How does Significant Figures work?
If i had a number: 1,007,000 is that with 4 sig figs or 7 sig figs?
I checked 5 different resources and gotten conflicting answers.
Help!
The answer will depend on what's being measured and how it's being measured.
If that number were the amount of shares of common stock of some public company that were traded today then it could be 7 significant figures. On the other hand, if it were the number of miles some object might be from the earth then there might be only 4 significant figures. If it's some kind of measurement then most likely it has only 4 sig. figures. If it's something that can be counted, and the process is extremely accurate and verifiable, then there could be more than four signif. figures.
So the short answer is...it depends.
It is hard to tell. If there was a period at the end, such as 1,007,000. then the answer is 7 sig figures. But with no period, we don't know if the zeros are sig or not. GENERALLY, I think the rule is not to count them if there is no period. In such practice, the number would be written as 1.007E+6. Then there would be no confusion and we would count 1, 0, 0, and 7 as sig figures.
The reason you get conflicting answers is this:
The notation for significant zeros is changing. The IBM keyboard is largely to blame. Years ago, trailing significant zeros could be labeled with an overscore (a line above the number) to indicate it was significant. We cant make overscores on the IBM keyboard. So panic has ensued.
Years ago, if your number had a significant zeros, the least significant zero had an overscore (I can type it with an underscore 1,007,000, (now the number has six significant digits), but no overscore. For awhile, bold was used to indicated the least significant zero (1,007,000, but that faded quickly. So now there is no method except shifting to scientific notation (decimals to the right of numbers and decimals are significant, ie 1.00700 is seven sig digits), or being told initially.
This above applies to measurements: as Roger pointed out, counting numbers, or defined numbers,(100years in a century) are infinitely precise. If 1007000 had been counted, it does not have seven significant digits, it has infinite significant digits..It cannot determine the precision of your final outcome. This confusion based on the disruption of typesetting by the IBM keyboard in computers in the last 20 years is probably the reason you got five different answers. The most common rules widely adhered to are here:
(Broken Link Removed)
There are only three rules cited there.
I remember just 17 years ago, texts listed as many as seven rules.
For Further Reading
Thanks for this refresher Bob. It's been awhile since I looked at signif. figs. I wasn't aware that the short-comings of the keyboard were partly to blame for the confusion here. I do remember using the bar, but I couldn't remember what the rules were for it. I think some sets of rules also tell how to make calculations with measurements and determine sig. figs., that might account for the different rule counts.
In any case -if you read this Summer- always look at what your text states and know what the instructor expects. You should be alright if you do that.
Determining the number of significant figures in a given number depends on the context and the rules you are following. Generally speaking, significant figures are the digits in a number that carry meaningful information or contribute to its precision.
In the case of the number "1,007,000," without any additional information, it is difficult to determine the exact number of significant figures. However, based on conventional rules, if there is no period at the end of the number, the zeros at the end are not considered significant unless there is an indication otherwise. In this case, if we assume that the zeros are not significant, then the number would have 4 significant figures (1, 0, 0, 7).
However, to avoid confusion and ambiguity, it is recommended to represent such numbers in scientific notation, where the number would be written as "1.007E+6" or "1.007 × 10^6." This notation explicitly shows that all digits are significant.
The conflicting answers you received may be due to differences in conventions, interpretations, or the lack of specific information about the number and the context in which it is being used. It is always advisable to consult reliable sources, such as textbooks or reputable websites, to understand the specific rules and guidelines for determining significant figures in different scenarios. Additionally, clarifying with your instructor or referring to the specific instructions given for your assignment can help ensure consistency and accuracy in your calculations.