![]() Went all the way down to the thousandths place. We get to the nearest one, but then we put another Once again, this decimal tells us that not only did So this is three significantįigures over here. Kind of a roughness only to the nearest tens place. The decimal point, it means that they measured The decimal point, it would be a little unclear Non-zero digits and everything in between, and trailing 0's To count leading 0's before the first non-zeroĭigit, I guess we could say. This was 0.052 kilometers, this would be the same thing asĥ2 meters, which clearly only has two significant figures. ![]() This leading 0, by the same logic that if To explicitly say, look, I measured this far. And the reason why we'reĬounting these trailing 0's is that whoever wrote this numberĭidn't have to write them down. Really giving you the precision are the 7, the 0, and the 0. Shifting it based on the units of measurement Sense why you only have three significant figures. Maybe, in fact, we justĮxactly 7.00 meters. Here was a measurement of kilometers, so if we This a little bit better, imagine if this right over It's not telling us how precise our measurement is. Because you're just like, thatĭoes help define the number. Uncomfortable that we're not including these 0's thatĪre after the decimal point and before this 7, that Thing right over here, the significant figures Information about how precise my measurement is? So on this first But the general way to thinkĪbout it is, which digits are really giving me Precise than the things that you actually measured, that Precision that you had, that the result isn't more When you do a big computation and you have a bunch ![]() Significant figures is just to make sure that The follow-on videos help explain why it can be so important to be able to clearly express the level of accuracy of a measurement with the measurement itself.įigures, sometimes called significant digits. Watch the videos again with this in mind and see if that helps. Thus "0.10000" means I measured something to the nearest one hundred thousandth and "0.1" means I measured to the nearest tenth. The world of scientists and mathematicians have settled on a particular convention, or agreed upon rule, that keeps all of us on the same page and understanding the same thing when we all read a given measurement. The point of significant figures is for one person to tell another person both the measurement of something AND the level of accuracy of that measurement. So, you can sort of figure out most of the rules from just a common sense approach using a simple situation - mathematicians love to do that. If they had measured the distance to that crazy a level, they would have told you they ran "5.0000 km". At the same time, you would know that they did NOT measure the distance to the closest cm - they were within a meter or so of exactly 5 km, but not down to the nearest cm. If, however, that same person told you they ran "5.00 km" then you would know they really meant they measured the distance to within 1 one-hundredth of a km (which would be one meter.) and they ran no less and no more than that. Both of these numbers would have an assumed accuracy of 1 significant figure. If they told you they had run 50 km, you would still assume an accuracy of a km or so - or to be precise, that they ran between 49.5 km and 50.5 km. Likewise if they ran 4.4 km they would report a 4 km run (and they were honest. And, if they told you they ran "5 km" then you would understand that they ran somewhere between 5.5 km and 4.5 km - if they had run 5.7 km, they would have said they ran "6 km" instead, rounding to the nearest km. For example, if someone told you they ran "005 km" you would know that they ran "5 km" - the leading zeros do not tell you anything differently or imply any greater or lesser level of accuracy. Wether or not a zero is "relevant" or not is a bit tricky to determine, but makes sense once you think things through carefully.
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