Difference between 1 significant figure and 1 decimal places

Examples: How many significant figures are in: 1. All numbers are significant. There are 3. The zeros are simply placeholders and locate the decimal. They are not trailing zeros. They are not significant. There are 5. The two zeros are not simply placeholders. One is between two significant digits and the other is a final, trailing zero in the decimal portion. Hence, they are both significant.

This is a bit confusing. It is somewhere between 1 and 4. In order to clarify, we need to convert this to scientific notation. If it were 4 x , there is one significant figure. If it were 4. Rules for Using Significant Figures For addition and subtraction, the answer should have the same number of decimal places as the term with the fewest decimal places.

For multiplication and division, the answer should have the same number of significant figures as the term with the fewest number of significant figures. In multi-step calculations, you may round at each step or only at the end. Exact numbers, such as integers, are treated as if they have an infinite number of significant figures.

They wrote them down to explicitly say, look, I measured this far. If they didn't measure this far, they would have just left these 0's off. And they would have just told you 7 meters, not 7. Let's do the next one. So based on the same idea, we have the 5 and the 2. The non-zero digits are going to be significant figures. You don't include this leading 0, by the same logic that if this was 0. So you don't want to count leading 0's before the first non-zero digit, I guess we could say.

You don't want to include those. You just want to include all the non-zero digits and everything in between, and trailing 0's if a decimal point is involved. I'll make those ideas a little bit more formal. So over here, the person did And then they wrote the decimal point.

If they didn't write the decimal point, it would be a little unclear on how precise this was. But because they wrote the decimal point, it means that they measured it exactly to be They didn't get and then round down. Or they didn't have kind of a roughness only to the nearest tens place.

This decimal tells you that all three of these are significant. So this is three significant figures over here. Then on this next one, once again, this decimal tells us that not only did we get to the nearest one, but then we put another trailing 0 here, which means we got to the nearest tenth. So in this situation, once again, we have three significant figures.

Over here, the 7 is in the hundreds. But the measurement went all the way down to the thousandths place. And even though there are 0's in between, those 0's are part of our measurement, because they are in between non-zero digits. So in this situation, every digit here, the way it's written, is a significant digit. So you have six significant digits. Now, this last one is ambiguous. The 37, it's not clear whether you measured exactly 37, Maybe you measured to the nearest one, and you got an exact number.

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I know I'm being knit-picky but I genuinely just want to know your thoughts on this. Would you call this 3 decimal places and 2 significant figures, or 2 decimal places and 2 significant figures. In the context of the assignment it doesn't matter a whole lot but I still think he should have written 2 significant figures. Since the results must be independent of representation and nobody would argue about the number of significant figures or decimal places here, this is the way to go for me.

I received some chemistry education both in the US and Germany. Unfortunately, my experience is that in Germany these two concepts are often confused, even on university level and by lecturers. All high school level books on Chemistry I looked at in the US contained a section on this and were clear and adamant.

There's no room for my two-pence on the matter. Pick out a random sampling of textbooks on Google Books, or even the Wikipedia article, and you can find the distinction clear as day, e. If we're being generous, maybe the problem was originally written to have the answer 0. I have since a long time a non-professional interest in numerics and the answer is unequivocal: You and TAR86 are right, the given answer is wrong. Sign up to join this community. The best answers are voted up and rise to the top.

Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Decimal places vs significant figures Ask Question. Asked 4 years ago. Active 4 years ago. All high school level books on Chemistry I looked at in the US contained a section on this and were clear and adamant.

There's no room for my two-pence on the matter. Pick out a random sampling of textbooks on Google Books, or even the Wikipedia article, and you can find the distinction clear as day, e. If we're being generous, maybe the problem was originally written to have the answer 0. I have since a long time a non-professional interest in numerics and the answer is unequivocal: You and TAR86 are right, the given answer is wrong. Sign up to join this community. The best answers are voted up and rise to the top.

Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Decimal places vs significant figures Ask Question. Asked 4 years ago. Active 4 years ago. Viewed 2k times. What's your 2 pence on the matter? Improve this question. Patrick Moloney Patrick Moloney 1 1 gold badge 7 7 silver badges 20 20 bronze badges.

The ideas are straightforward, but the details can be tricky. To round this number to 2 d.