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### Pre-Algebra 20 – Converting Repeating Decimal Numbers to Fractions

Pre-Algebra 20 – Converting Repeating Decimal Numbers to Fractions

Pre-Algebra 20 – Converting Repeating Decimal Numbers to Fractions

### Teacher resources Recurring decimals page 1 ^{[1]}

We have shown how to express fractions whose denominators have prime factors two or five as decimals. We now look at fractions whose denominators cannot be factored as products of twos and fives

We have met these previously in our discussion of division. (Obviously 3.0000… is not considered to be a recurring decimal.)

\(\dfrac{5}{27} = 0.185185185… = 0.\dot{1}8\dot{5}\). This is a recurring decimal and the dots above the digits 1 and 5 indicate that 185 are the recurring digits

### Fractions and Decimals ^{[2]}

a ratio of two numbers, also called a rational number). into a decimal fraction and the patterns that occur in such a decimal fraction

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indicates that there is a live interactive calculator in that section.. Converting a fraction to a decimal is just a division operation

### Expert Maths Tutoring in the UK ^{[3]}

It is very easy to convert a terminating decimal to a fraction, but how do we convert a repeating decimal to fraction? Repeating decimals are decimal numbers that do not terminate after a finite number of digits and in these numbers, one or more digits repeat themselves again and again. Repeating decimal to fraction conversion can be done by following some simple steps given below.

Repeating or recurring decimals are those decimal expansions that do not terminate or end after a specific number of digits. Such numbers have an infinite number of digits after the decimal point

But with repeating decimals, it is impossible to count the number of decimal places as it is infinite. So, there are some specific steps to be followed to convert repeating decimal to fraction

### Repeating Decimal to Fraction: Definition, Steps, Tricks, Facts ^{[4]}

Repeating decimal to fraction conversion is used to express a repeating or recurring decimal in the form of a fraction.. To convert a “terminating decimal” to a fraction, we simply count the number of digits after the decimal point (which are finite); then, we multiply and divide by the appropriate power of ten.

This is pretty simple, isn’t it? But what about repeating decimals where we cannot count the number of digits after the decimal point?. A repeating decimal (or a recurring decimal) is a decimal number in which a single digit or a group of digits after the decimal point is repeated infinitely.

Repeating or Recurring decimals have a repetitive pattern in the digits after the decimal point. With repeating decimals, it is not possible to count the number of decimal places as it is infinite

### Repeating decimal ^{[5]}

This article needs additional citations for verification. A 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

For example, the decimal representation of 1/3 becomes periodic just after the decimal point, repeating the single digit “3” forever, i.e. 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

Another example of this is 593/53, which becomes periodic after the decimal point, repeating the 13-digit pattern “1886792452830” forever, i.e. The infinitely repeated digit sequence is called the repetend or reptend

### How to Convert Repeating Decimals to Fractions: 9 Steps ^{[6]}

Our trained team of editors and researchers validate articles for accuracy and comprehensiveness. wikiHow’s Content Management Team carefully monitors the work from our editorial staff to ensure that each article is backed by trusted research and meets our high quality standards.

Sometimes, repeating decimals are indicated by a line over the digits that repeat. The number 3.7777 with 7 repeating, for instance, can also be written as 3.7

For instance, the number 0.4444 has a repeating decimal of 4. It is a basic repeating decimal in the sense that there’s no non-repeating portion to the decimal number

### Repeating Decimals and Fractions ^{[7]}

Please see our pre-algebra tutorial software program to learn all about fractions and decimals.. In this lesson we will learn about “repeating decimals”, and how we can express them as a fraction.

It turns out that every repeating decimal can be converted to a fraction. And once it is a fraction, it is easier to use if we need to do a calculation.

The first repeating decimal above is equal to the fraction 1/3. You may have known that, but there is a method we can use to find the fraction

### Repeating Decimal to Fraction Lesson ^{[8]}

– Demonstrate an understanding of the addition property of equality. – Demonstrate an understanding of the multiplication property of equality

– Learn the shortcut to convert a repeating decimal into a fraction. In our pre-algebra course, we learned how to convert from a decimal to a fraction and from a fraction to a decimal

A repeating decimal is a decimal number that repeats the same ending digit or pattern of ending digits forever. We generally place a bar over the digit or pattern of digits that repeat

### Repeating Decimal to Fraction (Conversion Method with Solved Examples) ^{[9]}

In mathematics, a fraction is a value, which defines the part of a whole. In other words, the fraction is a ratio of two numbers

The decimal number can be classified into different types, such as terminating and non-terminating decimals, repeating and non-repeating decimals. While solving many mathematical problems, the conversion of decimal to the fractional value is preferred, as we can easily simplify the fractional values

A terminating decimal is a decimal, that has an end digit. It is a decimal, which has a finite number of digits(or terms).

### How to Convert Repeating Decimals to Fractions, Part 2 ^{[10]}

In the last article, we learned how to turn simple repeating decimal numbers into fractions. Specifically, we learned how to convert decimals in which the same number repeats over and over again starting right after the decimal point

So today we’re going to continue where we left off last time and learn how to turn more complicated types of repeating decimals into fractions too.. Recap: How to Turn a Repeating Decimal Digit Into a Fraction

Our goal in that article was to understand how to convert simple repeating decimals to fractions. In particular, we looked at decimals like 0.111…, 0.444…, 0.777…, and any other decimal where the same number repeats forever starting right after the decimal point.

### Terminating and Repeating Decimals ^{[11]}

Any rational number (that is, a fraction in lowest terms) can be written as either a terminating decimal or a repeating decimal . If you end up with a remainder of , then you have a terminating decimal

The bar over the number, in this case , indicates the number or block of numbers that repeat unendingly.. See also Converting Repeating Decimals to Fractions .

### Repeating Decimal to Fraction Conversion Calculator ^{[12]}

Repeating Decimal to Fraction Conversion Calculator. You can use this repeating decimal to fraction conversion calculator to revert a repeating decimal to its original fraction form.

For instance, if you are converting 0.6 to 2/3, leave the non-repeating field blank.. When a fraction is represented as a decimal, it can take the form of a terminating decimal; for example:

You may wish to convert a fraction to a decimal to make adding and subtracting quantities more straightforward. However, it is common to encounter a repeating decimal in practical math when you convert fractions to percentages or decimals, and this reduces the accuracy of the calculation.

### Sources

- http://amsi.org.au/ESA_middle_years/Year8/Year8_1bT/Year8_1bT_R2_pg1.html#:~:text=The%20fraction%2016%3D0.16666,of%20an%20eventually%20recurring%20decimal.
- https://r-knott.surrey.ac.uk/Fractions/fractions.html#:~:text=These%20recurring%20fractions%20are%20of,which%20is%20142857%20endlessly%20repeated.
- https://www.cuemath.com/numbers/repeating-decimal-to-fraction/
- https://www.splashlearn.com/math-vocabulary/repeating-decimal-to-fraction
- https://en.wikipedia.org/wiki/Repeating_decimal
- https://www.wikihow.com/Convert-Repeating-Decimals-to-Fractions
- https://www.mathtutor.com/articles/repeating-decimals.html
- https://www.greenemath.com/Algebra2/5/RepeatingDecimaltoFractionLesson.html
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