# How to change repeating and non terminating decimals to fractions

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## Recurring Decimals as Rational Numbers Rational numbers, when written as decimals, are either terminating or non- terminating, repeating decimals. Converting terminating decimals into fractions is .

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In Part A of this lesson, we saw how to convert a terminating decimal number to a fraction. If a decimal is repeating in other words, after a while, some pattern of digits repeats over and over , then we have to use a different strategy. Let N be the number, and let n be the number of digits in the repeating block. For example,. Setting N equal to its value, multiply both sides of the equation by 10 n. Then subtract N from both sides. You will end up with an equation which you can solve for N as a fractional value.

Pre-algebra lessons. Understanding decimals. Converting repeating decimals to fractions. How to find function values. A few good examples to understand the concept.

## Terminating and Repeating Decimals

Rational numbers are whole numbers, fractions, and decimals - the numbers we use in our daily lives. They can be written as a ratio of two integers. This article concentrates on rational numbers. Clearly all fractions are of that form, so fractions are rational numbers. Terminating decimal numbers can also easily be written in that form: for example 0.

Use this calculator to convert a decimal number to a fraction. To convert a number with repeating decimals , enter the number of trailing decimal places digits from the end of the number to repeat. Further down the page, you'll find a guide on how to convert a decimal to a fraction. If you like my calculator, please help me spread the word by sharing it with your friends or on your website or blog. Thank you. Whilst every effort has been made in building this decimal to fraction calculator, we are not to be held liable for any special, incidental, indirect or consequential damages or monetary losses of any kind arising out of or in connection with the use of the converter tools and information derived from the web site. This decimal to fraction calculator is here purely as a service to you, please use it at your own risk.

From the previous concept of rational numbers, we are clear about the meaning of rational number. We have also seen as to how rational numbers can be converted to both terminating and non-terminating decimal numbers. Now, non- terminating decimal numbers can be further classified into two types which are recurring and non- recurring decimal numbers. Recurring numbers: Recurring numbers are those numbers which keep on repeating the same value after decimal point. These numbers are also known as repeating decimals. To show a repeating digits in a decimal number, often we put a dot or a line above the repeating digit as given below:. Non- recurring numbers: Non- recurring numbers are those, which do not repeat their values after decimal point. How do we Write a Non Terminating Recurring Decimal in the form P by Q? Part 2

## Repeating decimal

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. At present, there is no single universally accepted notation or phrasing for repeating decimals. The infinitely repeated digit sequence is called the repetend or reptend. If the repetend is a zero, this decimal representation is called a terminating decimal rather than a repeating decimal, since the zeros can be omitted and the decimal terminates before these zeros. However, every number with a terminating decimal representation also trivially has a second, alternative representation as a repeating decimal whose repetend is the digit 9.

Any rational number that is, a fraction in lowest terms can be written as either a terminating decimal or a repeating decimal. 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 decimal. Convert the fraction 5 8 to a decimal. This is a terminating decimal.

A repeating decimal, also known as a recurring decimal, is a decimal number that has a digit or digits that infinitely repeat at regular intervals. Repeating decimals can be tricky to work with, but they can also be converted into a fraction. Sometimes, repeating decimals are indicated by a line over the digits that repeat. The number 3. To convert a number like this to a fraction, you write it as an equation, multiply, subtract to remove the repeating decimal, and solve the equation. To convert repeating decimals to fractions, start by writing an equation where x equals your original number.

To convert a fraction to a decimal, divide the numerator top number by the denominator bottom number , using either calculator or pencil and paper. To convert a decimal to a fraction, begin by placing that decimal over the number 1. Then keep multiplying both the numerator top number and denominator bottom number by 10 until both are whole numbers. In both of these cases, the decimal forms of these numbers are terminating decimals — that is, the decimal can be written exactly in a finite number of decimal places. In other cases, however, a decimal is repeating — that is, it cannot be written exactly without the numbers repeating forever. Every fraction can be written as a decimal, either terminating or repeating. To write a fraction as a decimal, divide the numerator by the denominator.

If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Math 8th grade Numbers and operations Repeating decimals. Converting a fraction to a repeating decimal. Practice: Writing fractions as repeating decimals. Converting repeating decimals to fractions part 1 of 2. Practice: Converting repeating decimals to fractions.

## 1 thoughts on “How to change repeating and non terminating decimals to fractions”

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