Asked by Mai
When I round 6396 to 3 significant figures, I get 6400. I was double checking my work and used scientific notation for 6400, which is 6.4*10³, but when I counted the significant figures in scientific notation, I only get 2, which are 6 and 4, but there were supposed to be 3. Anyone can help to explain?
Answers
Answered by
Mai
Anyone help please
Answered by
oobleck
The problem is the rounding. Since you round up, it results in a loss of significant digits. If you are going to use scientific notation, and you want three sf's, then use 6.40*10^3
As explained here:
http://www.astro.yale.edu/astro120/SigFig.pdf
When a number ends in zeroes that are not to the right of a decimal point, the zeroes are not necessarily significant:190 miles may be 2 or 3 significant figures, 50,600 calories may be 3, 4, or 5 significant figures. The potential ambiguity in the rule can be avoided by the use of scientific notation. For example, depending on whether 3, 4, or 5 significant figures is correct, we could write 50,6000 calories as:
5.06×10^4calories (3 significant figures)
5.060×10^4calories (4 significant figures), or
5.0600×10^4calories (5 significant figures).
As explained here:
http://www.astro.yale.edu/astro120/SigFig.pdf
When a number ends in zeroes that are not to the right of a decimal point, the zeroes are not necessarily significant:190 miles may be 2 or 3 significant figures, 50,600 calories may be 3, 4, or 5 significant figures. The potential ambiguity in the rule can be avoided by the use of scientific notation. For example, depending on whether 3, 4, or 5 significant figures is correct, we could write 50,6000 calories as:
5.06×10^4calories (3 significant figures)
5.060×10^4calories (4 significant figures), or
5.0600×10^4calories (5 significant figures).
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