These figures may not be significant to you, but they matter to us, okay? Oh, and to Science. They matter a ton to Science.

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Science | Chemistry |

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

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

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

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

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

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

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

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

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

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

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

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

significant figures rule number two zeros between nonzero

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

when we started