 55, etc.

If we are exactly on this halfway value we round up to the next ten.

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Another method of rounding to the nearest 10, is to look at the number value that is in the “ones” position.

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Rounding to the Nearest 100

Rounding to the nearest 100 is very similar to rounding to tens.

For the hundreds, 400 and 500, the halfway point of 450.
Any values less than 450, will round off to 400.

Values that are bigger than 450 are getting closer towards 500, and round off to 500.

The exact middle value of 450, also rounds up to be 500, when taken to the nearest hundred.

Here is a flow chart which shows how to round to the nearest 100.

Image Source: http://www.helpingwithmath.com

Rounding to the Nearest 1000

Rounding to the nearest 1000, uses halfway points: 500, 1500, 2500, 3500, and so on.

2700 rounded off to the nearest 1000 could potentially be an answer of either 2000 or 3000.

The correct answer is 3000, because we are past the half way point of 2500, and thus closer to 3000 when we are at 2700.

An important reason we need to be able to round off, is to make it easier to compare items, especially on graphs.

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Another important application of rounding off is when dealing with money.

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In some countries like Australia, the lowest coin is 5 cents, and not even a one cent coin. So we would have to round off $25.03 cents worth of Petrol (Gasoline) to the nearest 5 cents. The customer actually pays $25.00 and not $25.05 .

This is interesting, because the customer actually got 3 cents worth of Petrol for free. (And we all know that free stuff is good!). Oil Companies are very interested in the total percentage of fuel which is given away for free like this per week at their outlets, and factor this into their pricing and profit calculations. In the real world, Mathematics is often not perfect !

Video Lessons on Rounding Off

Rounding to the nearest 10

[youtube http://www.youtube.com/watch?v=Y7FekoVid54]

Rounding to Tens and Hundreds

[youtube http://www.youtube.com/watch?v=UP7YmXJc7Ik]

The same video lesson by Math Vids Professor Perez is also at the following link:

http://www.mathvids.com/lesson/mathhelp/493-rounding-numbers

Online Lessons on Rounding Off

The following BBC Lesson has Fact Sheet sections, plus Worksheets and Tests that can be done.

http://www.bbc.co.uk/skillswise/numbers/wholenumbers/whatarenumbers/rounding/index.shtml

Here is another basic lesson on Rounding Numbers that includes some great number line worksheets at the end of it.

http://www.enchantedlearning.com/math/rounding/

Slideshow on Rounding Off

The following “Slideshare” presentation has a nice little poem in it that might help memorize the rounding off rules.

Click on the right hand aroow, or anywhere on the current slide with the hand symbol to advance through the presentation.

This slideshow presentation can also be viewed at this link:

http://www.slideshare.net/franc1md/rounding-powerpoint

Rounding Off Worksheets

The following online worksheet let’s you practice rounding to the nearest 10

http://interactive.onlinemathlearning.com/num_round.php?action=generate&mode=10&numProblems=10

This worksheet is on rounding to the nearest 100.

http://interactive.onlinemathlearning.com/num_round.php?action=generate&mode=100&numProblems=10

This next online worksheet is on rounding to the nearest 1000.

http://interactive.onlinemathlearning.com/num_round.php?action=generate&mode=1000&numProblems=10

Rounding Off Online Games

Spaceships Rounding to Tens Game

In this game we click on the spaceship that contains the correct answer.

http://www.free-training-tutorial.com/rounding/rounding-spaceships.html

Sharks Rounding to Hundreds Game

In this game we click on the Shark that contains the correct answer. However, we need to do this quickly before the sahrk eats the fish.
We get a nice explosion noise and effect when we click the correct shark.

http://www.free-training-tutorial.com/rounding/sharks.html

Bingo Rounding Game

This game covers rounding to the nearest 10 or 100.

How the game works is that we are given rounding off problems to do, and each answer gets circled on our Bingo Card.

We usually have 10 questions, and 10 bingo numbers, if we get them all correct, all 10 numbers should be circled by the last question.
It appears that we only us each answer number once.

It is important to click the NEXT button after each question, and do not click the Answer button, unless we are unable to work out the answer ourselves.

At the start, the helper person says we have to pick any 5 numnbers, but it seems that we have to do all 10 to complete the game, and so we are not sure what this start of game message means.

One strange thing, is that there not seem to be any “Bingo! you have won the game” message at the end. It is up to you to see that you have circled all the bingo numbers, and have thus succeeded.

http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_resources/848/rounding.swf

Rounding Off Tests

The following BBC Quizes are on rounding 10’s 100’s and 1000’s.

http://www.bbc.co.uk/skillswise/numbers/wholenumbers/whatarenumbers/rounding/quiz.shtml

Mr Ankers Test on Rounding to Tens

http://www.henryanker.com/Math/Number_Sense/Rounding/Rounding_Nearest_10_Set_01.swf

Mr Ankers Test on Rounding to the Nearest 100

http://www.henryanker.com/Math/Number_Sense/Rounding/Rounding_Nearest_100_Set_01.swf

Mr Ankers Test on Rounding to the Nearest 1000

http://www.henryanker.com/Math/Number_Sense/Rounding/Rounding_Near_1000_Set_03.swf

That rounds out a very big post.

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Enjoy,
Passy