What do significant figures tell us about a measurement

Identify the rule for each. All three numbers are significant rule 1. The leading zeros are not significant rule 3. The 3 and the 1 are significant rule 1 0. The 5, the 2 and the 9 are significant rule 1. The trailing zero is also significant rule 5. The 2 and the 1 are significant rule 1 and the middle zeros are also significant rule 2.

The number is ambiguous. It could have one, two or three significant figures. The 6 is a counting number. A counting number is an exact number. Answer b: four significant figures. Answer c: four significant figures. Answer d: Infinite Exact number Answer e: Ambiguous, could be two, three or four significant figure.

You might have read 46 mL; your friend might read the volume as 48 mL. All the answers are correct within the reading error of 1 mL. So, How many significant figures does our volume of 47 1 mL have? Answer - 2! The "4" we know for sure plus the "7" we had to estimate. First, note that the surface of the liquid is curved. This is called the meniscus. This phenomenon is caused by the fact that water molecules are more attracted to glass than to each other adhesive forces are stronger than cohesive forces.

The smallest division of this graduated cylinder is 1 mL. Therefore, our reading error will be 0. Therefore we have only 2 significant figures. Zeros used as placeholders are not significant. This would include all of the zeros in 0. We can use scientific notation to avoid misunderstanding. We would report the measurement as: 1. With the use of scientific notation every digit that appears is significant.

Here are some examples. But 4. Standard notation would not let us distinguish between the last two examples. They would both appear as Direct measurement is not the only way a number may contain significant digits. The number may be an Exact or Defined Number, it may be an integer, or the number could have been computed from numbers that have significant digits. This number has a mathematical definition and is exact.

Every digit you choose to display from this number is significant. Defined unit conversion values are also exact.

For example there are exactly 2. This is how the inch is defined. Because you're just like, that does help define the number. And that is true, but it's not telling us how precise our measurement is. And to try to understand this a little bit better, imagine if this right over here was a measurement of kilometers, so if we measured 0. This would be the exact same thing as 7.

Maybe, in fact, we just used a meter stick. And we said it's exactly 7. So we measured to the nearest centimeter. And we just felt like writing it in kilometers. These two numbers are the exact same thing. They're just different units. But I think when you look over here, it makes a lot more sense why you only have three significant figures.

These 0's are just shifting it based on the units of measurement that you're using. But the numbers that are really giving you the precision are the 7, the 0, and the 0. And the reason why we're counting these trailing 0's is that whoever wrote this number didn't have to write them down. 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.