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approximately questions

by salina

what do they mean approximately times this by this?

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Dec 29, 2010
Approximate Values
by: Staff

The question:

by Salina
(London, England)

The question:

what do they mean approximately times this by this?

The answer:

This is an excellent question. Approximation has a number of important uses in math.

A value which is APPROXIMATE is an INEXACT value which is close to the real value. Approximations are estimates.

Approximations are often used when an exact number cannot be computed because not enough information is available.

Approximations are also used to simplify a math problem. An approximation can often reduce the complexity of a problem, but still provide a reasonably accurate solution.

RANGE OF VALUES: An approximation is often given as a range of values.

A RANGE of values which approximates the exact value is used in every area of life. How much will lunch cost? Somewhere between £85 and £110 at one of the high end restaurants; or, £7 and £15 at the pub down the street. How much is your house worth? How much is your car repair? . . . and so on.

ROUNDING VALUES: A number is often approximated by rounding it to a certain number of decimal points.

For example, the square root of 2 = 1.4142135623730950488016887242097 (and so on). However, you can never compute an exact value for the square root of 2 because it is an irrational number. 1.4142135623730950488016887242097 is an approximation. You have no choice. You must use an approximation for the square root of 2.

In addition, it is not necessary to use 31 decimal points for most problems. The square root of 2 is usually rounded to something like 2.1414. The rounded number is another approximation.

A great deal of time in school is spent training students how approximate numbers by rounding them.

SIMPLIFY MATH PROBLEMS: Approximations are used to simplify formulas.

For example, if you are on the deck of a ship, how far can you see in clear weather? This is called the distance to the horizon.

There is a formula for calculating this distance.

• d = distance to the horizon
• D = diameter of the Earth
• h = height of the observer above sea level
• R = radius of the Earth

d = sqrt[h(D+h)]

Using an approximation, this formula can be reduced to the following:

d = 3.6 * sqrt(h)

d is the distance to the horizon (in kilometers)
h is the height above sea level (in meters)

Using the approximate formula, an officer standing on the deck of a ship can estimate the distance to the horizon in his head with very little effort.

STATISTICS: How close is the answer?

As an example, consider polls of likely voters taken prior to an election.

Suppose 56.5 % of likely voters favor candidate A + or – 3%. This is an APPROXIMATION which means that the real number of voters which favor candidate A is somewhere between 53.5% and 59.5% (a RANGE of POSSIBLE VALUES).

Thanks for writing.


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