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In decimal numbers greater than 1 (such as 3.75), the fractional part of the number is expressed by the digits to the right of the separator (with a value of 0.75 in this case). 3.75 can be written either as an improper fraction, 375 / 100 , or as a mixed number, 3 + 75 / 100 .
In the second step, they were divided by 3. The final result, 4 / 3 , is an irreducible fraction because 4 and 3 have no common factors other than 1. The original fraction could have also been reduced in a single step by using the greatest common divisor of 90 and 120, which is 30.
These include improper fractions as well as mixed numbers. Continued fraction: An expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on.
Thus, a measurement of time such as 3:23:17 (3 hours, 23 minutes, and 17 seconds) can be interpreted as a whole sexagesimal number (no sexagesimal point), meaning 3 × 60 2 + 23 × 60 1 + 17 × 60 0 seconds. However, each of the three sexagesimal digits in this number (3, 23, and 17) is written using the decimal system.
A simple fraction contains no fraction either in its numerator or its denominator. A fraction is in lowest terms if the only factor common to the numerator and the denominator is 1. An expression which is not in fractional form is an integral expression. An integral expression can always be written in fractional form by giving it the denominator 1.
[39] [40] The factorial number system is a mixed radix notation for numbers in which the place values of each digit are factorials. [41] Factorials are used extensively in probability theory, for instance in the Poisson distribution [42] and in the probabilities of random permutations. [43]
The simplified equation is not entirely equivalent to the original. For when we substitute y = 0 and z = 0 in the last equation, both sides simplify to 0, so we get 0 = 0 , a mathematical truth. But the same substitution applied to the original equation results in x /6 + 0/0 = 1 , which is mathematically meaningless .
Every terminating decimal representation can be written as a decimal fraction, a fraction whose denominator is a power of 10 (e.g. 1.585 = 1585 / 1000 ); it may also be written as a ratio of the form k / 2 n ·5 m (e.g. 1.585 = 317 / 2 3 ·5 2 ).