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These figures may not be significant to you, but they matter to us, okay? Oh, and to Science. They matter a ton to Science.
Chemistry: 2.1 Significant Figures and Scientific Notation 408 Views
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Description:
These figures may not be significant to you, but they matter to us, okay? Oh, and to Science. They matter a ton to Science.
Transcript
- 00:00
sweetie didn't before we get into this video we'd like you to start by writing
- 00:07
down all the digits of pi no writing okay we're getting a couple more things [Man jotting down notes in class]
- 00:12
all right so here's the problem with our request pi has an infinite number of
- 00:16
digits so if you were to actually write out all of its digits you'd never be [Man writing digits and gollum appears]
- 00:20
done fortunately the rule of significant
Full Transcript
- 00:23
figures lets us take a bit of a shortcut and only requires that we write down a [Man takes significant figure shortcut]
- 00:28
certain number of digits spending on a situation if we were performing a
- 00:32
calculation our answer is limited to the number of significant figures or sig [Girl using calculator]
- 00:38
figs as the cool kids column at reset in our unique precise number in other words
- 00:43
if we're multiplying 22.3 and 13.5 we're only going to include one two three sig
- 00:49
figs in our solution the other situation is when we're reading instrumentation in [Scientist reading instrument measurement]
- 00:54
which case the number of sig figs depends on the precision of the
- 00:58
instrument we're using the measure for now let's take a closer look at the
- 01:01
rules for calculation rule number one all nonzero digits are significant so if [Rule number one appears]
- 01:06
you've performed a calculation and your result is 114 write down 114 not 109 110
- 01:12
or no zeroes so smille rounding if you get a number that goes through the tens
- 01:16
place like 114 point 8 you write one 14.8 in this case you'd have four [Hand points to 114.8 number]
- 01:22
significant figures rule number two zeros between nonzero
- 01:27
digits are significant so if you get 104 well you still got three significant [Person shows three fingers]
- 01:32
figures even though one of them is a zero but as long as you've got some form
- 01:36
of a zero sandwich it counts rule number three trailing zeros zeros to the right [Girl takes bite of zero sandwich]
- 01:42
of a decimal point are significant so if your calculation comes out to one
- 01:46
hundred point zero degrees on the button you'd have four significant figures to
- 01:52
deal with all right finally rule number four leading zeros zeros to the left of
- 01:57
the first nonzero digits are not significant so say you come up with an [Boy appears with magnifying glass]
- 02:02
easy peazy number like 0.001 eight well one and the eight are significant the
- 02:10
zeros are not but we can't just write 18 correct
- 02:16
that's not the same thing as 0.0018 oh how right you are scientific notation is
- 02:21
basically just a shorthand way of writing out troublesome numbers in a way [Man writing out numbers in notepad]
- 02:25
that's easy to understand and won't give us carpal tunnel trying to write it for
- 02:30
0.0018 you write the first non-zero number we come across the one and make
- 02:36
it 1.8 times 10 to the negative third because we'd have to move the decimal
- 02:42
point three places to the right in order to get our 1.8 number now if something [Decimal points moves to the right]
- 02:48
had a measurement of zero point zero zero zero zero zero zero 95 - yikes we'd
- 02:54
write it as nine point five two times ten to the negative seventh and so on we
- 03:00
can use the scientific notation for numbers greater than zero - but when we
- 03:03
do the exponent is always positive like five hundred would be five times 10
- 03:09
squared Y squared well because we'd have to move the [Decimal points moves two places to the left]
- 03:13
decimal point two places to the left to get our five five hundred thousand would
- 03:18
be five times ten to the fifth and numbers greater than zero containing
- 03:23
decimals work to one thousand three hundred eighty eight point three would
- 03:27
be one point three eight eight three times ten to the third six point two
- 03:32
would be six point two times ten to the zero power switch is just one so yet the
- 03:37
zero power thing is also what Superman has when wearing a kryptonite necklace [Superman sitting on sofa with kryptonite necklace]
- 03:42
and that's it hopefully now you feel 1 times 10 squared percent smarter than
- 03:46
when we started
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