Significant figures
Please tell me if I'm understanding all this correctly -
• the significant figures in a given reading are all going to be consecutive digits, and of those consecutive significant digits, the last one is the one we're uncertain of, while we're certain of the rest.
• When we're writing down a reading made using a generic ruler, with its smallest unit being 1 millimeter, the reading cannot be something like 2.33 cm, it can only be 2.3 cm, even if we feel like the former reading is closer to the real value, judging by eyeing the gap between the 23 mm and 24 mm lines on the ruler.
• If we can see that the reading is equal to or greater than 2.35 cm, do we write down 2.4 cm or 2.3 cm?
59 Replies
Hello @Sam_2207!
Choose the Study Helper subject ping
Choose the subject for the respective doubt :)
1. yes. last one uncertain as in, could be + or - 1 because of any discrepancies in precision
2. yes
3. if this is for an actual lab experiment, doesn't matter tbh, its your call, and both values are within the limits of experimental error. just don't write 2.35cm.
the last one isn't for an actual experiment, i just wanted to know what would be the correct thing to do, since the whole point of making sure that our reading has the right number of significant figures is to relay how accurate our reading is
@Nimboi would you happen to know (´。＿。｀)
well maybe then you could eyeball it but convey the uncertainty
so if you see that the reading looks closer to 2.4 instead of 2.3, but you still want to convey the uncertainty, you could write 2.4 +/- 0.1 or 2.4 +/- 0.05
or just explicitly say in words that "the reading is in between 2.35 and 2.4cm"
it is scientific to look at the ruler, just don't accidentally pretend that the measurement is precise
ofc, i aint a scientist
Roger 🫡 shukriya!
I forgot how to close the thread and thank you for solving my doubts
no problem :)) you type +solved @the person who solved your doubts
tooting my own horn rn
One last thing
@Nimboi
I'm sorry for bugging you this much 🙇
Wait Ig 0.0 has 1 sig fig…
But if our reading is just
0
Does that reading have 0 sig figs?
That's so weird
And if our reading was 1 we'd have 1 sig fig
nahh honestly it's very refreshing to see someone actually curious about the subject
both have 2 sig figs
Socratic.org
How many significant figures are in 0? | Socratic
Zero When there is no decimal point, you ignore the zeros in terms of counting significant figures. If the question had asked how many significant figures are in 0., then there is one significant zero.
all u gotta do when thinking about sig figs is see if a digit improves the precision of the reading
the 0 before the decimal point makes the reading more precise (by narrowing it down into a range of 0-0.999...)
the 0 after the decimal point also makes the reading more precise (by narrowing it down into a range of 0.00000... - 0.09)
but, supposing that reading is written in centimeters, if we write it in meters, it'd turn into 0.000, and if we count the number of significant figures according to you, there are now 4 significant figures, but the number of significant figures shouldn't change just because we changed the unit of measurement in which we're reporting our reading
but if our reading is "0" instead of "1", isn't it still relaying the measurement to the same level of accuracy? and i wouldn't say that there is no information being relayed either...
you're correct, but to avoid confusion, if the reading is 0 then we just write it as 0. with a decimal instead
i think scientific notation avoids this problem
hang on lemme send a link im a lil rusty myself
alright
okay i think i got it
in the case of 0, you write it as 0 in any unit
because 0 just indicates nothing
"no length/volume/whatever"
its a bit dodgy there
for non zero numbers, you maintain the same amount of significant figures
0.5 cm would be converted to 0.005 m, which both have 1 significant figure
while you think that both of them look different, the way its generally conveyed that its the same amount of precision is to write it as 5 * 10^-1 cm or 5*10^-3 m, where only 5 is counted as the sig fig (this is scientific notation)
it doesn't look like a perfect system but it works
If we measure 0 cm using a ruler, doesn't our reading indicate that the length of whatever we were measuring lies between 0 cm and 0.05 cm?
We are measuring something after all
scientifically speaking, your ruler cannot measure a reading between 0 and 0.05, however you can add a personal note that it looks like the reading is between those 2 numbers (conveying the uncertainty as +/-)
or normally, you just get a more precise instrument
Hmm
its a human made system, its not gonna be perfect
but if it works, it works
I guess so
I'll have to take a minute to take it in though
But I think this explains it
Thanks a lot!!
your respect for knowledge is admirable i love it
its not just "look at it and move on"
Thanks but it doesn't seem like I'll be able to go far
eh i feel the same sometimes
but in the end who gives a shit
I tried changing a bit
if i feel profound, i feel profound
i hold that value very close to me, if i were asked to pick between my curiosity and going to college, i'd pick my curiosity
😆 ig that's true. I should think that way as well.
we'll get there!
all college does is catalyze your development
and that's great, you should be working for that
but it's not the end-all be-all
what takes an IITian 4 years to do, you could do in 10
does it matter? not really, atleast after those 10 years
I don't think I'm the kind of person who'd be able to do much on my own, unlike yourself
My environment affects me a lot and
i do fuck all on my own 💀 but i'm working on that
Well
Yeah
the more you look into the long term, the more your enthu matters
😭 well good on you for trying ig
i told myself that after 12th and entrance exams are over
I'm gonna try too
Try to study, which I haven't done since 2020
ill sit down and read einstein's relativity
paper
whatever i don't understand, i'll google
no time constraints, no exams
ought to be therapeutic as hell
riyal
That sounds cool
yeh :D
all i gotta do is make it thru now
My mind is at the level where thinking a little stresses me out so it'll take me a few years before I'm able to say something like this
stresses you out as in you don't feel good enough?
I feel uncomfortable thinking
Doesn't matter if it's studies or my interpersonal relations
your curiosity didn't give me that impression
but that's just a matter of time
our brains get better at things the more we do them
akin to going to the gym
That's what I'm betting on
when i look back at my 11th self and think about what i wasn't able to do
Wonder what'll be of my friendships by the time I start thinking properly
i often go "was i fucking dumb or what"
but its nice
its a sign of progress
my perspective is, just being able to think about whatever i want to is my ultimate freedom
i cannot believe i landed in a lucky enough spot to like science, and even if i'm not good at it right now, or maybe ever, i can still enjoy the shit out of it
That's me when I think of how I didn't realise how creepy I must've come off, staring at my crush back in 8th
lmaooo
character development hits hard
Science does seem so cool when you think of how much we've pushed the boundaries of our realities with time
It's like a superpower
exactly dude
Thingy
and we were born in such a position that we understand it
we are the universe looking back on itself
Yeah
Sho cool
ight ima go study mafs
try not to jump off challenge
Roger
byebye
Bbyee
+solved @Nimboi
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