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Rules for rounding numbers - Computers & Internet

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If the rightmost digit o be changed (rounded) is 1,2,3,4 replace it by 0 (round down). If it is 6,7,8, or 9 increase by 1 the penultimate digit (round up).
What to do if the last digit is 5? Most people round up. Some purists recommend to round up and down alternatively.

Posted on Nov 26, 2013

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Can you help my son on his rounding numbers


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http://www.fixya.com/troubleshoot/browse/homework

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https://www.mathsisfun.com/rounding-numbers.html
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How do I round a decimal when you have a lot of numbers after the decimal point?


You first have to decide what accuracy, that is how many decimals, are needed in the answer. There is a rule of thumb which says you should not quote more decimals than the accuracy of the data used in the calculation. Money calcs of course would usually use just 2 decimals.

So when dropping decimals round up the last remaining of the dropped decimal is 5 or over, otherwise it is unaltered. So 2.2361 rounded off to 3 dec is 2.236, and rounded to 2 dec it is 2.24.

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Since the next digit is less than five, round down to 0.307 .

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I need help with significant figures 3.414s 10.02s 58.325s 0.00098s


There are 4 sig figs (sfs) in 3.414.
Also,
  • 4 sfs in 10.02
  • 5 sfs in 58.325
  • 2 sfs in 0.00098

The rule I use is the "dot right-moving arrow" rule.
I know it seems weird, but it is a very powerful rule, always reliable!

Here is what you do:
If the number has a dot in it (that is, if it has a decimal in it), imagine an arrow swooshing from left to right through the number. Start counting sig figs as soon as the imaginary arrow strikes a non-zero digit. Every digit the arrow goes through after it hits that first non-zero digit, is a significant digit (sig fig). The total number of sig figs is the sum of the first non-zero digit + all the following digits the arrow goes through after that. Very simple, right?

As an example, in 0.00098, the arrow sweeps through the leading zeros without counting until it stikes the first nonzero digit, 9. (BONK!!) So you must count it and the following digit (8). So the total number of sfs is only 2 for this number. Try it on the other numbers for practice.

For a better closure, I guess I should explain the other related rule for sig figs:
The "no-dot left arrow" rule. You can use this rule when a number does not have a decimal in it. For example, the number 500 s. (I am using the same unit you gave in your quantities. As you can see, no decimal is shown. So you can not be sure the number has 3 sfs or not. It would only have 3 sig figs if you were informed it was an exact number. An exact number is a number which has been obtained by counting every object it represents. As in a classroom filled with 200 students, each one counted by their teacher during roll call.

To apply the no-dot left-moving arrow rule, simply imagine an arrow moving left until it hits the first non-zero digit. In this case, that digit is the 5, which is only one digit. Therefore, there is only 1 sig fig in 500 s.

Suggestion: Google up "sig figs" and get some more examples of quantities to practice counting sig figs. Also pay attention to the important related topic of proper rounding off of calculated quantities which have different numbers of sig figs. You will find this skill invaluable when you take a lab based chemistry or physics course!

Good luck!

###

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1 Answer

I am a number rounding me to the nearest thousand makes me a 1000.All my digits are even their sum is 12 they are in order from greatest to least and no digit is repeated what number am I


642.
They are all even numbers and they are all in order from greatest to lease. Their sum must add up to 12 also. so 6 +4 +2 = 12.
If you round it to the nearest 1000 you get 642.
Take each thing they are saying as 1 of your rules to get the number. And use that to eliminate numbers for example. 1 3 5 7 are all eliminated. then use numbers to get to 12 that must be even. Finally make sure they are from greatest to least.

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I am a number rounding me to the nearest thousand makes me a 1000.All my digits are even their sum is 12 they are in order from greatest to least and no digit is repeated what number am I ?


642.
They are all even numbers and they are all in order from greatest to lease. Their sum must add up to 12 also. so 6 +4 +2 = 12.
If you round it to the nearest 1000 you get 642.
Take each thing they are saying as 1 of your rules to get the number. And use that to eliminate numbers for example. 1 3 5 7 are all eliminated. then use numbers to get to 12 that must be even. Finally make sure they are from greatest to least.

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1 Answer

Need help with rounding up decimals


The general rule for rounding of decimals and numers is as follows;

If the number is 1 to 4 inclusive then it rounds down to 0
if the number is 5 to 9 inclusive then it rounds up to 10 then carry the 1 along 1 place to the left

Take a look at the following link for more details and some examples

http://www.dtc.dla.mil/qa/RR.htm.

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