Can you help me with significant digits?

[DLI848]

How many significant digits are in each of these?

50 people
23,000 seconds

[MatticusMania]

50 = 1 sig digit (5)

23,000 = 2 sig. digits (2 & 3)

[MakiSupaStar]

You got no chance getting a chick's number.

[MatticusMania]

Originally Posted by MakiSupaStar

You got no chance getting a chick's number.

Especially when you factor in the fact that I had no idea what a significant digit was until I did a quick Google search.

[jp58]

Originally Posted by DLI848

How many significant digits are in each of these?

50 people
23,000 seconds

SigFigs explained:

All non-zero numbers are significant.

Zeros-
Trailing zeros are never significant 23000, 50
Captive zeros are significant 409
Leading zeros are never important 0.395

[dmonroe]

Originally Posted by jp58

SigFigs explained:

All non-zero numbers are significant.

Zeros-
Trailing zeros are never significant 23000, 50
Captive zeros are significant 409
Leading zeros are never important 0.395

As a Physics student that actually sees a lot of my classmates confused about this I have to say this is the absolute BEST and simple to understand explanation I have seen anywhere, in any book, particularly the use of the word "captive".

[BassChuck]

42. The only truely significant digits.

[geeza]

Originally Posted by BassChuck

42. The only truely significant digits.

Except for my middle finger. Depending on the circumstances, it can be a significant digit.

[hover]

Originally Posted by geeza

Except for my middle finger. Depending on the circumstances, it can be a significant digit.

which is why I always fly the superfinger.

2 significant digits, and SOO close to the shocker.

[Downunderwonder]

50 is 50 not 51 52 or 53 etc. That's significant. Isn't it?

Lemme think, 55x 50 = 2750
@ 2 significant figures is 2800, at 1 significant figure is 3000

I vote for 50 being 2 sig figures.

[fdeck]

Significant figures are at best a crude rule of thumb for error propagation, codified in a way that makes it easy to mark homework assignments.

[fdeck]

Originally Posted by Downunderwonder

50 is 50 not 51 52 or 53 etc. That's significant. Isn't it?

Lemme think, 55x 50 = 2750
@ 2 significant figures is 2800, at 1 significant figure is 3000

I vote for 50 being 2 sig figures.

Depends. If you are doing homework, then you follow the rules given by the teacher. If you care about expressing yourself clearly, then you need better notation:

5.0e1 has 2 sigfigs
5e1 has 1 sigfig
50(2) is 50 plus or minus 2

[bassman03]

Originally Posted by Downunderwonder

50 is 50 not 51 52 or 53 etc. That's significant. Isn't it?

Lemme think, 55x 50 = 2750
@ 2 significant figures is 2800, at 1 significant figure is 3000

I vote for 50 being 2 sig figures.

50 is only one significant figure. If it were 50. (notice the decimal) it would be two because the decimal shows that it is right at fifty______ (fill in the blank) on the dot. Without the decimal it just means that it's somewhere in the 50s. Maybe 50.454 or 49.789, but 50 is just a good enough desk.

[bassybill]

The question is oversimplified, I think. There's not enough info in the OP to infer the accuracy of the figures quoted, and so you can't really say how many significant figures there are for that reason. Zeros can be significant or not, depending on the accuracy with which a stated quantity is known.

Exactly 50 (not 49 or 51) people is two significant figures. And exactly 23,000 seconds is five. But the OP doesn't say whether the figures are exact, or not.

[bassman03]

Originally Posted by bassybill

The question is oversimplified, I think. There's not enough info in the OP to infer the accuracy of the figures quoted, and so you can't really say how many significant figures there are for that reason. Zeros can be significant or not, depending on the accuracy with which a stated quantity is known.

Exactly 50 (not 49 or 51) people is two significant figures. And exactly 23,000 seconds is five. But the OP doesn't say whether the figures are exact, or not.

Extremely valid point.

[Cabazon]

Originally Posted by bassybill

The question is oversimplified, I think. There's not enough info in the OP to infer the accuracy of the figures quoted, and so you can't really say how many significant figures there are for that reason. Zeros can be significant or not, depending on the accuracy with which a stated quantity is known.

Exactly 50 (not 49 or 51) people is two significant figures. And exactly 23,000 seconds is five. But the OP doesn't say whether the figures are exact, or not.

With the given information, and the way they are written, there is one sig fig in 50, and two in 23,000, not a chance of 2 and 5, depending on what isn't given.

[Brad Barker]

trailing zeroes can certainly be significant. if the result of an experiment is reported as 5.00000, then all digits are significant since they tell how precise the measurement was performed. (of course, you also need an error estimate, and that's what really determines the number of sig figs...)

[dmonroe]

Originally Posted by Brad Barker

trailing zeroes can certainly be significant. if the result of an experiment is reported as 5.00000, then all digits are significant since they tell how precise the measurement was performed. (of course, you also need an error estimate, and that's what really determines the number of sig figs...)

According to every Physics Professor I have come in contact with as well as all of the Physics books I own or have read this is ABSOLUTELY WRONG!

However when working a problem the rules for significant digits in your final answer are these:
RULE: When multiplying or dividing, your answer may only show as many significant digits as the multiplied or divided measurement showing the least number of significant digits.

RULE: When adding or subtracting your answer can only show as many decimal places as the measurement having the fewest number of decimal places.

[bassybill]

Originally Posted by Cabazon

With the given information, and the way they are written, there is one sig fig in 50, and two in 23,000, not a chance of 2 and 5, depending on what isn't given.

Originally Posted by wikipedia

The significance of trailing zeros in a number not containing a decimal point can be ambiguous. For example, it may not always be clear if a number like 1300 is accurate to the nearest unit (and just happens coincidentally to be an exact multiple of a hundred) or if it is only shown to the nearest hundred due to rounding or uncertainty. Various conventions exist to address this issue:
A bar may be placed over the last significant digit; any trailing zeros following this are insignificant. For example, 13ŌO has three significant digits (and hence indicates that the number is accurate to the nearest ten).
The last significant digit of a number may be underlined; for example, "20000" has two significant digits.
A decimal point may be placed after the number; for example "100." indicates specifically that three significant digits are meant.[1]
However, these conventions are not universally used, and it is often necessary to determine from context whether such trailing zeros are intended to be significant. If all else fails, the level of rounding can be specified explicitly.

My emphasis.

http://en.wikipedia.org/wiki/Significant_figures

[dmonroe]

Originally Posted by bassybill

My emphasis.

http://en.wikipedia.org/wiki/Significant_figures

And of course we all know Wiki is always right.