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Okay, I know one of you here is a teacher and please forgive me for forgetting who you are. I'm studying for a test to become a CPhT and one of the math problems was this:

Round to the nearest two numbers: 0.1450

Now I've always been told, along with everyone I've asked about this problem, 0 to 4 you round down, 5 to 9 you round up. So the answer should be 0.15 right? The answer in the book said it is 0.14. Reason: 50 is a whole number and 4 is an even number therefore the answer is 0.14. I need to know how they figured that out.

Well, you could be nice enough to share the answer with me as it's driving me totally insane trying to figure it out

RED ONE.. It has to do with the placement of the decimals.. but like you I have always gone by the 5 and up 4 and below down..:-5

Rounding Off Decimals

Objectives

After completing this unit, you should be able to:

Determine whether a decimal should be rounded up or down.

Round up decimals.

Round down decimals.

Rounding Off

Rounding off a decimal is a technique used to estimate or approximate values. Rounding is most commonly used to limit the amount of decimal places. Instead of having a long string of decimals places, or even one that goes on forever, we can approximate the value of the decimal to a specified decimal place.

We can round to any place. After rounding, the digit in the place we are rounding will either stay the same, referred to as rounding down, or increase by 1, referred to as rounding up. The question now becomes, when do we round up or down?



When to Round Up

Rounding up means that we increase the terminating digit by a value of 1 and drop off the digits to the right. If the next place beyond where we are terminating the decimal is greater than or equal to five, we round up. For example, if we round 5.47 to the tenths place, it can be can be rounded up to 5.5.



When to Round Down

If the number to the right of our terminating decimal place is four or less (4, 3, 2, 1, 0), we round down. This is done by leaving our last decimal place as it is given and discarding all digits to its right. For example, if we round 6.734 to the hundredths place, it can be rounded down to 6.73.





Example

Round 0.24 to the tenths place.

The answer here is 0.2.

We wish to round 0.24 to the tenths place. That means we only want one digit to appear after the decimal point, so .24 will round to .2 or .3, whichever is closer.



There is a 4 in the hundredths place. Since this is less than 5, we round down, meaning we leave the 2 in the tenths place and drop the 4 off the end.



Example

Round 12.756 to the tenths place.

The number 12.756 should be rounded up to 12.8.

We wish to round 12.756 to the tenths place. That means we only want one digit to appear after the decimal point. In this example, there are two digits that appear to the right of the tenths place.



When rounding off 12.756, look only at the digit in the place directly to the right of the tenths place (the hundredths place). Check to see if the digit in the hundredths place is 5 or greater or less than 5. In this case the digit in the hundredths place is a 5, therefore we round up from 7 to 8.





Rounding Off in Everyday Life

Rounding occurs all the time in everyday life. For example, cash registers are programmed to round off automatically to the nearest hundredth. Since one cent is one hundredth of a dollar, what we are charged must be rounded off to the hundredths place. For example, if the sales tax is 8.25%, or .0825, you could have the following table of taxes charged for different sale amounts.



Amount of Sale (dollars) Sales Tax* (dollars) Total Amount (dollars)

5.00 .41 5.41

10.50 .87 11.37

20.75 1.71 22.46

31.00 2.56 33.56

55.50 4.58 60.08

78.75 6.50 85.25

*Sales tax is charged at the rate of 8.25%

The middle column, Sales Tax, was obtained by multiplying the first column by 0.0825, which is the rate of sales tax.

Amount of Sale x 0.0825 = Sales Tax

Notice that the Sales Tax column only goes out to the hundredths place. Let's try this multiplication for a couple of rows to determine if the creators of the table used rounding without telling us.

First Row

Amount of Sale = $5.00

Sales Tax Rate = 0.0825



5.00 x .0825 = 0.4125

On the table, the Sales Tax is listed as 0.41. As we can see, the Sales Tax was rounded down to the closest cent.



Second Row

Amount of Sale = $10.50

Sales Tax Rate = 0.0825



10.50 x .0825 = .86625

On the table, the Sales Tax is listed as 0.87. Here we can see, the Sales Tax was rounded up to the closest cent.

This table gives a typical example of how rounding is used everyday.

Now that you've had a chance to read about rounding off decimals, and seen a real life example, try the practice on rounding off the decimals.

Maths meets Nature

The British snake, The Adder, is close to extinction because it can't multiply

This is EXACTLY how it is written:

Round the following to the two places:

9. 1.0035

10. 0.0255

11. 0.1550

12. 0.1450

Now, the answers:

9. 1.00

10. 0.03

11. 0.16

12. 0.14

The Red One wrote: This is EXACTLY how it is written:

Round the following to the two places:

9. 1.0035

10. 0.0255

11. 0.1550

12. 0.1450

Now, the answers:

9. 1.00

10. 0.03

11. 0.16

12. 0.14


In question 12, 50 = 50, and the previous number (4) is even. We round down to 0.14.

This makes no sense to me since there is a 5 next to the 4 that should be rounded up not down.

GRRRRRRRRRRRRRR :-5

This is aggrevating.

Is this a course in Splitting Hairs?

Well there you have it.. neither one is right or wrong..!! :-2 of course your dealing with $$$$ then I'm rounding up if it has to do with me..

May I respectfully suggest that you could argue that either is perfectly correct

could the catch be the way the problem is worded?



"Round to the nearest two numbers:" and not

"Round to the nearest 100's" or 1000's.



Just a dumb hickabilly so I have no answer other than I would round it to 0.15 and be happy with it....

Rules for rounding off:

If the first nonsignificant digit is a 5 and is followed by zeros........drop the 5 and

1. increase the lat significant digit by one if it is ODD

2. leave the last significant digit the same if it is EVEN.

The new math has nothing to do with 0-4 or 5-9. Go figure - I had to relearn that rule.

It also depends if it is a statistical rounding of numbers:

Some statisticians prefer to round 5 to the nearest even number. As a result, about half of the time 5 will be rounded up, and about half of the time it will be rounded down. In this way, 26.5 rounded to the nearest even number would be 26”it would be rounded down. And, 77.5 rounded to the nearest even number would be 78”it would be rounded up.

Sorry Red, I'm a Mathematics Teacher. I've taken up to "Advanced Calculus and Analytic Geometry." The highest math known to mankind.

The answer to number 12 is:

0.15

If the question is, which number is it closer to, 0.14 or 0.15, then the answer is 0.15 for exactly the reasons you've said. The rule states that 5's must round up. (We had to break it somewhere!)

The only thing I could possibly think of is if a company, such as a bank, wanted a little extra profit margin, they might round down the half-penny and keep it for themselves. But that's still not good math.

Moreover, the break their own stupid rule in the previous question by rounding up instead of down. Some kind of "it was even" statement isn't good enough to change a set math theorem, so you're right and they're wrong.

Call them on it, call the test prep people and say that you've found a faulty question. Sometimes they reward people for that, since high stakes testing is worth millions of dollars. I once found a misprint in a math textbook and I had a Lear jet full of lawyers in my classroom the next day. They gave me free samples for life.

Also, I believe the question should ask you to round to two decimal places. This is something that can be very confusing if it's not worded properly. A number would normally refer to the items to the left of the decimal point.

Jives wrote: Sorry Red, I'm a Mathematics Teacher. I've taken up to "Advanced Calculus and Analytic Geometry." The highest math known to mankind.

The answer to number 12 is:

0.15

If the question is, which number is it closer to, 0.14 or 0.15, then the answer is 0.15 for exactly the reasons you've said. The rule states that 5's must round up. (We had to break it somewhere!)

The only thing I could possibly think of is if a company, such as a bank, wanted a little extra profit margin, they might round down the half-penny and keep it for themselves. But that's still not good math.

Moreover, the break their own stupid rule in the previous question by rounding up instead of down. Some kind of "it was even" statement isn't good enough to change a set math theorem, so you're right and they're wrong.

Call them on it, call the test prep people and say that you've found a faulty question. Sometimes they reward people for that, since high stakes testing is worth millions of dollars. I once found a misprint in a math textbook and I had a Lear jet full of lawyers in my classroom the next day. They gave me free samples for life.


Oh that would be wonderfully funny! If that could/would actually work for me then my boys' school should receive free math books for centuries to come! LOL As for the book I'm studying there are TONS of mistakes! My hubby and his uncle are both math wizards to me, they can look at a problem tell you the answer but not how to work it out. My hubby almost failed math because the teacher thought he was cheating due to the fact he didn't work the problems out and wrote one on the board and my hubby looked at it and told him the answer, there was never a problem after that. I on the other hand wasn't so lucky, I struggled with everything, and still do, if I don't have a pen and paper most of the time I can't tell you the answer but I've gotten much better than I was two years ago.

That problem just stumped us all. I still say it's 0.15. I thank all of you for your input and help. I really appreciate it!

Kelly