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?
2 answers
Anyone help please
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).
5 answers