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mathdad
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My question concerns repeated and nonrepeated decimals. Are both rational numbers? Can you give an example for each?
RTCNTC said:My question concerns repeated and nonrepeated decimals. Are both rational numbers? Can you give an example for each?
MarkFL said:A repeating decimal number is rational because you can always express such a number as the string of repeating digits over an equal number of 9's (one of the tricks my father taught me as a child). For example, we may write:
\(\displaystyle 0.\overline{154}=\frac{154}{999}\)
A non-repeating decimal is irrational since it cannot be expressed as the ratio of one integer to another. $\sqrt{2}$ is an example of a non-repeating decimal.
Repeated decimals have a pattern of digits that repeats indefinitely, while nonrepeated decimals do not have a repeating pattern and continue infinitely without repeating digits.
To convert a repeated decimal to a fraction, you can set up an equation where the repeating digits are represented by x. Then, solve for x and use it as the numerator of the fraction. The denominator will be a number with the same number of digits as the repeating pattern, followed by the same number of 9s.
No, not every decimal can be converted to a fraction. Non-terminating decimals that do not have a repeating pattern cannot be converted to fractions.
A nonrepeating decimal will have a finite number of digits after the decimal point, while a repeating decimal will have a pattern of digits that repeats indefinitely.
Repeated and nonrepeated decimals are commonly used in calculations involving measurements, such as converting between metric and imperial units. They are also used in financial calculations and in science and engineering for precise measurements and calculations.