To change a number from standard notation to scientific notation, move the decimal so that all the 0s are to the right of the decimal. Another way to think about it is to move the decimal so that there is only one non-zero digit to the left of the decimal. Count the number of places that you moved the decimal. This number tells you what factor of ten you must multiply the "new" number by in order to get the original number in standard notation. The number of spaces that you moved the decimal will tell you what is the exponent of 10. If you moved the decimal to the left, the exponent will be positive. If you moved the decimal to the right, the number will be negative.
Here we’re given a bunch of numbers that have lots of zeros and we’re asked to write them in scientific notation. So I’m going to start with this problem thinking about where my decimal place is. I’m going to count how many times I’m multiplying by moving it to the left; 1, 2, 3, 3, 4, 5, 6, 7, that means I’m going to have 1.56 times 10 to the 7th.
This number is the same thing as 1.67 times 1 with 7 zeros behind it. That’s how it got to be so big. Here I’m doing the process backwards. My decimal point is moving to the right. There we go. I’m going to stop so that I have an A value that’s between 1 and 10. So I moved 1, 2, 3, 4, 5 places so my answer will be 5.3 times 10 to the negative, because I moved in the right direction, negative how much was it? 1, 2, 3, 4, 5; 10 to the negative 5th exponent.
This last one is really similar, I want to move over my decimal place until I get an A value that’s between 1 and 10 so it will look like 5. Sometimes people like to write it as 5.0 times 10 to the negative 5th. I personally prefer scientific notation to these kinds of numbers where you have to write lots and lots of zeros. I think this is a lot easier and shorter than this whole stuff and the nice thing about it is that these are equivalent statements in Math and Science classes. So anytime you write this your reader will know that you actually meant this number.
One other thing that I wanted to point out to you is that sometimes students look at this and say why don’t you just round that? That’s like zero. Well we have to get really precise especially when we are moving into the time of like nanotechnology and numbers that are really, really small or thinking about world populations and national debts that are in the trillions of dollars, like really, really big. Scientific notation lets you be precise without having to write these long, long, long numbers.
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