1.2 Scientific Notation and Significant Figures Flashcards
Scientific notation is great for writing very large or very small numbers
Properly in scientific notation there should only be one digit to the left of the decimal point
Do 472,000
do 0.007349
4.72x10^5
7.349x10^-3
What is the point of significant figures?
Lets us know how precisely we actually know a #
For significant figures say someone ask you how far it was from phenex to portland and you said 3000 miles. Well thats not going to be exact. So we often don’t think of 0’s as signfiicant. So in this case were really only as sure as that first 3, so its kind of +/-999
“actually its like 2700 miles”
* Well now I’ve got signfiicant figures in both the 1000s and the 100s place - so now its more percise +/- 99 miles
“actually its like 2740 miles”
* so now weve got sig figs down to the 10s places, meaning the only ones were not sure about is that last 0 in the 1’s place, meaning were sure +/-9 miles
“actually its 2739.1 miles”
* so down were significant all the way down the 10ths place
* it has 5 significant figures
Significant figures
Rule 1: If number starts off w/ 0’s they’re never significant
* 0.00047 = 2 sig figs - say just putting a couple 0’s infront of a random number like 005400. Well obvisouly those 0’s infront arent signfiicant. Its the same idea here
* significant figures about measured or known persision, not placement
* those 0’s help line up where 47 is on the number line, but they dont tell us anything about how percise the measurement is. They’re just like arrows pointing, not rulers measuring.
Rule 2: numbers ending in 0 when they’re to the left handed side of a decimal = insignficant
* 5400 = 2 sig figs - for same reason as we showed above. Were only sure down to the hunndreds place so it could be +/-99 of this number
* if we really did mean 5400 excatly we could just change to scientific notation 5.400x10^3 and now these 0’s are to the right of the decimal - meaning these numbers are signfiicant meaning we now have our 4 sig figs
Rule 3: If you end a number with 0’s to the right hand side of a decimal, those 0’s are significant
* 2.5400 = 5 sig figs - this is a way of saying we know this number really really well (all the way down to the 1000ths place)
*
Rule 4: 0’s in the middle of the number are always signficiant
* 200.16 = 5 sig figs
Multiplcation w/ Sig figs
2.73 x 6.584 = 18.0 (the zero is signfiicant because its to the right of the decimal)
* 2.73 = 3 sig figs
* 6.584 = 4 sig figs
* use 3 sig figs
Your answer can’t be more percise than your least percise answer - so you use the number w/ the least sig figs and write your answer based off of it
1540 + 327.4 + 0.267
line them up like you did in grade school
Your answer can’t be more percise than your least percise digit. So its the most percise decimal place in the least percise digit
* 1540 = percise to the 10s place
* 327.4 = percise to the 10ths place
* 0.267 = percise to the 1000ths place
Use 1540 - so round full answer to 10s place
1867.7 –> 1870
This actually makes loads of sense, because if you added them without this rule you’d be getting a digit more percise than your least percise. For instance if im using 1540 and get an answer like 1867.7, thats way more percise - which we cant get more percise
Refresher: The fraction bar is a grouping symbol, meaning that its like adding paranthesis around the stuff on the top, then the same w/ the stuff on the bottom. So you’re not breaking PEMDAS because you’re doing the partnehsis first then dividing.
Start by adding
4.23+7.6 = 11.83. However, we round to the 10ths place because the 7.6 is only accurate down to the 10ths place = 11.8 / 0.50
11.8/0.50 = 23.6
* now remember in division its only about the number of sig figs (not the weird addition/subtraction rules)
* numberator = 3 sig figs
* denominator = 2 sig figs (leading 0 not significant, trailing 0 is significant)
= 24
How close to the true value you are
accuracy
How close multiple different independ measurements are to eachother (not to the true value) - essentially relability
Precision
1) accurate and precise
* Has high valdidity and relability
2) precise (not near the right value but are reliable becuase they get the same vlaue over and over)
* very repeatible = very precise
3) Neither accurate or precise
Think about it like this, you could do scientifc notation and get
1.64x10^-3 and would get that same value without even having to know those leading 0’s were there. Those leading 0’s are not signficant = 3 significant digits
Only 2 significant digits
basically saying were sure to the 10000’s place but after that it gets fuzze (could be +/- 1000)
6
entrapped 0’s are always significant
You could also recognize this by writing the number in scientific notation 1.400001x10^3 - showing that you need all those 0’s to get that correct #
Leading 0’s are not signficiant
write the scientific notation 1.70600x10^-3 to realize this
Zeros to the right of the decimal are significant and the zeros in between signficant figures are signficant and therefore 7.200 has a total of 4 significant figures
* you could also write out the scientific notation 7.200x10^2
