2008-03-07 Science For All Americans 第9章 ”数学世界”



Fractions are numbers we use to stand for a part of something or to compare two quantities. One common kind of comparison occurs when some magnitude such as length or weight is measured―that is, is compared to a standard unit such as a meter or a pound. Two kinds of symbols are widely used to stand for fractions, but they are numerically equivalent. For example, the ordinary fraction 3/4 and the decimal fraction 0.75 both represent the same number. Used to represent measured magnitudes, however, the two expressions may have somewhat different implications: 3/4 could be used to simply mean closer to 3/4 than to 2/4 or 4/4, whereas 0.75 may imply being closer to 0.75 than to 0.74 or 0.76―a much more precise specification. Whole numbers and fractions can be used together: 1 1/4, 1.25, 125/100, and 5/4, for instance, all mean the same thing numerically.


More flexibility in mathematics is provided by the use of negative numbers, which can be thought of in terms of a number line. A number line lays consecutive numbers at equal intervals along a straight line centered on zero. The numbers on one side of zero are called positive, and those on the other side, negative. If the numbers to the right of zero are positive, the numbers to the left of zero are negative; if distance above sea level is positive, distance below sea level is negative; if income is positive, debt is negative. If 2:15 is the scheduled time of lift-off, 2:10 is "minus 5 minutes." The complete range of numbers―positive, zero, and negative―allows any number to be subtracted from any other and still give an answer.


分数は,何かの部分を表すために,もしくは二つの量を比較するために用いられる数である.よくある比較は,長さや重さのような数量を計るときになされる―すなわち,メートルやポンドのような標準の単位量との比較である.分数を表すのには二種類の記号が広く用いられているが,それらは数値的には等価である.たとえば,通常の分数 3/4 と十進法の小数 0.75 は共に同じ数を表す.しかし,計測された数量を表す際には,この二つの表現は少々異なったものを意味することとなる:計測値 3/4 は2/4よりも4/4よりも単に3/4により近いことを示すために用いられるのに対し,計測値0.75は0.74より0.76よりも0.75に近いことを暗に意味している―より正確な特定を行っていることとなる.整数と分数は併せて使われうる.例えば1 1/4, 1.25, 125/100, そして 5/4のようなものである.これらは数値的にはすべて等しい.







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