Rounding to significant figures

[raanikeri]

A question asks me to round 12014 to 3 significant figures.
Why is the answer 12000?
12000 only has 2 significant figures - the 1 and the 2, isn't it?

 

[MathLover1]

12000 is correct

(1,2,0 are 3 significant figures)

 

[raanikeri]

12000 is correct

View attachment 1145 (1,2,0 are 3 significant figures)

but according to this website https://ccnmtl.columbia.edu/projects/mmt/frontiers/web/chapter_5/6665.html
and many other websites, trailing zeroes in a whole number with no decimal are not counted as significant figures. I'm puzzled as to why you think the first trailing zero in 12000 is significant, but not the other trailing zeroes. I can't find a rule that says that. My textbook is even worse.. only states some of the rules in the website I linked here and not even all of the rules.

 

[MathLover1]

Significant Figures Rules

1. Non-zero digits are always significant
2. Zeros in between non-zero digits are always significant
3. Leading zeros are never significant
4. Trailing zeros are only significant if the number contains a decimal point

References

• Khan, Salman "Significant Figures," The Khan Academy.
• Weisstein, Eric W. "Significant Digits," MathWorld--A Wolfram Web Resource.

 

[raanikeri]

Significant Figures Rules

1. Non-zero digits are always significant
2. Zeros in between non-zero digits are always significant
3. Leading zeros are never significant
4. Trailing zeros are only significant if the number contains a decimal point

View attachment 1146


References

• Khan, Salman "Significant Figures," The Khan Academy.
• Weisstein, Eric W. "Significant Digits," MathWorld--A Wolfram Web Resource.

The table shown below the 4 rules doesn't seem to correlate with the rules. It says the first trailing zero after 78, in 78000, is significant, but not the 2 other trailing zeroes. Then it says both the trailing zeroes in 78800 are significant. Pray tell me, how do I know when to consider a trailing zero as significant?

 

[MathLover1]

in your case given number is whole number
12014 and 0 is between 2 and 1, therefore significant

Any zeros between two significant digits are significant.
If a zero is found between significant digits, it is significant.
Significant zeros will be zeros to the right of non-zero significant digits. (in your case 0 to the right of 2)

 

[raanikeri]

in your case given number is whole number
12014 and 0 is between 2 and 1, therefore significant

Any zeros between two significant digits are significant.
If a zero is found between significant digits, it is significant.
Significant zeros will be zeros to the right of non-zero significant digits. (in your case 0 to the right of 2)

But if zeros to the right of non zero significant digits are significant, why isn't 12000 considered to have 5 significant numbers? Why aren’t all the zeros at the end counted as significant? But yet in the case of 78800, all the zeros at the end are counted as significant and therefore 78800 is 5 significant Figures?

 

[MathLover1]

78800 is written in decimal form as 78800. and you can add zeros 78800.000 which is same

 

[nycmathguy]

78800 is written in decimal form as 78800. and you can add zeros 78800.000 which is same

You are a true math professional. You never have anything negative to say about each question posted. Keep up the good work.