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# How do I round a decimal?

Sparda
Umm, I kinda forgot how to round a decimal number. I feel stupid about this. Anyone mind telling me how to round a decimal to the tenth and to the hundreaths?

Example: 10.3763 To Tenths place
Example: 72.1564 To Hundreaths place

Thx and sorry for bad spelling.
If the next digit past your rounding digit is greater than 5, then you round up.
ie 10.3763 to 10.4
Liu

x.y //tenths
x.xy //hundredths
x.xxy //thousandths
Sparda
Thank you. I know have a better understanding of this.
peaceninja
hmm, were these examples for your understanding or were these questions from the homework assignment?

! !
Scott
Someone told me the real way to round was to round UP half the time and DOWN half the time when you have exactly .5 . I hadn't heard of that before.
Blaster
10.1553 would also be rounded up to 10.2 5 and above is to be rounded up when it is next to the rumber that you are rounding to.
peaceninja
 Scott wrote: Someone told me the real way to round was to round UP half the time and DOWN half the time when you have exactly .5 . I hadn't heard of that before.

you would not round up/down with X.5 because of the X.0.

X.0 is always rounded down to X.0 and not up to (X+1).0

X.5 is always rounded up to (X+1).0 and not down to X.0

if you round up half the time and round down half the time with X.5, then you should do the same with X.0.

Another way to think about it is even distribution:

X.0, X.1, X.2, X.3, X.4 are all rounded down

X.5, X.6, X.7, X.8, X.9 are all rounded up

So it evens out this way!

Good idea though, it's intuitive at first thought...
zjosie729
I always hated the fact that you have to round up when you have a .5 or .05 or when you have something 5. I think it shouldn't be rounded up or down. Just stay as .5 or .05 or something.
Liu
 zjosie729 wrote: I always hated the fact that you have to round up when you have a .5 or .05 or when you have something 5. I think it shouldn't be rounded up or down. Just stay as .5 or .05 or something.

Sometimes it's just easier to round up/down. Example, paying for food with a bunch of friends. You don't want to pay exact cents, just round up to the nearest dollar.
DynamicNames
Example: 10.3763 To Tenths place - 10.4
Example: 72.1564 To Hundreaths place - 72.20

I'm pretty sure that you have to look over at the number after the place you are looking at, and then either increasing the current number-place if it is 5 or higher, or 4 or lower. Then, after that, you can take out all the numbers after the number-place you just rounded. Hopefully that helps you.
poiko123
About the point of rounding a 5:

The correct (or perhaps just scientific) way to round when it ends in only a five is look at the preceding number. Evens round down; odds round up.
To clarify:
(rounding to the tenths place)
2.35 --> 2.4
2.85 --> 2.8
2.353--> 2.4
2.8533-->2.9

The reason behind this, is so that the error due to rounding averages itself out. Just figured I'd add that to the convo.
Kaisonic
5 always rounds up. I dunno where you guys are hearing these things, but here's what you do:

Look at the number AFTER the number you want to round to. If you want to round to the tenths place, look at the hundredths number. If the hundredths number is 5 or greater, increase the tenths number by 1 and end the decimal. If the hundredths number is 4 or lower, keep the tenths number the same and end the decimal.

Examples:
2.54 to the tenths = 2.5
2.55 to the tenths = 2.6
2.5475 to the hundredths = 2.55
2.3445 to the thousandths = 2.345
2.4459 to the tenths = 2.4

One thing to note, like the last one above, is that you're ONLY looking at the number AFTER the place you're rounding to, not rounding number by number to achieve an answer of 2.5. (2.4459 -> 2.446 -> 2.45 -> 2.5 = NOT correct)
NuniPio
 Sparda wrote: Umm, I kinda forgot how to round a decimal number. I feel stupid about this. Anyone mind telling me how to round a decimal to the tenth and to the hundreaths? Example: 10.3763 To Tenths place Example: 72.1564 To Hundreaths place Thx and sorry for bad spelling.

i guess wat everyone above me has said should quite cover this.. or do still need more explaining?
Blu_Spykz
 peaceninja wrote: hmm, were these examples for your understanding or were these questions from the homework assignment? ! !

Lol my exact thought. Came here to refresh my own mind - I'd actually forgotten that Rounding, decimals, equations and the such existed.
Davidgr1200
The worst variation I have seen was in a program at work.
The rule was:
If greater than 0.5 round up to the nearest integer
If less than 0.5 round down to nearest integer
If =0.5 use 0.5!!!
tribe
3.5647----> 3.3

12.831----->12.9

Not sure what you mean, but use a calculator!
Soulfire
Generally, we always round a 5 up. So 1-4 rounds down and 5-9 rounds up.
littletomi714
The first thing you should know is that if it's five or more, it goes up. And if it is four or less, it goes down.
Okay, part two:
When you look at the places, you look at the one to the right of it.
Look what number it is.
If it is 4 or less, then remove that number and all others after it, and replace with zeros. If it is higher than five, then increase the number before by one and remove all numbers after and replace with zeros.
Agent ME
 tribe wrote: 3.5647----> 3.3 12.831----->12.9 Not sure what you mean, but use a calculator!

Lol - 3.5647 ----> 3.6
Arnie
Agent ME wrote:
 tribe wrote: 3.5647----> 3.3 12.831----->12.9 Not sure what you mean, but use a calculator!

Lol - 3.5647 ----> 3.6
Yes, and 12.831-->12.8

 poiko123 wrote: About the point of rounding a 5: The correct (or perhaps just scientific) way to round when it ends in only a five is look at the preceding number. Evens round down; odds round up.
Who told you that??
a.Bird
Arnie wrote:
 poiko123 wrote: About the point of rounding a 5: The correct (or perhaps just scientific) way to round when it ends in only a five is look at the preceding number. Evens round down; odds round up.
Who told you that??
It's called the round-to-even method. You decide what the last digit to keep is. If the next digit is 6 or more, add 1 to your last digit. If the next digit is 4 or less, leave your last digit as it is. If the next digit is 5, however, you round your last digit up if it's odd and down if it's even. Or if your last digit is even and the next digit is 5 but is followed by a non-zero digit then you round up.

3.16 --> 3.2
3.14 --> 3.1
3.15 --> 3.2 (1 is odd)
3.25 --> 3.2 (2 is even)
3.253 --> 3.3 (5 is followed by a non-zero digit)
rnankori
It's not exactly relavent, but...

In exams in Israel the students should round to 2 figures after the dote...

as this : 3.46, 4.23, 8.76

I see that you all round it to one figure: 1.4, 4.3, 6.3

Is this what is expected? actually in high school here students shouldnt round at all. they should leave the answer as a fracture, as this:

31/7 23/12 or as this 4 3/7 2 1/12

how is it in the states? and other places?
Arnie
No, we are just using 1 decimal as example. As far as I know, in science the rounding of a number is dependent on the numbers used to calculate it. Eventually those numbers are experimentally found and then the accuracy of the instruments plays a key role.

In multiplication / division, the number with the smallest amount of significant numbers is the standard. In addition / substraction, the number with the smallest amount of decimals is the standard.

Only with maths this is different, there we are told the amount of decimals if we have to round anything. That's obvious since in maths there usually are no experimentally found numbers.

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