# Rounding to significant figures

Discussion in 'Basic Math' started by raanikeri, Nov 27, 2021.

1. ### raanikeri

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

raanikeri, Nov 27, 2021

2. ### MathLover1

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12000 is correct

(1,2,0 are 3 significant figures)

MathLover1, Nov 27, 2021
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3. ### raanikeri

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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.

raanikeri, Nov 27, 2021
4. ### MathLover1

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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

MathLover1, Nov 27, 2021
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5. ### raanikeri

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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?

raanikeri, Nov 27, 2021
6. ### MathLover1

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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)

MathLover1, Nov 27, 2021
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7. ### raanikeri

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But if zeros to the right of non zero significant digits are significant, why isn't 12000 considered to have 5 significant numbers? Why arenâ€™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?

raanikeri, Nov 27, 2021
8. ### MathLover1

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

MathLover1, Nov 27, 2021
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