Here, there are 6 zeros placed after 1 because the power of 10 is 6. When the power is positive, 10 x = '1 followed by x number of zeros'.įor example, 10 6 = 1,000,000.By using these two examples, we can conclude two things that are very useful to calculate the powers of 10. If x is negative, then we apply the property of exponents, a -m = 1/a m and then we apply the same logic as explained earlier. If x is positive, we simplify 10 x by multiplying 10 by itself x times. The powers of 10 are of the form 10 x, where x is an integer. This means that we need to multiply 10 seven times, that is, 10 7 = 10 × 10 × 10 × 10 × 10 × 10 × 10 For example, 10 to the 7th power means 10 7.
Now, let us try to understand it the other way round. Here, 10 is the base and 9 is the power and this is read as 10 to the ninth power. Therefore, exponents help to express this easily and this value (10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 1000000000) can be expressed as 10 9. Now, if we need to multiply 10 thirty times, it would be even more difficult to write the product with so many zeros. If we multiply 10 a couple of times it becomes difficult to write the number as in this case, 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 1000000000. These numbers which are written as exponents are the powers of 10. Here is a number line with the two prefixes in problem sixteen marked:Ĭompute the absolute, exponential distance between two given prefixes:The powers of 10 means when 10 is multiplied a certain number of times, the product can be expressed using exponents. Repeat: you will use the proper exponential value (like 10 5) in a solution to a problem you will NEVER use just the exponent (the 5) in a solution.
Power of ten for prefixes how to#
The 5 is only used in descriptions about how to determine the distance. In other words, 10 5 is used in the solution to the problem the 5 by itself will never be used. In the problems to follow, the exponential form will be the one used. Done as an exponent, the absolute exponential distance between kilo- and centi- is 10 5. The absolute exponential distance between 3 and -2 is 5, not 1. For example, someone might mentally do the distance between kilo and centi by comparing the exponents of positive 3 and negative 2 and getting one. What you should do is compare the two exponents as if they were placed on a number line made of exponents and the compute the absolute exponential distance between them. The distance between kilo and centi is 10 5. For example, the absolute distance between milli and centi is 10 1. The skill I'm talking about is figuring out the absolute, exponential distance between two prefixes. It is an important skill that goes somewhat untaught, so I've decided to address it. It seems that everybody just assumes students pick it up somewhere in a math class. The reason is that this particular skill isn't really mentioned by chemistry (or physics) teachers. This next set of problems deserves some comment. Problems concerning the exponential distance between two prefixes This makes it a prime target for teachers to test.
Given either the name or the symbol of the prefix, give the other:Ī word to the wise: deca- (symbol = da) is a little used unit prefix. Here are only some possible problems (of many): Problems could give any one and ask for one or both of the others.
There are three items - name, symbol, and size - that must be known. Notice anything? And, no, I did not copy them. For example, centigram means we are count in steps of one one-hundredth of a gram, μg means we count by millionths of a gram.įor another presentation of these prefixes, please go here. These skills will be necessary in order to correctly convert one metric unit to another.Ī metric prefix is a modifier on the root word and it tells us the unit of measure. Note for the future: you will need to determine which of two prefixes represents a bigger amount AND you will also need to determine the exponential "distance" between two prefixes. There is even someone selling an e-book for metric prefix flashcards. Here is a search for metric prefix flashcards. In order to properly convert from one metric unit to another, you must have the prefixes memorized. A brief discussion of the basic metric units.
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