Using Scientific Notation
Using Scientific Notation Geo Labs Gioppo 2012 ©
Introduction
We use scientific notation to make it more convenient to write out very large, or very small numbers. It also helps us avoid making mistakes when writing the numbers, like having one too many (or too less) zeros. Think of it as a short hand system –that happens to be based on powers of ten. You’ve done this before in school, remember 101 = 10, 102 = 100 103 = 1000, etc.? This is the same idea, we just write it a little differently: 101 is written 1x101, 102 is written 1x102, & so on. Once you learn it, it really is simpler.
As an example, the mass of the Earth is roughly 5,980,000,000,000,000,000,000,000 kilograms ... that’s a lot of zeroes ! But if we use scientific notation we can write the earth’s mass like this: 5.98 x 1024 kg. Isn’t that a lot easier to read & to write?
How To Do It
For a number greater than one, you move the decimal point to the left (if there isn’t one, assume it’s at the end) as far as you can go, then count the number of places it moved. For example, 10,000 = 1x104. Not to confuse things, but this can also be written as 10x103. Now, let’s go the other way with a number less than one. 0.0001 = 1x10-4. Again, we’re moving the decimal over as far as it can go, but since we’re moving it to the right, you’ll need to add that negative sign. It’s important to note here, that this is not a negative number, as in it’s not less than zero. The negative sign just implies that it’s a number smaller than one.
Now, I keep saying move the decimal over as far as you can go … well, how far is that ? Sometimes its obvious, sometimes its not. Let’s take the example above where we discuss the mass of the earth. We bring the decimal over to between the last two numbers, but keep the decimal points out to three digits. You’re probably wondering if you could have stopped at the eight ? Yes, but we typically don’t . So, even though you could write it 598 x
Introduction
We use scientific notation to make it more convenient to write out very large, or very small numbers. It also helps us avoid making mistakes when writing the numbers, like having one too many (or too less) zeros. Think of it as a short hand system –that happens to be based on powers of ten. You’ve done this before in school, remember 101 = 10, 102 = 100 103 = 1000, etc.? This is the same idea, we just write it a little differently: 101 is written 1x101, 102 is written 1x102, & so on. Once you learn it, it really is simpler.
As an example, the mass of the Earth is roughly 5,980,000,000,000,000,000,000,000 kilograms ... that’s a lot of zeroes ! But if we use scientific notation we can write the earth’s mass like this: 5.98 x 1024 kg. Isn’t that a lot easier to read & to write?
How To Do It
For a number greater than one, you move the decimal point to the left (if there isn’t one, assume it’s at the end) as far as you can go, then count the number of places it moved. For example, 10,000 = 1x104. Not to confuse things, but this can also be written as 10x103. Now, let’s go the other way with a number less than one. 0.0001 = 1x10-4. Again, we’re moving the decimal over as far as it can go, but since we’re moving it to the right, you’ll need to add that negative sign. It’s important to note here, that this is not a negative number, as in it’s not less than zero. The negative sign just implies that it’s a number smaller than one.
Now, I keep saying move the decimal over as far as you can go … well, how far is that ? Sometimes its obvious, sometimes its not. Let’s take the example above where we discuss the mass of the earth. We bring the decimal over to between the last two numbers, but keep the decimal points out to three digits. You’re probably wondering if you could have stopped at the eight ? Yes, but we typically don’t . So, even though you could write it 598 x