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Is there any way we could shoehorn the word exponential into the definition?

...and (wince) could someone please explain what a floating point number is?

I get (for the first time) Phil's description of bias above and why JDAWs intended method introduces a risk of bias. I also get that JDAW is confident that that bias does not compromise the integrity of the thing to which the method will be applied. Let's all hope he is correct in that assertion.

So, is the point floating in the number or in my glass of Rioja?

DRT wrote:...and (wince) could someone please explain what a floating point number is?

For your purposes it is a real number (so a number not necessarily a whole number or a precise fraction), stored to some finite precision in a moderate amount of computer space.

There’s plenty of other stuff, but — trust me — you don’t care.

Anyway, the risk of bias is of slight concern to me. (OK, I don’t care about small bias in either direction, but I might care about the appearance of bias.) I will investigate the suggested sources.

jdaw1 wrote:

DRT wrote:...and (wince) could someone please explain what a floating point number is?

For your purposes it is a real number (so a number not necessarily a whole number or a precise fraction), stored to some finite precision in a moderate amount of computer space.

Thank you. Would (for an idiot) "a number with a defined number of decimal places" work as an imprecise definition?

jdaw1 wrote:the risk of bias is of slight concern to me. (OK, I don’t care about small bias in either direction, but I might care about the appearance of bias.) I will investigate the suggested sources.

I will work on the basis that the value my unintended challenge has added will be rounded down to zero.

Well, I am pleased I asked here: Phil and Wikipedia have changed my mind.

Current favourite:
> Each [thing] shall then be [maths in words], rounded to the nearest thousandth of a basis point; an exact half of a thousandth of a basis point of yield being rounded to the nearest even multiple of a thousandth of a basis point.

I am also coming closer to Daniel’s view: should these threads be split into a new thread?

Yes.

Note for those coming to this thread at a later date.
In Excel, if A1 is in percentage points rather than basis points, this is

• = IF( ABS(A1-ROUNDDOWN(A1,5)-5E-6)<1E-10, ROUND(A1/2,5)*2, ROUND(A1,5) )

(100bp = 1%.)

DRT wrote:

jdaw1 wrote:

DRT wrote:...and (wince) could someone please explain what a floating point number is?

For your purposes it is a real number (so a number not necessarily a whole number or a precise fraction), stored to some finite precision in a moderate amount of computer space.

Thank you. Would (for an idiot) "a number with a defined number of decimal places" work as an imprecise definition?

More accurately, “… of significant figures”.

I don't know what an insignificant figure is, so that doesn't help me.

1.23456789012345678 is to 17 decimal places and 18 significant figures.
12345678901234567.8 is to 1 decimal place and 18 significant figures.

When writing decimal, the figures to the left are more ‘significant’, those to the right are less so. So these are to the 18 most significant figures.

Hi, I have a question about port, am I in the wrong place?

djewesbury wrote:Hi, I have a question about port

Ask away. Pray, what question?

Actually, I might know the question, so I’ll jump to the answer: Port is fortified wine from the Douro Valley in Portugal.

Did that help?

jdaw1 wrote:1.23456789012345678 is to 17 decimal places and 18 significant figures.
12345678901234567.8 is to 1 decimal place and 18 significant figures.

When writing decimal, the figures to the left are more ‘significant’, those to the right are less so. So these are to the 18 most significant figures.

That makes no sense. There are 18 "numbers" and one decimal point in each example, both of which are stated to have the same number of significant figures.

Please provide an example of an insignificant number.

djewesbury wrote:Hi, I have a question about port, am I in the wrong place?

Yes.

Is the accuracy proportional to the size of a number (≈ significant figures), or is it absolute (the number of digits to the right of the decimal point)? E.g., a number bigger than a billion could be given to 1 part in a billion (9 significant figures), despite being given to zero decimal places. But if a number was of size about 1, and was given to 1 part in a billion, there would be several digits after the decimal point.

jdaw1 wrote:Is the accuracy proportional to the size of a number (≈ significant figures), or is it absolute (the number of digits to the right of the decimal point)? E.g., a number bigger than a billion could be given to 1 part in a billion (9 significant figures), despite being given to zero decimal places. But if a number was of size about 1, and was given to 1 part in a billion, there would be several digits after the decimal point.

{sigh}

I just got it.

1,000,000,000.000000001 does not have nineteen significant numbers, it has ten.

But how many significant numbers does 1,234,567.890123 have?

...and what is the threshold between significant and insignificant?

If it is subjective I will be very disappointed.

DRT wrote:I just got it.

1,000,000,000.000000001 does not have nineteen significant numbers, it has ten.

But how many significant numbers does 1,234,567.890123 have?

You have’t got it.

1,000,000,000.000000001 has nineteen significant digits (it is given correct to about one part in 10^19), but only ten decimal places (because it is accurate to 10^-10).

The mass of the sun is 1.98855×10^30 kg. That is six significant figures: i.e., to about one part in just under a million. But it is to a negative number of decimal places — if to six decimal places it would have been correct to the milligram (difficult, as the sun loses mass by about 4.26 million metric tons per second, that number being given to three significant figures).

jdaw1 wrote:You have’t got it.

+1

Let's leave it there.

DRT wrote:

jdaw1 wrote:You have’t got it.

+1

Let's leave it there.

No. Please don't. This has been a fascinating way to lose 10 minutes of my life.

However, DRT did ask for an example of an I significant number. Here is such an example .

Happy to help.