so today we're going to discuss scientific notation your learning objectives are to be able to write a number in standard notation and translate that into scientific notation you'll also learn how to convert a number written in scientific notation to standard notation scientists require the use of scientific notion notation we use scientific notation to help us write numbers without all the zeros for example look at the number of atoms in 12 grams of carbon that's a very large number we need a way to avoid writing all the zeros so we use scientific notation to exceed writing so many zeros let's talk about how to read scientific notation we use the capital n times 10 to the lowercase n or our exponent where capital n is a number between 1 and 10 and lowercase n is a positive or negative integer going back to the number of atoms in 12 grams of carbon instead of writing all dov'è zeros we move the decimal place to the left by counting all of these zeros 1 2 3 4 5 all the way past the 2 so the decimal is in between the 6 and the 0 so we counted 23 digits here so our exponent will be positive 23 so we would write our number as 6.022 times 10 to the 23rd or we could also write a really small number by moving the decimal to the right by Counting all these zeroes and past the first non-zero digit and if we did that for the mass of a single carbon atom we count up to 23 so we would write 1.99 times 10 to the negative 23 so we have to put a negative there because the number is smaller than 1 let's take a look for example the number 568 point 7 to 6 let's say we want to write this number in scientific notation the first thing we're gonna do is move the decimal to the left so that we have one number in front of the decimal so we write five point six eight seven six two now we move the decimal two spaces to the left so we know that our exponent exponent is going to be positive so writing it all out we write five point six eight seven six two times ten to the two let's do an example where we have a number less than one in this case we want to move the decimal to the right until we pass the first nonzero number you're going to move one two three four five and six spaces to the right now because we are moving the decimal to the right our exponent is going to be negative six so this number here is written in scientific notation is seven point two two times ten to the negative six make sure the negative is in there otherwise you're stating a completely different quantity now let's go over how to write common notation from scientific notation take for example eight point seven six two times ten to the four this number is larger than zero so in this case we're going to need to move the decimal to the right so let's move that on over one two three four spots because our exponent is 4 so our answer is eighty-seven thousand six hundred and twenty this try another example let's say we have a number less than one here we have three point O two times ten to the negative six we need to move the decimal place to the left six spaces because our exponent is negative six let's count it out one two three four five six so our answer is zero point zero zero zero zero zero three zero two our own express each of the following numbers in scientific notation on the left hand side and on the right hand side of the slide express each of the following numbers in standard notation or common notation