Decimal place and significant figure

  • #1

Main Question or Discussion Point

I am confusing on how many decimal places or significant figures we should use. When i am doing some exercise, the answers provided vary from 1 decimal place to 2or3 decimal places. I wonder do we have a standard value of decimal place/significant figure that is generally accepted? Thanks.
 

Answers and Replies

  • #2
Char. Limit
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I like to use 5. But it really depends on personal preference... I remember that in some circles, there are actually required rules. Something like:

Addition keeps the number of decimal places that the addend with the smallest number of significant decimal places had.
Multiplication keeps the number of (significant) digits that the factor with the fewest (significant) digits had.
 
  • #3
HallsofIvy
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"Number of decimal places" is an elementary school concept designed to let kids who are just learning "long division" know when they can stop!

"Significant figures", on the other hand, are important in applications. Every number in applications is either the result of counting (and so an integer) or a measurement- and all measurements have an "accuracy". If, for example, you measure using a ruler marked to mm, you should be able to say which mm mark your measurement is closest to and so measure accurately to the nearest mm. If you give the measurement in meters, then you have "three decimal place accuracy".

As to how many significant figures you keep in calculations, that should be determined by the situation, not "personal preference". No calculation can be more accurate than the least accurate measurement- no calculation should have more decimal places than the fewest decimal places in any of the numbers used in the calculation.
 
  • #4
symbolipoint
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Part-way through college in one of the more quantitative science courses, was the first time I received any instruction about significant figures & relation to place value, and topics of accuracy. That was somewhat confusing at the time, although with practice the ideas became much easier to manage.

Interesting- if you have a couple of measurements to use in a calculation (multiplication and or division involved) and they are maybe 3 sigfigs each, and if you use a calculator to get a seven or eight or more or so number of figures then several of them are really meaningless. You must round, at best, to only 3 signif figures.

If you step on a scale to weigh yourself, and the scale shows marks only to the nearest pound, you cannot say then, that you weigh 175.308 pounds. The ".008 part is nonsense. The ".3" part is maybe also suspect.
 

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