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In order to convert a rational number represented as a fraction into decimal form, one may use long division. For example, consider the rational number 5 / 74 : 0.0 675 74 ) 5.00000 4.44 560 518 420 370 500 etc. Observe that at each step we have a remainder; the successive remainders displayed above are 56, 42, 50.
Thus, it is often useful to convert repeating digits into fractions. A conventional way to indicate a repeating decimal is to place a bar (known as a vinculum) over the digits that repeat, for example 0. 789 = 0.789789789.... For repeating patterns that begin immediately after the decimal point, the result of the conversion is the fraction with ...
An irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and −1, when negative numbers are considered). [1]
Drill bit sizes are written as irreducible fractions. So, instead of 78/64 inch, or 1 14/64 inch, the size is noted as 1 7/32 inch. Below is a chart providing the decimal-fraction equivalents that are most relevant to fractional-inch drill bit sizes (that is, 0 to 1 by 64ths).
By {{Convert}} default, the conversion result will be rounded either to precision comparable to that of the input value (the number of digits after the decimal point—or the negative of the number of non-significant zeroes before the point—is increased by one if the conversion is a multiplication by a number between 0.02 and 0.2, remains the ...
In mathematics, "rational" is often used as a noun abbreviating "rational number". The adjective rational sometimes means that the coefficients are rational numbers. For example, a rational point is a point with rational coordinates (i.e., a point whose coordinates are rational numbers); a rational matrix is a matrix of rational numbers; a rational polynomial may be a polynomial with rational ...
Alternatively, one can use digit-conversion tables. The ones provided below can be used to convert any duodecimal number between 0.1 and BB,BBB.B to decimal, or any decimal number between 0.1 and 99,999.9 to duodecimal. To use them, the given number must first be decomposed into a sum of numbers with only one significant digit each. For example:
In the SI system and generally in older metric systems, multiples and fractions of a unit can be described via a prefix on a unit name that implies a decimal (base-10), multiplicative factor. The only exceptions are for the SI-accepted units of time (minute and hour) and angle (degree, arcminute, arcsecond) which, based on ancient convention ...