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sweetie didn't before we get into this video we'd like you to start by writing

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down all the digits of pi no writing okay we're getting a couple more things [Man jotting down notes in class]

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all right so here's the problem with our request pi has an infinite number of

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digits so if you were to actually write out all of its digits you'd never be [Man writing digits and gollum appears]

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done fortunately the rule of significant

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figures lets us take a bit of a shortcut and only requires that we write down a [Man takes significant figure shortcut]

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certain number of digits spending on a situation if we were performing a

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calculation our answer is limited to the number of significant figures or sig [Girl using calculator]

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figs as the cool kids column at reset in our unique precise number in other words

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if we're multiplying 22.3 and 13.5 we're only going to include one two three sig

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figs in our solution the other situation is when we're reading instrumentation in [Scientist reading instrument measurement]

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which case the number of sig figs depends on the precision of the

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instrument we're using the measure for now let's take a closer look at the

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rules for calculation rule number one all nonzero digits are significant so if [Rule number one appears]

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you've performed a calculation and your result is 114 write down 114 not 109 110

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or no zeroes so smille rounding if you get a number that goes through the tens

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place like 114 point 8 you write one 14.8 in this case you'd have four [Hand points to 114.8 number]

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significant figures rule number two zeros between nonzero

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digits are significant so if you get 104 well you still got three significant [Person shows three fingers]

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figures even though one of them is a zero but as long as you've got some form

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of a zero sandwich it counts rule number three trailing zeros zeros to the right [Girl takes bite of zero sandwich]

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of a decimal point are significant so if your calculation comes out to one

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hundred point zero degrees on the button you'd have four significant figures to

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deal with all right finally rule number four leading zeros zeros to the left of

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the first nonzero digits are not significant so say you come up with an [Boy appears with magnifying glass]

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easy peazy number like 0.001 eight well one and the eight are significant the

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zeros are not but we can't just write 18 correct

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that's not the same thing as 0.0018 oh how right you are scientific notation is

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basically just a shorthand way of writing out troublesome numbers in a way [Man writing out numbers in notepad]

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that's easy to understand and won't give us carpal tunnel trying to write it for

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0.0018 you write the first non-zero number we come across the one and make

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it 1.8 times 10 to the negative third because we'd have to move the decimal

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point three places to the right in order to get our 1.8 number now if something [Decimal points moves to the right]

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had a measurement of zero point zero zero zero zero zero zero 95 - yikes we'd

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write it as nine point five two times ten to the negative seventh and so on we

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can use the scientific notation for numbers greater than zero - but when we

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do the exponent is always positive like five hundred would be five times 10

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squared Y squared well because we'd have to move the [Decimal points moves two places to the left]

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decimal point two places to the left to get our five five hundred thousand would

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be five times ten to the fifth and numbers greater than zero containing

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decimals work to one thousand three hundred eighty eight point three would

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be one point three eight eight three times ten to the third six point two

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would be six point two times ten to the zero power switch is just one so yet the

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zero power thing is also what Superman has when wearing a kryptonite necklace [Superman sitting on sofa with kryptonite necklace]

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and that's it hopefully now you feel 1 times 10 squared percent smarter than

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when we started

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