decimal expansion formula
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Numbers Without End
Sometimes in math it can feel like the numbers we see go on and on without any real pattern. And sometimes, that's indeed the case. However, more often, those numbers do end up either terminating or forever repeating.
When we express a number as a decimal, it is called decimal expansion. Decimal expansion is the form of a number that has a decimal point, either actual or implied. Examples of numbers with actual decimal points are 10.2 and 0.0084. An example of a number with implied decimal points is the whole number 17, which could actually be written as 17.000000000000. We often leave off the repeating zeros for ease of reading and figuring.
Decimals either terminate or repeat, which is a characteristic of rational numbers. When we use the term rational in math, we're not talking about a number that makes logical sense. Rational numbers can either be written as a fraction of two whole numbers or a ratio.
Finite and Repeating Decimals
Rational decimals that end with repeating zeroes are known as finite decimals, like 6/3 = 2 or 10/2.5 = 4. They're the opposite of infinite or forever. Rational decimals that are finite are those that originate from a fraction with a denominator that is a product of 2, 5, or both. For example, 3/8, 13/25, and 7/50 are all finite decimals because:
Sometimes in math it can feel like the numbers we see go on and on without any real pattern. And sometimes, that's indeed the case. However, more often, those numbers do end up either terminating or forever repeating.
When we express a number as a decimal, it is called decimal expansion. Decimal expansion is the form of a number that has a decimal point, either actual or implied. Examples of numbers with actual decimal points are 10.2 and 0.0084. An example of a number with implied decimal points is the whole number 17, which could actually be written as 17.000000000000. We often leave off the repeating zeros for ease of reading and figuring.
Decimals either terminate or repeat, which is a characteristic of rational numbers. When we use the term rational in math, we're not talking about a number that makes logical sense. Rational numbers can either be written as a fraction of two whole numbers or a ratio.
Finite and Repeating Decimals
Rational decimals that end with repeating zeroes are known as finite decimals, like 6/3 = 2 or 10/2.5 = 4. They're the opposite of infinite or forever. Rational decimals that are finite are those that originate from a fraction with a denominator that is a product of 2, 5, or both. For example, 3/8, 13/25, and 7/50 are all finite decimals because:
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