# How to turn a recurring decimal into a fraction

Convert Decimals to Fractions

Dec 12,  · Converting Basic Repeating Decimals 1. Locate the repeating decimal. For instance, the number has a repeating decimal of 4. It is a basic repeating 2. Rewrite the decimal as an equation. Write it out so that x equals the original number. In 62%(54). In most books a recurring decimal is represented by placing a dot above the number or numbers that repeat. All recurring decimals can be represented as fractions. To find this fraction we need to generate two equations which have the same repeating part and subtracting one from the other to eliminate it.

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Converting repeating decimals to fractions When converting repeating decimals to fractions, just follow the five steps below carefully. Homepage Pre-algebra lessons Understanding decimals How to find the relative minor of a major key repeating decimals to fractions.

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Introduction

Let x equal the repeating decimal you are trying to convert to a fraction. Step 2: Examine the repeating decimal to find the repeating digit(s). Step 3: Place the repeating digit(s) to the left of the decimal point. Step 4: Place the repeating digit(s) to the right of the decimal point. Step 5. Converting a recurring decimal to a fraction can be a stand alone exam question so it is certainly a skill you want to master. Example: Write 0.\dot1 4 \dot7 as a fraction in its simplest from. Step 1: Make your number equal to x. x= 0.\dot1 4 \dot7. Step 2: Multiply both sides by \textcolor{blue}{10} for each decimal place that isn’t recurring (If there are none, it stays as Step 1). How Do You Turn a Fraction Into a Repeating Decimal? Did you know that a fraction just represents a division? To turn a fraction into a decimal, divide the numerator by the denominator. In this tutorial, see how to convert a fraction into the repeating decimal it represents.

General Education. Wondering how to convert decimals to fractions? Or how to convert fractions to decimals? How do you convert a decimal to a fraction? Any decimal, even complicated-looking ones, can be converted to a fraction; you just need to follow a few steps. Below we explain how to convert both terminating decimals and repeating decimals to fractions. A terminating decimal is any decimal that has a finite other of digits.

In other words, it has an end. Examples include. Next, you want to multiply both the top and bottom of your new fraction by 10 for every digit to the left of the decimal point.

In our example,. The final step is reducing the fraction to its simplest form. The simplest form of the fraction is when the top and bottom of the fraction are the smallest whole numbers they can be. Now we need to simplify. Since and are both even numbers, we know we can divide both by 2. A repeating decimal is one that has no end. The decimal. Multiply by whatever value of 10 you need to get the repeating digit s on the left side of the decimal.

We want that six on the left side of the decimal, which means moving the decimal place over one spot. So we multiply both sides of the equation by 10 x 1 or In this example, with 6 as the repeating digit, you only want one 6 on the left of the decimal.

If the decimal was 0. If it helps, you can picture all repeating decimals with the infinity bar over them, so. Next we want to get an equation where the repeating digit is just to the right of the decimal.

First, make the decimal equal to x, and determine the repeating digit s. Next, get the repeating digits on the left side of the decimal again, you only want one set of repeating digits on the left. This involves moving the decimal three places to the right, so both sides need to be multiplied by 10 x 3 or Now get the repeating digits to the right of the decimal.

The decimal needs to be moved over one space, so both sides need to be multiplied by 10 x 1. Since the numerator is larger than the denominator, this is known as an irregular fraction. Sometimes you can leave the fraction as an irregular fraction, or you may be asked to convert it to a regular fraction. The easiest way to convert a fraction to a decimal is just to use your calculator.

We explain both these methods in this section. We want the denominator, in this case 8, to equal a value of Next we want to get the denominator to equal 1 so we can get rid of the fraction. Note that this method only works for a fraction with a denominator that can easily be multiplied to be a value of Check out the example below.

There is no number you can multiply 3 by to make it an exact multiple of 10, but you can get close. Below is a chart with common decimal to fraction conversions.

For quick estimates of decimal to fraction conversions or vice versa , you can look at our chart of common conversions and see which is closest to your figure to get a ballpark idea of its conversion value. Want to know the fastest and easiest ways to convert between Fahrenheit and Celsius? We've got you covered! Check out our guide to the best ways to convert Celsius to Fahrenheit or vice versa. Are you learning about logarithms and natural logs in math class?

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Choose Your Test. How to Convert Decimals to Fractions How do you convert a decimal to a fraction? Converting a Terminating Decimal to a Fraction A terminating decimal is any decimal that has a finite other of digits.

Step 1 Write the decimal divided by one. Step 2 Next, you want to multiply both the top and bottom of your new fraction by 10 for every digit to the left of the decimal point. Step 3 The final step is reducing the fraction to its simplest form. Example Convert. Converting a Repeating Decimal to a Fraction A repeating decimal is one that has no end.

Step 2 Multiply by whatever value of 10 you need to get the repeating digit s on the left side of the decimal.

Step 3 Next we want to get an equation where the repeating digit is just to the right of the decimal. Step 1 We want the denominator, in this case 8, to equal a value of Step 2 Next we want to get the denominator to equal 1 so we can get rid of the fraction. Common Decimal to Fraction Conversions Below is a chart with common decimal to fraction conversions. Decimal Fraction 0.

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