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home / primary math / number / approximate number
An approximate number is a number that is close but not exactly equal to another number. It is the counterpart to exact numbers. There is no uncertainty in an exact number, while the definition of an approximate number is one in which uncertainty exists.
One way to think of approximate numbers is as numbers that arise through measurement or calculation. An exact number on the other hand, can be thought of as one that arises from counting. For example, there are 4 clovers on a four-leaf clover. 4 is an exact number. If the leaf of a four-leaf clover measured 7 cm, the 7 cm is an approximate number. This is because the measured length, while closer to 7 cm than it is to 7.1 cm or 7.2 cm, is still only an approximate measure. There is no way to exactly measure the length of the leaf. With highly precise tools, the measured value can be very close to the exact value, but we can never be certain that the measured value is exact.
Example
Chad saw a sign at the grocery store that stated: 3 candy bars for $1.00. At this rate, what was the cost of each candy bar?
$1.00 ÷ 3 = 0.3, where the line over the 3 indicates that it repeats indefinitely. This means that the real value is somewhere between $0.33 and $0.34, since 0.3 cannot be expressed exactly in decimals. Both $0.33 and $0.34 are approximate numbers for the exact cost of each bar. It is not possible to charge Chad $0.3, so instead we could say that he was charged $0.33 for two candy bars, and $0.34 for the third candy bar.
Rounding
There are many different ways to round numbers. Rounding to an integer, as we did above, is the most common.
Rounding down to an integer
Rounding down to an integer is referred to as taking the floor, which means rounding towards negative infinity.
Half values are rounded towards negative infinity.
Rounding up to an integer
Rounding up to an integer is referred to as taking the ceiling which means rounding towards positive infinity.
Half values are rounded towards infinity.
Rounding towards zero
Rounding towards zero is referred to as truncating, which means rounding away from infinity.
Half values are rounded away from infinity.
Rounding away from zero
Rounding away from zero means rounding towards infinity.
Half values are rounded towards infinity.
There are also other rounding methods, but these are some of the most common.
Approximate Value is the metric which is an estimate of a player’s value, making no fine distinctions, but, rather, distinguishing easily between very good seasons, average seasons, and poor seasons.
Alternative method shall be assigned according to the following rules shown here
Before the ’73-74 season, steals, blocks and turnovers weren’t kept as official stats. In the credits formula, those stats are just omitted as they tend to cancel each other out to some degree when included anyway.
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In mathematics, making an approximation is the act or process of finding a number acceptably close to an exact value; that number is then called an approximation or approximate value. Approximating has always been an important process in the experimental sciences and engineering, in part because it is impossible to make perfectly accurate measurements. Approximation also arises because some numbers can never be expressed completely in decimal notation. In these cases approximations are used. For example, irrational numbers, such as pi (π), are nonterminating, nonrepeating decimals. Every irrational number can be approximated by a rational number, simply by truncating it. Thus, π can be approximated by 3.14, or 3.1416, or 3.141593, and so on, until the desired accuracy is obtained.
Another application of the approximation process occurs in iterative procedures. Iteration is the process of solving equations by finding an approximate solution, then using that approximation to find successively better approximations, until a solution of adequate accuracy is found. Iterative methods, or formulas, exist for finding square roots, solving higher order polynomial equations, solving differential equations, and evaluating integrals.
The limiting process of making successively better approximations is also an important ingredient in defining some very important operations in mathematics. For instance, both the derivative and the definite integral come about as natural extensions of the approximation process. The derivative arises from the process of approximating the instantaneous rate of change of a curve by using short line segments. The shorter the segment the more accurate the approximation, until, in the limit that the length approaches zero, an exact value is reached. Similarly, the definite integral is the result of approximating the area under a curve using a series of rectangles. As the number of rectangles increases, the area of each rectangle decreases, and the sum of the areas becomes a better approximation of the total area under investigation. As in the case of the derivative, in the limit that the area of each rectangle approaches zero, the sum becomes an exact result.
Every function can be expressed as a series, the indicated sum of an infinite sequence. For instance, the sine function is equal to the sum: sin(x) = x — x3/3! + x5/5! — x7/7!+.... In this series the symbol (!) is read "factorial" and means to take the product of all positive integers up to and including the number preceding the symbol (3! = 1 × 2 × 3, and so on). Thus, the value of the sine function for any value of x can be approximated by keeping as many terms in the series as required to obtain the desired degree of accuracy. With the growing popularity of digital computers, the use of approximating procedures has become increasingly important. In fact, series like this one for the sine function are often the basis upon which handheld scientific calculators operate.
An approximation is often indicated by showing the limits within which the actual value will fall, such as 25 ± 3, which means the actual value is in the interval from 22 to 28. Scientific notation is used to show the degree of approximation also. For example, 1.5 × 106 means that the approximation 1,500,000 has been measured to the nearest hundred thousand; the actual value is between 1,450,000 and 1,550,000. But 1.500 × 106 means 1,500,000 measured to the nearest thousand. The true value is between 1,499,500 and 1,500,500.
Synonym of approximation.
An approximate value by defect of a number is a value that is close to this number, less than it, as close as possible, and with a requested level of precision.
- The number 3.1415 is an approximate value by defect of the number π.
An approximate value by excess of a number is a value that is close to this number, greater than it, as close as possible, and with a requested level of precision.
- The number 3.1416 is an approximate value by excess of the number π.