# What Causes A Repeating Decimal In The Long Division Algorithm?

In the division algorithm, if the remainder is zero, then the algorithm terminates, resulting in a terminating decimal. remainder repeats, the calculations that follow will also repeat in a cyclical pattern causing a repeating decimal.

## What is the rule for a repeating decimal?

The rule states that the period of a repeating decimal should be written first in the numerator of an ordinary fraction.

## What causes a decimal to repeat?

Just divide the numerator by the denominator . If you end up with a remainder of 0 , then you have a terminating decimal. Otherwise, the remainders will begin to repeat after some point, and you have a repeating decimalrepeating decimalA repeating decimal 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.https://en.wikipedia.org › wiki › Repeating_decimalRepeating decimal - Wikipedia.

## What is a repeating decimal example?

Recurring Decimal, also called as repeating decimal, is a decimal number only that consists of digits repeating after a fixed interval after the decimal. For example, 46.374374374..., 5173.838383... etc.

## Are repeating decimals significant?

Re: Repeating Decimal There are no special rules for significant figures for nonterminating decimals. When performing your calculations do not round nonterminating decimals. So on your calculator, for example, enter (1/3) instead of 0.333 since (1/3) is more accurate.

## Is 0.333 repeating a rational number?

To show that 0.333… is rational. To show that 0.4545… is rational. A rational number is any number that can be expressed as the ratio of two integers. All terminating and repeating decimalsrepeating decimalsA repeating decimal 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.https://en.wikipedia.org › wiki › Repeating_decimalRepeating decimal - Wikipedia can be expressed in this way so they are irrational numbers.

## How do you divide a repeating decimal?

Divide using long division. Add a decimal point and zeros to the dividend as needed. Once you find a repeating pattern, stop dividing. Put a line above the repeating digits in your answer.

## Is 0.333 repeating rational or irrational?

And also 0.3333 is non-terminating as the decimal is not ending or the remainder for 1/3 is not zero. So from 2) 0.333 is an irrational and it is non terminating.

## What does it mean if the decimal repeats?

A repeating decimalrepeating decimalA repeating decimal 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.https://en.wikipedia.org › wiki › Repeating_decimalRepeating decimal - Wikipedia, also called a recurring decimal, is a number whose decimal representationdecimal representationThe decimal expansion of a number can be found in the Wolfram Language using the command RealDigits[n], or equivalently, RealDigits[n, 10]. ), or continue infinitely without repeating (in which case the number is called irrational).https://mathworld.wolfram.com › DecimalExpansionDecimal Expansion -- from Wolfram MathWorld eventually becomes periodic (i.e., the same sequence of digits repeats indefinitely).