Читать книгу Physics I For Dummies - Steven Holzner - Страница 31

Physicists have a way of getting their minds into the darndest places, and those places often involve really big or really small numbers. Physics has a way of dealing with very large and very small numbers; to help reduce clutter and make them easier to digest, it uses scientific notation.

In scientific notation, you write a number as a decimal (with only one digit before the decimal point) multiplied by a power of ten. The power of ten (10 with an exponent) expresses the number of zeroes. To get the right power of ten for a vary large number, count all the places in front of the decimal point, from right to left, up to the place just to the right of the first digit (you don’t include the first digit because you leave it in front of the decimal point in the result).

For example, say you’re dealing with the average distance between the sun and Pluto, which is about 5,890,000,000,000 meters. You have a lot of meters on your hands, accompanied by a lot of zeroes. You can write the distance between the sun and Pluto as follows:

The exponent is 12 because you count 12 places between the end of 5,890,000,000,000 (where a decimal would appear in the whole number) and the decimal’s new place after the 5.

Scientific notation also works for very small numbers, such as the one that follows, where the power of ten is negative. You count the number of places, moving left to right, from the decimal point to just after the first nonzero digit (again leaving the result with just one digit in front of the decimal):

If the number you’re working with is larger than ten, you have a positive exponent in scientific notation; if it’s smaller than one, you have a negative exponent. As you can see, handling super large or super small numbers with scientific notation is easier than writing them all out, which is why calculators come with this kind of functionality already built in.

Here’s a simple example: How does the number 1,000 look in scientific notation? You’d like to write 1,000 as 1.0 times ten to a power, but what is the power? You’d have to move the decimal point of 1.0 three places to the right to get 1,000, so the power is three: