How to Represent Numbers in Scientific Notation

TenMarks teaches you how to represent numbers in scientific notation.

How to Represent Numbers in Scientific Notation Now let’s learn about scientific notations. We’ll try two problems. First one, wants us to convert from the standard form or regular number to a scientific notation. Scientific notation is a quick way to represent really large numbers, like this one. What we do is fairly simple. To convert a number from standard form to scientific notation, here’s what we do. We move the decimal spot, the decimal point to after the first digit. So a standard scientific notation is basically a number which is less than (<1) x 10 raised to the power of something. So what we do in order to get there is first move the decimal point which is here, or a whole number, the decimal point is at the end. We move it all the way till after the first digit here. So it’s 7.800000. Second, we count how many places we moved. How many places that we moved? One, two, three, four, five, six, we moved it six places. So what we do is we take 7.8 – remember, anything after the decimal, if it’s got zeros at the end, it can be dropped. 7.8 x 10 raised to 6. If we move six places, we multiply whatever we got times 10, which is the base, raised to the power of 6. Relatively simple. Take the number, move it six decimal places, move the decimal spot, six places to the left to get here, which means I got 7.8 as the first number which is between 1 and 10. Alright, it is between 1 and 10. So 7.8 is the answer, times, how many places that we moved? 10, raise that to the power. 7.8 x 10 raised to the sixth. That’s the value. Let’s do the other way around. Convert from a scientific notation to standard form. This is a scientific notation. First place, between 1 and 10. Second is, 10 to the power of something. Well, two ways of doing it. One, we can use patterns to figure out 10 to the 5, equals 10 x 10 x 10 x 10 x 10, which is a 100,000. I can multiply 9.5 x 100,000 to get 950,000. That’s one way of getting the answer. We break this into standard form and then just multiply. The other way of doing it, is we take 9.5, add a bunch of zeros at the end because it makes more difference anyway. If we are multiplying via a number, which is 10 raised to the power of 5, you move the decimal spot five places to the right. One, two, three, four, five, this is what we raising. What do we get? 95, followed by one, two, three, four zeros. One, two, three, four – 950,000. That’s exactly the same answer as this one. Alright, 950,000 we can do it either way. I personally prefer taking the decimal spot and moving it five spaces to the right because that’s the easiest way to manage it.