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Representations of Numbers

Primarily, when numbers are used for data purposes, they are represented in three ways. The three representations discussed here – fractions, decimals, and percents – are similar in that they are all used to indicate parts of a whole.

Fractions are composed of two numbers, a numerator and a denominator. Generally, fractions are used to represent a portion of a whole, like ¾ of a pie. The denominator represents the total of the considered set (four slices equals a whole pie), and the numerator represents the quantity of the set considered (three slices eaten). For example, Barry Bonds had 373 at bats in the 2004 baseball season, and managed 135 hits. This information can be represented as a fraction – 135/373.

Decimals, like fractions, represent number quantities between whole integers (quantites less than one), indicated by numbers to the right of a period. By dividing Barry Bond's total at bats by number of hits, we can establish that 135/373 is equal to about .362. Major League Baseball usually expressed batting expressing batting average as a decimal> so that total number of hits and at-bats are both taken into consideration.

Percents are taken directly from either fractions or decimals. Percent means ‘out of one hundred’ in Latin, and, accordingly, is a representation of a portion of a whole when the whole is adjusted to one hundred. Percents are the numerator when a fraction is adjusted to have a denominator of 100. Continuing the Barry Bonds example, 135/373 hits, when mathematically adjusted to be a fraction> with a denominator of 100, is very, very close to 36/100. Therefore, Barry Bonds gets a hit in 36% of his at-bats.

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