I Used to Know That_ Stuff You Forgot From School - Caroline Taggart [19]
Decimal fractions that are less than 1 can be written either 0.25 or just .25—it’s the same thing.
☞ RECURRING DECIMALS
Not everything divides neatly into tens, so sometimes a decimal fraction can be no more than an approximation. For example, ⅓ is 0.333 recurring—no matter how many threes you add, you will never get a decimal that is exactly equal to one third.
If a decimal recurs, you can be certain that it’s the same as some common fraction. For example, 0.222 recurring is ; 0.142857142857142857 recurring is . A recurring decimal is sometimes indicated with a dot above the last digit, which is sort of the equivalent of ellipses (…) or “etc., etc., etc.”
Pi is different (see page 73). Its decimal expansion goes on forever but without recurring, because it isn’t the same as any common fraction. Pi is called a transcendental number, and it’s probably the only one you’ll ever meet.
☞ PERCENTAGES
Percent means by a hundred, so anything expressed as a percentage is a fraction (or part, if you prefer) of 100. So 25 percent is twenty-five parts of 100, or or 0.25. If you’ve been paying attention, you’ll know that this is the same as ¼.
Similarly, 50 percent is , which can be canceled down to , which is , which is ½.
Mean, Median, and Mode
In arithmetical terms, mean is simply a fancy word for average. You calculate a mean by adding a group of numbers together and dividing by the number of numbers. (Strictly speaking, this is the arithmetic mean—there are other sorts of mean, too, but of interest only to mathematicians.) So the mean of 4, 8, 12, and 16 is the total of the four numbers, divided by 4:
4 + 8 + 12 + 16 = 40 divided by 4 = 10.
And it works for any number of numbers. For example, if a class of 11 children gets the following marks on an exam—55, 57, 57, 65, 66, 69, 70, 72, 75, 79, and 83—the total of the marks is 748. Divide that by 11, and you get a mean of 68.
The median of a set of values is literally the middle one. In the set of grades above, it is 69. There are five marks lower than 69 and five marks higher than 69—never mind their actual values. The median of an even number of values is the average of the middle two. For example, the median of 1, 4, 9, 16, 25, and 36 is 12.5—halfway between 9 and 16.
The mode of a set of values is the most common value. The mode of our set of marks is 57, because it is the only one that occurs more than once.
Measurements
Metric units and imperial (or what we will refer to as American) units are two different ways to measure the same things. Just as Fahrenheit and Celsius both measure temperature but in different ways (see page 94), so the metric system and system of American units quantify length, weight, and all sorts of other things, using different units. Metric units are also sometimes called SI units, which stands for Système Internationale.
The metric system calculates in tens or multiples of tens. The system of American units doesn’t, and to the uninitiated it can seem pretty random. (American units used to mean something sensible, such as the foot was the length of a man’s foot and the yard was the distance from his nose to the tip of his outstretched arm.)
☞ LENGTH
In American units length is measured in inches, feet, yards, and miles, and occasionally also in chains and furlongs. There are 12 inches in a foot, 3 feet (36 inches) in a yard, 22 yards in a chain, 10 chains in a furlong, and 8 furlongs (1,760 yards, 5,280 feet) in a mile. Other units are still in use for some special purposes, such as the fathom (6 feet) for measuring the depth of the sea, and the hand (4 inches) for measuring the height of a horse.
The basic unit of length in the metric system is the meter, with subdivisions and multiples for measuring little things and big things. Most commonly used are the millimeter