In astronomy, we often find it useful to define special units. Many textbooks use a variant gram, centimeter, and second "cgs". metric units of the kilogram, meter, and second for mass, length, and time "mks". In physics (including astronomy), the "official" units are the so-called S.I. The centimeter is an exception to this "rule", but is used so commonly that it is included here. The prefixes that are usually used, by tradition, are almost always in multiples of 1000 (kilo-, milli-, micro-). For example, the standard unit of length is the meter, abbreviated "m". It is often useful to use words to describe exponents, and this is a common practice when using metric units. Here, we used another rule of algebra you probably heard about in school: the "commutative property (or rule) of multiplication", a fancy was to say that it doesnt matter what order you multiply two numbers in, the product is the same either way (2x4 = 4x2 = 8). Likewise, we can multiply and divide numbers as long as we follow the rules we discovered before:Ģx10 3 x 4x 0 32 = 2 x 4 x 10 3 x 10 32 = (2x4)x10 3+32 = 8x10 35 We generally write these as was done in this last case, a decimal number between 1 and 10 time the power of 10. Most numbers are not simple multiples of 10, but they still can be expressed using powers-of-10 notation. Thus, when you raise a number to a higher power, the final number can also be expressed in the same way, with the final exponent being equal to the original exponent TIMES that power. This suggests that when dividing two numbers with the same base, the result can be found by subtracting the exponents: What number do you get when you add the two exponents (1 and ≱)? Answer: 0 What is one-tenth of ten (or equivalently ten divided by ten)? Answer: 1 What then? Lets figure it out by taking a specific example: Now, the exponent can also be a negative number.
For ANY values a and b, it is always true that Notice that the exponent "6" is just the sum of the other two exponents "3" and "3"! This, in fact is a basic rule whenever you multiply two numbers with the same "base" (in this case, 10). You should verify these using your calculator.ġ,000,000=10 x 10 x 10 x 10 x 10 x 10 = 10 6 Such numbers can be expressed as a decimal number times 10 raised to some exponent or power. It is often convenient to use scientific notation to work with such numbers. In astronomy, we often deal with very large and very small numbers.
0 kommentar(er)
