I Used to Know That_ Stuff You Forgot From School - Caroline Taggart [20]
To convert between the two:
• 1 inch = 2.54 centimeters, so to convert inches to centimeters, multiply by 2.54. To convert centimeters to inches, divide by 2.54. Remember that a centimeter is shorter than an inch, so you should have a larger number of centimeters.
• 1 yard = 0.91 meters; 1 meter = 1.09 yards, or 3.3 feet. Yards and feet are shorter than meters, so you will have a larger number of them.
• 1 mile = 1.6 kilometers; 1 kilometer = 0.625 (⅝) of a mile. This time the metric unit is smaller, so you have more kilometers than miles.
• A nautical mile is about 1.15 miles, or exactly 1,852 meters.
☞ WEIGHT
In American units weight is measured in ounces, pounds, a hundredweight (short), and tons: 16 ounces (oz.) = 1 pound (lb., from libra, Latin for pound); 100 pounds = 1 hundredweight (short); 200 hundredweight (2,000 lb.) = 1 ton. This is sometimes called a short ton, because the imperial system in the U.K. uses a long ton of 2,240 lb. And they also use a measurement of stones (14 pounds = 1 stone).
In the metric system weight is measured in grams or kilograms. (You can have milligrams and centigrams, but a gram is already pretty small, so unless you’re a pharmacist or something of that sort, you don’t often need them.) A kilogram is 1,000 grams.
• 1 gram (or g) = about 0.0353 ounce, so to convert grams to ounces, multiply the number of grams by .0353. To convert ounces to grams, divide by .0353.
• 1 kilogram (or kilo or kg) is about 2.2 pounds, so multiply kilograms by 2.2, divide pounds by 2.2.
• A metric ton is 1,000 kilograms, or 2,205 pounds, just a bit more than an American ton.
☞ VOLUME
In the American system volume is measured in fluid ounces, pints, quarts, and gallons; in the metric system it is measured in liters. This becomes even more complicated because the value of the units in the United States differs from the imperial system in the U.K.
In the United States 16 fluid ounces make a pint. But the U.S. pint and gallon are smaller than the U.K. ones. To convert U.S. pints to liters, divide by 2.1.
In the U.K. 20 imperial fluid ounces make 1 imperial pint, 2 imperial pints make 1 imperial quart, and there are 4 quarts (8 pints) in an imperial gallon. A liter is about 1.75 pints, so to convert imperial pints to liters, divide by 1.75; to convert liters to imperial pints, multiply by 1.75 (pints are smaller, so you will have more of them).
Algebra and Equations
Algebra is the branch of math that uses symbols (normally letters of the alphabet) to represent unknown numbers, along the lines of a + b = 5. If you assign a value to a, you can calculate b: If a = 2, then b = 3. This is known as an algebraic equation.
The main thing to remember when solving equations is that one side of the = sign is equal to the other side, so anything that you do to one side, you need to do to the other.2
For example, to solve the equation
3a + 1 = 16 - 2a,
you first add 2a to each side, giving:
5a + 1 = 16.
Then subtract 1 from each side, giving
5a = 15.
Now you can divide both sides by 5 and announce proudly that a = 3.
☞ SIMULTANEOUS EQUATIONS
A simultaneous equation is a more complicated form of algebraic equation, in which you have two or more unknowns. The general rule is that you must have exactly the same number of equations as you have unknowns in order to find the value of each. If you have fewer equations, there will be lots of solutions and no way to choose between them. If you have too many equations, there will be no solution at all.
This assumes that the equations are all different and don’t contradict each other. For example:
a + b = 6,
2a + 2b = 12
are no good as a pair of simultaneous equations, because they both say exactly the same thing, while:
a + b = 6,
a + b = 7
will not work either, because there’s no way both of them can be true at the same time.
Here’s a look at a better-behaved set of simultaneous