hey it's professor Dave, let's talk sig figs. he knows a lot about the science stuff, professor Dave explains. humans have a need to communicate their experiences with one another. how far apart are two cities? when did something happen and how long before it happens again?
this is why we developed units of measurement. some correlate with natural phenomena like a day or a year which are based on the motion of the earth, but many are arbitrary. like most units of length and mass. when we participate in measurement we have to be aware of some limitations. for example, how many people are in this crowd? can we say 10,000?
what about 10,400? or 10,472? we have to be careful not to make an estimate that is more precise than our measuring abilities allow. so when we use measuring devices we only estimate one digit further than the level of precision inherent in the instrument. here we could estimate 2.33 centimeters but not 2.33481, we do not have access to that level of precision.
so any measurement will have a certain amount of significant figures or sig figs associated with it that display how precise it is. here are the rules for determining how many sig figs are in a value. one, any digit that's not zero is significant. two, zeros in between other non-zero digits are significant.
leading zeros, ones that come before the first non-zero digit, are not significant. and trailing zeros, the ones that come after the last non-zero digit, are only significant if they are decimal zeros. so 10,000 only has one significant figure which really means it's about 10,000 not exactly 10,000.
If we bring back that same crowd and one more person shows up, can we estimate 10,001? No, because we have only estimated to one sig fig, so anything from 9,500 to 10,499 would round to our estimate of 10,000. When we do calculations, we have to pay attention to the number of sig figs.
If we are adding or subtracting, our answer will have as many decimal places as the value with the least number of decimal places. If we are multiplying or dividing, our answer will have as many sig figs as the value with the least number of sig figs. Whatever our answer is, we will have to round up or down at the appropriate digit.
5 or higher means round up, 4 or below means round down. Let's check comprehension. thanks for watching guys, subscribe to my channel for more tutorials, and as always feel free to email me