Can a repeating decimal be a fraction? Can a terminating decimal be a fraction?

Accepted Solution

Answer:Can a repeating decimal be a fraction: Converting repeating decimals to fractions. Every repeating decimal can be written as a fraction. A quick trick for converting a repeating decimal is to place the repeating numbers in the numerator of a fraction over the same number of 9s, and then reduce if necessary.Can a terminating decimal be a fraction: A terminating decimal can be written as a fraction simply by writing it the way you say it: 3.75 = three and seventy-five hundredths = , then adding if needed to produce a fraction: . So, any terminating decimal is a rational number.Step-by-step explanation:Can a repeating decimal be a fraction: A repeating or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely repeated portion is not zero. It can be shown that a number is rational if and only if its decimal representation is repeating or terminating (i.e. all except finitely many digits are zero). For example, the decimal representation of 1/3 becomes periodic just after the decimal point, repeating the single digit "3" forever, i.e. 0.333.... A more complicated example is 3227/555, whose decimal becomes periodic at the second digit following the decimal point and then repeats the sequence "144" forever, i.e. 5.8144144144.... At present, there is no single universally accepted notation or phrasing for repeating decimals.Can a terminating decimal be a fraction: The decimal numeral system (also called base-ten positional numeral system, and occasionally called denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as decimal notation.