Significant digits in calculation

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SUMMARY

The discussion centers on the application of significant figures in calculations involving multiplication and division. A participant calculates the conversion of 20 kiloseconds to hours and minutes, concluding that the final answers should reflect the significant figures of the initial measurement. The participant determines that for 20 kiloseconds, which has 1 significant figure, the conversion yields 6 hours and 333 minutes, while acknowledging that different interpretations of significant figures can lead to varying correct answers, such as 5.6 hours and 330 minutes as provided in the reference book.

PREREQUISITES
  • Understanding of significant figures in mathematical calculations
  • Basic knowledge of unit conversion (kiloseconds to hours and minutes)
  • Familiarity with rounding rules in numerical analysis
  • Ability to perform basic arithmetic operations (multiplication and division)
NEXT STEPS
  • Research the rules of significant figures in scientific calculations
  • Learn about unit conversion techniques for time measurements
  • Explore rounding methods and their implications in numerical results
  • Study examples of significant figures in various scientific disciplines
USEFUL FOR

Students in mathematics or science courses, educators teaching numerical analysis, and professionals in fields requiring precise calculations, such as engineering or physics.

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Hello everyone:
I am trying to figure out the how many significant figures (sf), should I keep in the final
answer for multiplication and division
1. How many hours and minutes are 20 kiloseconds?



2.



3. for hours: 20*10e3 / 3600 = 5.5555 hrs
20 has only 1 significant figure (trailing zero doesn't count), hence the answer should have 1 sf, that means I should round answer to the single digits. my final answer is 6 hr. My book give 5.6 hr as the answer.
please let me know my approach is correct

for minutes 20*10e3 / 60 = 333.333 minutes
keep only 1 sf in the result,that leads my answer to 333 minutes
my book give 330 and the final answer
 
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Your book appears to be choosing 2 significant digits. However you could just as well choose 3 sf and still be correct. I would state what I'm using for sf, in my solution. To 3 sf, hours would be 5.56hr. If you see the answer in your book as 5.6hr, you should realize, both answers are correct.
 

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