Decimal place and significant figure

[Michael_Light]

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.

 

[Char. Limit]

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.

 

[HallsofIvy]

"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.

 

[symbolipoint]

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.

 

[CellCoree]

Dear student,

Thank you for your question. Decimal places and significant figures are both important concepts in scientific measurements and calculations. While they may seem similar, they serve different purposes and have different rules for determining their values.

Decimal places refer to the number of digits after the decimal point in a number. For example, in the number 3.14159, there are five decimal places. Decimal places are important for maintaining accuracy and precision in measurements. The general rule for determining the number of decimal places is to use the same number of decimal places as the measurement instrument. For example, if you are using a ruler with millimeter markings, your measurement should have three decimal places (0.001).

On the other hand, significant figures refer to the number of digits in a number that are known with certainty. This includes all the digits that are known for sure, plus one estimated digit. For example, in the number 3.14159, there are six significant figures. Significant figures are important for indicating the precision of a measurement. The general rule for determining the number of significant figures is to use all the digits that are certain, plus one estimated digit. For example, if a measurement is given as 3.1 cm, it has two significant figures because the 3 is certain and the 1 is estimated.

In terms of a standard value for decimal places and significant figures, there is no universally accepted value. The number of decimal places and significant figures needed will depend on the specific measurement or calculation being performed. It is important to follow the rules mentioned above to ensure accuracy and precision in your work.

I hope this explanation helps to clarify the difference between decimal places and significant figures. If you have any further questions, please do not hesitate to ask.

Best regards,