How many numbers in scientific notation

If you need a scientific calculator see our resources on scientific calculators. Basic Calculator. Scientific Notation Converter. Operand 1. So we can use standard words such as thousand or million , prefixes such as kilo, mega or the symbol k, M, etc.

Example: 3. Example: 0. Example: it is easier to write and read 1. In general, students have difficulty with two things when dealing with numbers that have more zeros either before OR after the decimal point than they are used to. They often do not understand:.

Scientific notation is a way to assess the order of magnitude and to visually decrease the zeros that the student sees. It also may help students to compare very large or very small numbers But students still have little intuition about scientific notation. Teaching them to recognize that scientific notation is a short hand way to better understand big and small numbers can be useful to them in all aspects of their academic career.

In science, often we work with very large or very small numbers. It seems like a lot of work to keep track of all those zeros. Fortunately, we can easily keep track of zeros and compare the size of numbers with scientific notation. Scientific notation allows us to reduce the number of zeros that we see while still keeping track of them for us.

For example the age of the Earth see above can be written as 4. This means that this number has 9 places after the decimal place - filled with zeros unless a number comes after the decimal when writing scientific notation. Then times 10 to the second, you're going to get We're going to have to add a 0 there, because we have to shift the decimal again. And then 10 to the fourth, you're going to have 74, Notice, I just took this decimal and went 1, 2, 3, 4 spaces.

So this is equal to 74, And when I had 74, and I had to shift the decimal 1 more to the right, I had to throw in a 0 here. I'm multiplying it by Another way to think about it is, I need 10 spaces between the leading digit and the decimal. So right here, I only have 1 space. I'll need 4 spaces, So, 1, 2, 3, 4. Let's do a few more examples, because I think the more examples, the more you'll get what's going on. So I have 1. This is in scientific notation, and I want to just write the numerical value of this.

So when you take something to the negative times 10 to the negative power, you shift the decimal to the left. So this is 1. So if you do it times 10 to the negative 1 power, you'll go 1 to the left. But if you do times 10 to the negative 2 power, you'll go 2 to the left. And you'd have to put a 0 here. And if you do times 10 to the negative 3, you'd go 3 to the left, and you would have to add another 0.

So you take this decimal and go 1, 2, 3 to the left. So our answer would be 0. And another way to check that you got the right answer is if you have a 1 right here, if you count the 1, 1 including the 0's to the right of the decimal should be the same as the negative exponent here.

So you have 1, 2, 3 numbers behind the decimal. That's the same thing as to the negative 3 power. You're doing 1,th, so this is 1,th right there.

Actually let's mix it up. Let's start with something that's written as a numeral and then write it in scientific notation. So let's say I have , So that's just its numerical value, and I want to write it in scientific notation. So this I can write as-- I take the leading digit-- 1. And if you want to internalize why that makes sense, 10 to the fifth is 10, So it's 1. You have five 0's. That's 10 to the fifth.