How to Determine Significant Figures in Multiplication/Division?

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Discussion Overview

The discussion revolves around determining significant figures in multiplication and division, specifically in the context of a calculation involving the numbers 0.00420 and 60. Participants explore how to apply the rules of significant figures based on the nature of the numbers involved.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant states that the result of multiplying 0.00420 by 60 should reflect the lowest number of significant figures from the two numbers involved.
  • Another participant points out that the number 60 is ambiguous and may have infinite significant digits if it is considered an exact conversion factor, thus requiring more context to determine its significance.
  • Some participants argue that since 60 lacks a decimal point, it should be treated as having only 1 significant digit unless specified otherwise.
  • There is a suggestion that if 60 is used as a conversion factor, it should not limit the significant figures in the result.

Areas of Agreement / Disagreement

Participants express differing views on how to treat the number 60, with some asserting it has 1 significant digit while others argue it could be considered exact depending on context. The discussion remains unresolved regarding the treatment of 60.

Contextual Notes

The discussion highlights the ambiguity surrounding the classification of whole numbers as significant figures and the dependence on context for determining their significance.

parabolic1
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just a quick question... (not a HW question)

i know that when you do multiplication/division between numbers you take the lowest amount of sig figs of the two and apply it to your answer... HOWEVER:

what would be the answer for a question such as:

0.00420 x 60 = ?

the first part has 3 sig figs, while the second part has 1... although I've heard you don't count whole integers, so would the answer be

0.252 or 0.3 ?

thanks
 
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The "60" is ambiguous. For example if you are converting from minutes to seconds, 60 is exact, so it has to be treated as having infinite significant digits. To answer your question you need more context.
 
Since there's no decimal point with the '60', it has 1 significant digit.
 
Andy Resnick said:
Since there's no decimal point with the '60', it has 1 significant digit.

On the other hand, if the 60 is meant to be a conversion factor (i.e, between minutes and seconds, or hours and minutes), then it is to be treated as an exact number that doesn't limit the significant figures.

But yes, if it's just part of the data then 1 significant figure, definitely.
 

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