Basic Algebra and Geometry Made a Bit Easier Lesson Plans:
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Lesson 93: Scientific Notation
This lesson introduces an easy concept which usually comes up at least once on every math test. It's useful when you need to describe very large numbers.
In math, there is often a need to write very large numbers. The most common example is when we need to describe very large distances in space. For example, Alpha Centauri is the closest star to our solar system. It is 25,800,000,000,000 miles away. That's 25.8 trillion miles. Large numbers like that can be cumbersome to work with. What we really want is just a general idea of how far away it is, relative to other stars, for example.
We can represent this number in scientific notation as 2.58 x 1013 miles. What that means is that we start with the number 2.58, and we move the decimal point 13 spaces to the right, adding as many zeroes as we need to. In real life we probably wouldn't actually do that, but seeing the number in scientific notation would give us an idea of how large it is.
For example, if we had another number multiplied by 1015, we would know that it is 100 times bigger. Each additional power multiplies the number by 10. We could say that the number is two orders of magnitude greater. Again, this is important to scientists who frequently work with such very large numbers.
Scientific notation can also be used for very small numbers. This is useful for scientists who work with very small distances, such as the size of cells, which of course could only be seen under a microscope. Such an object might measure 7.6 x 10-18 meters. The negative exponent tells us to take the decimal point, and move it that many places to the left, adding as many zeroes as we need.
In scientific notation, we always use a number which is greater than or equal to 1, but less than 10. It may have a decimal component to it. We multiply it by a power of 10, either positive or negative, to tell us how many places to move the decimal point left or right.
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